Education A path through The Default Library ======================================== How people learn, how teaching works, how learning is measured and how school systems around the world are built. Step 1. Learning Sciences: How People Learn ------------------------------------------- Why: Memory, practice and the science of learning. A lesson can feel clear, students can nod, and a week later most of it is gone. The science of learning explains why, and which few habits change the outcome. A teacher explains fractions with a lovely diagram. The class nods, the quiz that afternoon goes well, and a month later half the room cannot say which of two fractions is larger. Nobody was lazy and the explanation was good. What failed was a belief almost everyone holds: that understanding something once means you will still have it. The learning sciences are the research fields that test that belief: cognitive and developmental psychology, classroom experiments, and the design of instruction. Their best-supported results are surprisingly stable and surprisingly unlike intuition. Practice that feels smooth tends to work worse than practice that feels effortful. A sentence you reread is more familiar, not better known. A beginner and an expert are not the same kind of learner with different amounts of knowledge; they need different teaching. This piece goes beyond the basics of memory. The library already covers the forgetting curve, active recall and flashcards, so here we ask the next questions: what is learning made of, why does the bottleneck matter, when does a good technique stop working, and how big are the effects really? The course in one box Who takes itEducation majors, usually in year 1 or 2, and psychology, neuroscience and instructional-design students. Teacher-preparation standards such as the US InTASC model standards and the UK Core Content Framework (2019) both build on this material, and the Education Endowment Foundation's evidence reviews are organised around it. What it is forExplaining how knowledge is acquired, kept and transferred, and turning that into teaching and study methods that are tested rather than assumed. Comes afterCognitive Psychology (35/22) and Learning & Behavior (35/23). Leads toCurriculum & Instructional Design (36/54) and Teaching Reading & Mathematics (36/56), and through them Assessment & Measurement (36/55) and Classroom Practice & Educational Technology (36/60). What this piece gives youYou will not be able to run a classroom experiment, which is what Research Methods in Psychology (35/19) is for. You will know seven ideas that guide teaching, which are well supported and which are not. Easier first reads: Memory: How to Make Things Stick (17/04), How to Learn Anything Faster (17/01) and The Default Course's Memory & Spaced Repetition. The toys below are labelled illustrations, not data about you. Learning is a change in long-term memory, built from what you already know Strip away the jargon and learning, for most school purposes, means that something is stored in long-term memory that was not there before, and that you can use it later in a new place. Kirschner, Sweller and Clark put it bluntly in 2006: if nothing has changed in long-term memory, nothing has been learned. This does not make learning "just memorising". Understanding is a rich structure of linked memories, which psychologists call a schema. The consequence is that prior knowledge does most of the work. In 1973 William Chase and Herbert Simon showed chess masters and beginners boards for a few seconds. Masters rebuilt real game positions far better, but on boards with the pieces placed at random their advantage mostly vanished. They did not have bigger memories; they had stored patterns. In a 1988 study of reading by Recht and Leslie, children who were poor readers but knew a lot about baseball understood a baseball passage better than good readers who knew little about the game. What you can learn next depends on what you hold now. new learning = new material + the schemas you can attach it tothis is why the same lecture is clear to one student and noise to another A graduate's habit: before asking "was my explanation good?", ask "what could this learner hook it to?" Many wrong answers are not random; they are reasonable ideas built on an earlier, partial schema (children who think a heavier ball must fall faster have watched feathers and stones). Good teaching finds the existing idea and works from it. Working memory is the bottleneck, so load is the design problem Cognitive Psychology (35/22) gave the number: working memory holds roughly four chunks at once, and only briefly. John Sweller turned that into an instructional theory in the 1980s, cognitive load theory. It separates three kinds of load. Intrinsic load is how many elements of the task must be held in mind together (it depends on the task and on what you already know). Extraneous load is effort wasted by how the material is presented, such as a diagram on one page and its labels on another, which forces you to hold one while hunting for the other (the split-attention effect). Germane load, effort spent building schemas, is the one you want, and later versions of the theory fold it into the first two. The early signature result is the worked-example effect. Sweller and Cooper (1985) found that beginners in algebra learned more from studying solved problems than from solving the same number of problems, because searching for a method eats the working memory that learning needs. Then comes a twist, the expertise reversal effect (Kalyuga and colleagues, 2003): the same worked example that helps a novice can slow an expert, because the expert must now process guidance they do not need. The right amount of help depends on the learner. Interactive · A load budget (illustrative bookkeeping) Pick a task and a learner. The task has a number of interacting elements. A fluent learner chunks them into fewer. Then add the things that make presentation worse or better. Capacity is four slots. Turn on JavaScript to use this toy. Key result: a task with five interacting elements needs five slots for a beginner, more than the four available, and only two for a fluent learner, so the same lesson overloads one and under-challenges the other. The numbers are bookkeeping, not measurements: element counts and chunk sizes are chosen for illustration, and real load is not measured in slots. The direction of each effect is what the research supports. Retrieval beats rereading, but the win shows up only after a delay The library's memory course covers the testing effect. The detail worth keeping is when it appears. In 2006 Henry Roediger and Jeffrey Karpicke had students study prose passages, then either restudy or take recall tests without feedback, and tested everyone after 5 minutes, 2 days or 1 week. On the 5-minute test, restudying was better. On the 2-day and 1-week tests, the students who had been tested remembered far more, even though restudying made them feel more confident. If you measure learning right after a lesson, the weaker method looks fine. That is the central trap of the field: performance during or right after practice is not learning. Robert Bjork named the useful opposite desirable difficulties (1994): conditions that slow immediate performance and improve lasting learning, such as retrieving instead of rereading. The word "desirable" matters. Difficulty that does not require retrieval or thought, like a badly printed handout, is just difficulty. Interactive · Predict, then reveal Two students studied the same passage. One reread it; one tried to recall it. Who has more left at the chosen delay? Pick a guess, then move the delay. Test delay2 days reread   tested Turn on JavaScript to use this toy. Key result: restudying leads at 5 minutes; testing leads at 2 days and 1 week. The curves are invented (exponential decay with made-up starting points and speeds) so the crossing is visible. The real experiments found the same crossing, with different numbers. Spacing has a best gap, and it depends on when you need the memory Spacing beats cramming; the memory course shows that. The next question is how far apart to space. Nicholas Cepeda and colleagues (2008) taught more than a thousand people facts and varied both the gap between two study sessions and how long they waited for the final test. The best gap grew as the test got further away, but as a share of the delay it shrank: roughly a tenth to a fifth of the delay for tests weeks or months ahead, and a smaller share for tests a year ahead. An earlier study by Harry Bahrick and colleagues (1993) had followed language learners for years and found relearning every 56 days beat every 14 or 28 days for long-term retention. The reason is a trade-off. A longer gap means the memory has faded more, so a successful retrieval strengthens it more, but if it has faded too far the review fails and becomes relearning from scratch. The toy below is a deliberately small model of that trade-off. Move the delay and the gap and watch the best gap move. Interactive · Find the best gap (toy model) Days until the test, after the review35 Days between first study and the review3 Turn on JavaScript to use this toy. Key result: in the toy, the best gap is about 2 days for a test a week away and about 11 days for a test a year away, so the best gap grows while its share of the delay falls. Toy model: the memory fades with a time constant of 5 days. A review that succeeds (chance equals what is left) multiplies that time constant by up to 9; one that fails gives no boost. All constants are invented. A single review cannot carry a memory for a year, which is why real plans use several, as the memory course shows. Mixing problem types feels worse and works better Textbooks usually give ten problems of one kind, then ten of the next. That is blocked practice. Interleaved practice mixes the kinds. During practice, blocked looks better: you know which method to use because the last problem used it. Mixed practice forces you to decide which method fits, and that decision is the skill an exam, or life, will test. In a 2007 study by Doug Rohrer and Kelli Taylor, students who practised volume formulas in mixed order did worse during practice and, on a test a week later, roughly three times as well as the blocked group. Kornell and Bjork (2008) found the same with paintings: people learned artists' styles better from mixed sets but, on average, believed the blocked sets had worked better. Interleaving is not free. It helps most when the categories are easily confused and the learner can already do each kind, and it is a poor fit for a first encounter with something brand new. Dunlosky and colleagues (2013) rated it moderate in utility, with less classroom evidence than retrieval or spacing. Interactive · Three kinds of problem, twelve slots Turn on JavaScript to use this toy. Key result: in blocked order the problem type changes only twice in 12; in a fully mixed order it changes 11 times. The sequence and the count of switches are computed live. The bars show the shape of the published finding (better during practice when blocked, better later when mixed) with round invented numbers, not the data of any one study. Feeling that you learned is not learning If effortful methods work better but feel worse, learners will often choose the wrong ones. This is why metacognition, judging your own learning, is part of the course. Fluent, familiar material produces an illusion of competence: you recognise it, so you think you could produce it. Self-testing exposes the gap, which is a second benefit of retrieval: it corrects your own forecast. The same trap sits under the best-known myth in education, learning styles: the idea that people learn better when taught in their preferred mode (visual, auditory, kinaesthetic). Many people do report preferences, and most teachers have been told to teach to them. But the claim that matters is the matching hypothesis: that people given their preferred format learn better than people given another. Pashler, McDaniel, Rohrer and Bjork reviewed this in 2008 and found almost no studies designed to test it properly, and the few that were did not support it. The test has a clear shape, shown below. What does help is matching the format to the content: a map is better shown than described, whoever is looking. Interactive · What the data would have to look like (invented numbers) Turn on JavaScript to use this toy. Key result: learning styles predict a crossover, with each group scoring best on its own format. A format that is simply better, or a preference that changes nothing, shows no crossover. Evidence has grades, and effect sizes need honest reading "Research shows" is not one thing. The Education Endowment Foundation's Teaching and Learning Toolkit (England) and the US What Works Clearinghouse both grade approaches by strength of evidence, size of effect and cost. Dunlosky and colleagues (2013) did it for ten study techniques. Putting the results together gives a rough map: StrengthExamples StrongRetrieval practice; spacing; worked examples for beginners; explicit teaching of early reading; feedback that tells learners what to do next Mixed or moderateInterleaving; self-explanation; metacognitive strategies; growth-mindset messages Weak or not supportedRereading; highlighting; summarising as a study method; teaching to learning styles An effect size such as Cohen's d says how far apart two groups' averages are in standard deviations. John Hattie's Visible Learning (2009) pooled hundreds of meta-analyses and used d = 0.40 as a "hinge point" for what is worth doing. Critics, including Robert Slavin, Dietmar Terhart and Bergeron and Rivard (2017), argue that comparing d values across studies of different designs and ages is misleading and that some of the averaging is statistically unsound. Matthew Kraft (2020) suggested that for well-designed studies on standardised achievement tests, 0.05 is small, 0.05 to 0.20 is medium and above 0.20 is large, much lower than the old rule. Growth-mindset messages are a live example: Sisk and colleagues' 2018 meta-analyses found small average effects, and the 2019 US national experiment by Yeager and colleagues found an average gain of about a tenth of a grade point, concentrated among lower-achieving students in supportive schools. Their authors and critics read those numbers differently. Interactive · What does an effect size mean? Effect size d0.40 Turn on JavaScript to use this toy. Key result: at d = 0.4, a randomly chosen student from the taught group beats a randomly chosen student from the other group about 61 times in 100, not 100. Computed live from the normal distribution: the chance a random treated student beats a random control is Φ(d/√2), and the average treated student sits at the Φ(d) percentile of the control group. It assumes equal spread and bell-shaped scores. What a graduate just sees Learning is a lasting change in long-term memory; a clear explanation that leaves no trace has taught nothing. Prior knowledge is the hook; the same lesson lands differently on different learners. Working memory is the bottleneck, so cut waste, split steps and show worked examples to beginners. Help that supports a novice can hamper an expert (expertise reversal). Testing yourself beats rereading, and the difference shows after a delay, not in the next ten minutes. The best gap between reviews grows with how long you need the memory. Mixed practice feels worse and transfers better. Feeling fluent is not knowing, and "learning styles" fail the one test that would matter. Every "it works" has a grade and an effect size, and both should be asked for. Where it shows up next Curriculum & Instructional Design (36/54): worked-example fading, sequencing and the guidance debate all follow from load and prior knowledge. Teaching Reading & Mathematics (36/56): decoding, fluency and number sense are schemas that must be automatic before comprehension and problem solving can happen. Assessment & Measurement (36/55): if performance is not learning, tests have to be built to tell them apart, and testing itself is a learning tool. Classroom Practice & Educational Technology (36/60): flashcard apps, adaptive tutors and AI helpers are judged by these ideas, for example whether an AI that gives the answer removes the retrieval. In the world: language apps, driving schools, medical training, pilot simulators and corporate courses all face the same bottleneck and the same temptation to measure what is easy. If you want to go deeper 📘 Textbooks. Susan Ambrose and colleagues, How Learning Works: Seven Research-Based Principles for Smart Teaching (Jossey-Bass, 2010), the usual university teaching-centre text; and Dale Schunk, Learning Theories: An Educational Perspective (Pearson, recent editions) for the theories side. Check for the current edition. 📘 Gentler. Peter Brown, Henry Roediger and Mark McDaniel, Make It Stick (Harvard, 2014), and Daniel Willingham, Why Don't Students Like School? (Jossey-Bass, 2009; second edition 2021). 🌐 Free text. National Research Council, How People Learn: Brain, Mind, Experience, and School (2000), free to read at nap.nationalacademies.org. 🌐 Free course. MIT OpenCourseWare 5.95J Teaching College-Level Science and Engineering (Fall 2015), which applies this research to teaching. The takeaway Learning is a change in long-term memory, limited by a small working memory and built on what is already there. The methods that last, retrieval, well-spaced review, mixed practice and worked examples for beginners, feel harder than the ones that do not, so feeling is a poor guide. Ask of any claim how strong the evidence is and how big the effect. Try this: pick something you learned last month. Without looking, write down what you remember, then check. Note which parts you were sure of and wrong about. That gap is the illusion of competence, measured on you. Sources & Further Reading Sources. Kirschner, Sweller and Clark, Educational Psychologist 2006; Chase and Simon, Cognitive Psychology 1973; Recht and Leslie, Journal of Educational Psychology 1988; Sweller, Cognitive Science 1988; Sweller and Cooper, Cognition and Instruction 1985; Chandler and Sweller 1991; Kalyuga, Ayres, Chandler and Sweller, Educational Psychologist 2003; Cowan, Behavioral and Brain Sciences 2001; Roediger and Karpicke, Psychological Science 2006 (PubMed 16507066); Bjork 1994; Cepeda, Vul, Rohrer, Wixted and Pashler, Psychological Science 2008; Bahrick, Bahrick, Bahrick and Bahrick, Psychological Science 1993; Rohrer and Taylor, Instructional Science 2007; Kornell and Bjork, Psychological Science 2008; Dunlosky, Rawson, Marsh, Nathan and Willingham, Psychological Science in the Public Interest 2013; Pashler, McDaniel, Rohrer and Bjork, Psychological Science in the Public Interest 2008; Hattie 2009; Bergeron and Rivard, McGill Journal of Education 2017; Terhart, Journal of Curriculum Studies 2011; Kraft, Educational Researcher 2020; Sisk et al., Psychological Science 2018; Yeager et al., Nature 573, 2019; Education Endowment Foundation Toolkit; What Works Clearinghouse. All toy-model outputs were computed in node. This piece describes research and gives approximate figures where studies differ. 📘 Ambrose et al., How Learning Works 📘 Brown, Roediger and McDaniel, Make It Stick 🌐 How People Learn (free) Step 2. Cognitive Psychology: A Narrow Beam and a Rebuilding Crew ----------------------------------------------------------------- Why: Attention, memory and thinking. You attend to very little, hold about four chunks, and rebuild every memory as you use it. That design is clever, and it is why a confident witness can be sincerely wrong. You are sure you remember where you parked, who was at the party, which of two cars cut you off. You can see it. Then a photo, a receipt or another person disagrees, and the picture you were so sure of turns out to have been assembled, a little at a time, after the fact. Or: you are at a busy table, talking, and across the room someone says your name. You never heard the rest of that conversation, yet your own name pulled you out of this one. Or you try to keep a phone number in your head while a friend reads you another, and one of them simply vanishes. Cognitive psychology is the study of those ordinary moments: how a mind takes in a flood of input, keeps a little of it, stores a fraction of that, and rebuilds the rest on demand. A graduate stops trusting the feeling of "I clearly remember" and starts asking how the memory was built. This matters in classrooms, in cockpits, and, as we will see, in courtrooms. The course in one box Who takes itEvery psychology degree, usually in year 2. Neuroscience, linguistics, computer science (AI) and education majors take a version of it, and law students meet its memory half. What it is forExplaining how attention, memory, reasoning and language work, by experiments that time people, count their errors and compare conditions. Comes afterSensation & Perception (35/21), which itself needs Biological Psychology (35/20). Leads toDevelopmental Psychology (35/24), and beyond psychology to Behavioral Economics (34/46), Machine Learning (34/32) and, for lawyers, Civil Procedure & Evidence (35/08) and Criminal Law & Procedure (35/07). What this piece gives youYou will not be able to design an experiment, which is what Research Methods in Psychology (35/19) is for. You will have felt the limits of your own attention and memory on this page, and you will know why a confident eyewitness is not the same as an accurate one. Gentler first reads: Memory: How to Make Things Stick (17/04) and The Biases That Fool Everyone (17/02). The demos below are one-person toys timed on your device, not studies. Attention is a narrow beam, and most of the world falls outside it You are bombarded with far more than you can process, so the mind selects. In 1953 Colin Cherry played people two voices, one in each ear, and asked them to repeat one. They could, and could say almost nothing about the other voice, except that it was a voice, and that their own name, if it appeared there, often got through. Broadbent's 1958 filter model was the first answer: a bottleneck lets one channel through. Later models made the filter leakier, and the debate over how early or late the filter acts is still alive. The vivid modern version is inattentional blindness. In the famous 1999 "gorilla" experiment by Daniel Simons and Christopher Chabris, viewers counting basketball passes often failed to notice a person in a gorilla suit walking through the scene; in most groups about half missed it. Nothing is wrong with their eyes. What you see is what you attend to, and you cannot tell what you are missing, because the missing is not marked. The cleanest way to feel the limit is the Stroop effect (J. Ridley Stroop, 1935). Reading a word is so automatic that it intrudes when you try to name the colour of its ink. The conflict costs time you can measure. Interactive · Stroop on your own device Tap the colour of the ink, not the word. Six easy trials (word and ink agree), then six hard ones (they conflict). Your device times each tap. Ready? Start Press Start. A twelve-trial toy shows the effect for you. It is not a measurement of you, and timing on a phone screen adds noise. Most people are slower on the conflicting trials, often by a tenth of a second or more, and make more errors. Nothing "loaded" more information; two automatic processes simply fought over one response. A graduate carries the lesson everywhere: attention is a single narrow beam that can be split only at a cost, which is why a phone call hurts driving even when the phone is hands-free. Working memory holds about four chunks, not seven digits Hold a phone number in your head and you are using working memory: the scratchpad where you keep things while you use them. George Miller's 1956 paper "The Magical Number Seven, Plus or Minus Two" made 7 famous. Later work, above all Nelson Cowan's 2001 review, argued the true limit is nearer four chunks once you stop people from rehearsing and regrouping. The word that matters is chunk: a unit that is one thing to you. The letters F-B-I-C-I-A-N-A-S-A are ten items, or three chunks if you know the acronyms. Baddeley and Hitch (1974) described this scratchpad as a small set of parts, a loop for sounds, a sketchpad for pictures and a controller that directs attention. A graduate remembers the practical points. The store is small. It is easily overwritten. And the way out is not more effort but better chunking, which is why experts seem to have enormous memory in their own field, and ordinary memory outside it. Interactive · Digit span, with and without chunks One at a time In groups of three Digits to remember Ready? Show digits Check Pick a length and press Show digits. Digits are generated fresh each time, shown for 0.7 s each (groups get a longer pause between them). Try 7 plain, then 9 in threes. Most readers manage around six or seven plain digits and do noticeably better on longer strings when they are grouped, because three groups of three are three chunks. That is not a trick. It is the whole mechanism of memory improvement: the number stays small; the chunk gets bigger. Encoding and retrieval: what goes in decides what comes out Remembering has two halves. Encoding is how the information is processed on the way in; retrieval is how you get it back. In 1972 Fergus Craik and Robert Lockhart argued that deeper processing (what does this mean to me?) beats shallow processing (what does it look like?), and the result has held up well. A second idea, encoding specificity, says a cue works to the extent it matches how the memory was laid down. In a well-known 1975 study, Godden and Baddeley had divers learn word lists on land or underwater; words were recalled better in the place they were learned. The context effect is real but modest and not always found, so treat "study where you'll be tested" as a small bonus, not a rule. And then there is time. Hermann Ebbinghaus (1885) measured his own forgetting of nonsense syllables and found that loss is fastest at first and then flattens. A 2015 replication of his work (Murre & Dros) found the same shape. The graduate's practical conclusion is the spacing effect: reviewing something just as it begins to fade slows the next fall. The toy below uses a simple exponential model with made-up constants, so it shows the shape of the idea, not your forgetting. Interactive · Forgetting curve and review (illustrative model) No review One review, day 1 Days 1, 3, 7, 14 Model: retention = e−t/S. Start with S = 3 days (made up). Each review resets retention to 100% and multiplies S by 2.5 (also made up). Real forgetting depends on the material and the person. With no review, almost nothing is left by day 30 in this model (under 0.01%). With one review, about 2%. With four spaced reviews, about 87%. The numbers are invented; the reason spacing beats cramming is the finding. Memory is rebuilt each time, not replayed The folk picture is a video recording. The research picture, which goes back to Frederic Bartlett's 1932 Remembering, is a reconstruction: when you recall, you assemble the memory from fragments plus what you know about how things usually go. That makes memory efficient and error-prone, and the errors are not random. They move toward what makes sense. A neat way to see it is the paradigm that James Deese (1959) and Henry Roediger and Kathleen McDermott (1995) turned into a standard tool. Study a list of words that all circle one unlisted word, for example bed, rest, tired, dream, nap, then later say which words you saw. People often "recognise" the unlisted word, here sleep, nearly as readily as words that were really on the list. Try it. Interactive · A false memory, on demand Fifteen words appear, 1.2 s each. Then twelve words follow, one at a time; tap whether each was on the list. Ready? Start the list Was on the listWas not Press Start. The list is from the Roediger–McDermott (1995) study, built around the unlisted word "sleep". In the test, half the words were studied, two were unrelated, and two were related but not shown. The same machinery explains Elizabeth Loftus's best-known results. In 1974 Loftus and John Palmer showed people films of car crashes and then asked how fast the cars were going when they "smashed into" or "contacted" each other. The "smashed" group guessed about 41 mph; the "contacted" group about 32. A week later, those asked with "smashed" were more likely to report broken glass that was never in the film. In 1995 Loftus and Jacqueline Pickrell planted a false childhood memory of being lost in a shopping mall, and about a quarter of the 24 participants reported remembering it. Critics have noted that "remembering" in these studies is partial, and that planting a whole memory is harder than planting a detail. The settled point is narrower and still important: suggestion after the event can change what people report, and they can't feel the change. Eyewitnesses: sincere, confident and sometimes wrong This is where memory science meets the law. In the United States, the Innocence Project reports eyewitness misidentification in about 69% of the first 367 DNA exonerations it counts (the share was about 75% in older snapshots, when there were fewer cases). Countries differ in how they run and weigh identifications, but human memory is the same everywhere. The American National Academy of Sciences' 2014 report Identifying the Culprit reviewed the evidence and recommended practices such as blind lineup administration and recording how confident a witness is at the first identification. The fairest summary has two halves, and researchers disagree about their weights. Many studies show that confidence at trial, after months of repeated questioning, tells you little about accuracy. John Wixted and Gary Wells (2017) argued that the first confidence statement, from an uncontaminated lineup, is quite informative: high-confidence initial picks are usually right, and low-confidence picks often wrong. Both can be true, because "confident" at trial is not the same thing as "confident at the start". To see the structure, borrow signal detection theory. A witness gets a familiarity signal for each face. The culprit's signal is stronger by an amount d′ (sensitivity). The witness also has a bar (the criterion): how familiar a face must feel before they pick it. A lineup puts the possible culprit among five look-alike fillers. When the culprit is absent, a witness who feels pressure to choose will still choose. Interactive · A lineup, simulated 20,000 times Witness sensitivity d′ Bar for picking someone Toy model: six faces, equal-variance normal familiarity, the witness picks the most familiar face if it clears the bar. Culprit present and absent are equally likely. A real witness is messier. Notice what the sliders show. With d′ at 0, the witness knows nothing and the picks are noise. With a low bar, the witness picks someone nearly every time, and in culprit-absent lineups that someone is innocent. Raising the bar costs correct IDs but removes most of the false ones. That is why reformers focus on procedure: blind administration, fair fillers, and not telling the witness "good, you picked the suspect". Heuristics: fast rules that mostly work, and sometimes don't Amos Tversky and Daniel Kahneman's 1974 paper "Judgment under Uncertainty: Heuristics and Biases" showed that people judge probability by shortcuts. Availability: what comes easily to mind seems common, so after a news story people overestimate plane crashes. Representativeness: what resembles a type seems likely to belong to it, which is how the "Linda" problem (1983) leads many to rate "feminist bank teller" as more probable than "bank teller", though a subset can never be more probable than the whole. Anchoring: a number you've just heard drags your estimate toward it. Gerd Gigerenzer and others argue that heuristics are not just errors: in the right environment, simple rules do well, and the "biases" are partly artefacts of how problems are posed. Kahneman's side says the errors are systematic and costly. Both agree that the way you present numbers matters. A classic case from Tversky and Kahneman involves a witness again. Interactive · The taxi problem A cab hit a pedestrian at night. Some cabs in the city are Blue, the rest Green. A witness says the cab was Blue. Tested in similar light, the witness gets the colour right some of the time. Share of cabs that are Blue Witness accuracy Illustrative numbers; the 15% and 80% are the classic textbook version. Imagine 1,000 cabs and count. With 15% Blue cabs and an 80% accurate witness, the chance the cab really was Blue is about 41%, not 80%. Out of 1,000 cabs, 150 are Blue and the witness calls 120 of them Blue; of 850 Green cabs, the witness wrongly calls 170 Blue. So 120 of 290 "Blue" reports are right. In Tversky and Kahneman's report, most people answered near the witness's 80%, ignoring the base rate. Counting people instead of multiplying probabilities (Gigerenzer's "natural frequencies") makes the right answer much easier to find. Language and thought: does the word shape the idea? Edward Sapir and Benjamin Lee Whorf are credited with the idea that language shapes thought. The strong version, that you cannot think what you cannot say, has been rejected: people think about things for which they have no word, and babies think before they speak. The weak version, that language nudges attention and memory, has support. Berlin and Kay (1969) showed that colour terms across languages follow a near-universal order, suggesting biology constrains the vocabulary. And Winawer and colleagues (2007) found that Russian speakers, whose language has separate basic words for light blue (goluboy) and dark blue (siniy), were quicker to tell apart two blues that straddle that line, an advantage that vanished when they had to repeat a string of digits at the same time. Other claims, such as grammatical gender making speakers describe objects differently, are more contested, and several famous language-and-thought results have been hard to replicate. Say "language nudges" and stop there. The replication crisis touches this whole course. In 2015 the Open Science Collaboration tried to repeat 100 published psychology studies; about 97% of the originals had significant results and about 36% of the replications did. Cognitive-psychology effects, which are usually within-person and measured in milliseconds, fared better than social ones. Stroop, serial-position and false-memory effects replicate easily. Treat very large claims from small studies with caution, and see Research Methods in Psychology (35/19). What a graduate just sees Attention is a narrow beam: what you did not attend to is not "seen but forgotten", it was never stored. Working memory holds about four chunks. Better chunking, not harder trying, is how people hold more. How deeply you process something when it goes in decides how easily it comes out. Review at the edge of forgetting beats re-reading in one sitting. Recall is reconstruction. A vivid, detailed, confident memory can still be wrong. Questions asked after an event can change the memory without any feeling of change. A witness's accuracy depends on procedure: how the lineup was run and how soon confidence was recorded. When someone gives you a probability, ask for the base rate; count cases instead of multiplying fractions. Language nudges thought; it does not cage it. Where it shows up next Developmental Psychology (35/24): memory, attention and reasoning are not fixed. Children's working memory and theory of mind grow, and older adults' processing speed slows while vocabulary keeps growing. Behavioral Economics (34/46): the heuristics-and-biases programme is where much of the field began; its replication record is mixed, as the economics piece says. Machine Learning (34/32): human memory as a rebuild-from-cues system resembles models that fill gaps with likely content, which is both a strength and the source of confident errors. Law: Criminal Law & Procedure (35/07) and Civil Procedure & Evidence (35/08) meet eyewitness memory directly. Courts in different countries weigh identifications differently, and a number of jurisdictions have adopted lineup reforms. In the world: air traffic and cockpit design (attention and workload), interface design, teaching (spacing and retrieval practice), police interviewing, and the warnings on any "I remember it clearly" claim. If you want to go deeper 📘 Textbook. Michael Eysenck and Mark Keane, Cognitive Psychology: A Student's Handbook (Routledge / Psychology Press). A common UK and international choice, thorough and research-heavy. 📘 Textbook. Daniel Reisberg, Cognition: Exploring the Science of the Mind (W. W. Norton). A common US choice, easier on the first read. 📘 Gentler. Daniel Schacter, The Seven Sins of Memory (Houghton Mifflin, 2001), and Daniel Kahneman, Thinking, Fast and Slow (2011), noting that some priming studies in the latter did not replicate. Elizabeth Loftus's TED talk "The fiction of memory" is short. 🌐 Free course. MIT OpenCourseWare 9.00SC Introduction to Psychology (Fall 2011), whose lectures include memory and cognition; the free Noba chapters cover each topic here. The takeaway The mind is a narrow beam of attention, a four-chunk scratchpad and a long store that it rebuilds each time it is used. That design is efficient, and it means vividness and confidence are not evidence of accuracy. Good procedure, such as spaced review, blind lineups and counting cases instead of trusting a feeling, is how people protect themselves from their own minds. Try this: this week, when you are sure about a detail from last month, find something that can check it (a message, a photo, a receipt). Notice how often the gist is right and a detail has quietly moved. Sources & Further Reading Sources. Cherry 1953 and Broadbent 1958 (selective attention); Stroop 1935; Simons & Chabris 1999, Perception 28; Miller 1956, Psychological Review 63; Cowan 2001, Behavioral and Brain Sciences 24; Baddeley & Hitch 1974; Craik & Lockhart 1972; Godden & Baddeley 1975; Ebbinghaus 1885 and Murre & Dros 2015, PLoS ONE (replication); Bartlett 1932; Deese 1959 and Roediger & McDermott 1995, JEP: Learning, Memory, and Cognition 21; Loftus & Palmer 1974, Journal of Verbal Learning and Verbal Behavior 13 (mean estimates by verb: "smashed" about 41 mph, "contacted" about 32 mph); Loftus & Pickrell 1995, Psychiatric Annals 25 (24 participants, about a quarter reported the false event); Innocence Project (eyewitness misidentification in 69% of 367 DNA exonerations in its current count, earlier figure about 75%); National Research Council 2014, Identifying the Culprit; Wixted & Wells 2017, Psychological Science in the Public Interest 18; Tversky & Kahneman 1974, Science 185, and 1983 (Linda); Gigerenzer & Hoffrage 1995; Berlin & Kay 1969; Winawer et al. 2007, PNAS 104; Open Science Collaboration 2015, Science 349. Every number an interactive shows was computed in node: taxi problem 120/290 = 41.4%; lineup model at d′ 1.5, bar 1.5 gives 45% correct picks, 35% no pick when the culprit is present and a 5.5% innocent-suspect pick when absent; forgetting model, day 30: under 0.01% with no review, 2.1% with one review, 87.2% with reviews on days 1, 3, 7 and 14 (S grows from 3 to about 117 days). 🌐 MIT OCW 9.00SC Introduction to Psychology 🌐 Elizabeth Loftus, "The fiction of memory" (TED) 📘 Eysenck & Keane, Cognitive Psychology: A Student's Handbook 📘 Schacter, The Seven Sins of Memory This describes research, not medical or legal advice. If you are struggling with your memory, mood or wellbeing, a doctor or local service can help; findahelpline.com lists free helplines by country. Step 3. Learning & Behavior: Surprise Is the Teacher ---------------------------------------------------- Why: How behaviour and habits are learned. Signals learn to predict, actions are shaped by what follows, and the size of the surprise decides how much changes. From Pavlov's dogs to dopamine and the 66-day habit. Your phone buzzes and, before you decide anything, your hand is already moving. A song from your school years comes on and you feel something that has nothing to do with the room you are in. You pull the lever on a vending machine that ate your coins last week, and press it again, hard, as if that would help. None of these needed a thought. They are the footprints of learning that happens without anyone teaching you: a signal that now predicts something, an action that paid off, a reward that came a little less or a little more than expected. Psychologists once thought of this as a rat-and-pigeon topic. It turned out to be the machinery under advertising, games, addiction, parenting, classroom management, and even the training of artificial agents. A graduate of this course keeps one idea above the rest: learning is driven by surprise. When the world matches your prediction, nothing is learned. When it doesn't, the size of the surprise decides how much you change. The course in one box Who takes itEvery psychology degree, usually in year 1 or 2 (the Psychology route here puts it in year 1). Neuroscience, education and animal-behaviour majors take it too; computer scientists meet its twin as reinforcement learning. What it is forExplaining how experience changes behaviour, with rules that were worked out on animals and then shown to hold, with complications, in people. Comes afterNothing: it has no prerequisite. Biological Psychology (35/20) is a good companion. Leads toDevelopmental Psychology (35/24), and beyond it Clinical Psychology (35/27, where exposure therapy rests on extinction), Behavioral Economics (34/46) and Machine Learning (34/32). What this piece gives youYou will not be able to design a training programme. You will see why intermittent rewards hold behaviour so tightly, what an "error signal" is, and why a habit takes longer than a month. Gentler first reads: How Habits Actually Form (02/05) and Dopamine Is Not the Pleasure Chemical (01/08). The toys here are models and one-person demos, not studies. Classical conditioning: a signal learns what it predicts Ivan Pavlov was studying digestion in dogs (work that won him the 1904 Nobel Prize in Physiology or Medicine) when he noticed that the dogs began to salivate before the food arrived, at the sight of the keeper or the sound of his steps. He turned the nuisance into the experiment. A neutral signal, such as a bell, repeatedly came just before food. The food (the unconditioned stimulus) already caused salivation. After enough pairings, the bell (the conditioned stimulus) caused it too. The modern reading is less "association by closeness" and more "the bell became a forecast". The signal has to be informative: if food arrives just as often without the bell, the bell stays meaningless, however often they co-occur (Robert Rescorla, 1968). Biology also sets limits. In a famous 1966 experiment, John Garcia and Robert Koelling found that rats readily link a taste with later sickness, even hours later, but do not as readily link a flashing light and noise with sickness. It is why one bad oyster can end a love of oysters for years. Humans do the same. A brand jingle that predicted a good time, a sound linked to a bad dentist visit, and the sinking feeling at a certain email notification are all classical conditioning. The evidence for fear learning in humans is not the 1920 "Little Albert" demonstration, which had one baby, no proper controls and an unsettled aftermath: researchers still dispute the child's identity and health. Later laboratory work established the effect properly, with consent, and with ways to undo it. That undoing is extinction: present the bell without the food and the response fades. The old association is not erased; it is overlaid by a new, competing one, which is why fear can return after a break and why exposure-based therapies work by repeating safe encounters. (A hint of Clinical Psychology, 35/27.) Interactive · Which kind is it? Classical: a signal comes to predict an outcome that happens anyway. Operant: an action is followed by a consequence that changes how often it recurs. Tap your answer. Question 1 of 4. Operant conditioning: consequences shape what you do next Edward Thorndike (1898) put cats in puzzle boxes and watched them stumble onto the latch, then do it faster each time. He called it the law of effect: an action followed by a satisfying result becomes more likely. B. F. Skinner (The Behavior of Organisms, 1938) built on it, with a box in which an animal's lever pressing was recorded and rewarded under rules the experimenter set. The vocabulary is a trap, so here it is in one table. "Positive" and "negative" mean added or removed. "Reinforcement" and "punishment" mean the behaviour becomes more or less likely. Behaviour more likelyBehaviour less likely Something addedPositive reinforcement: praise after tidyingPositive punishment: a scolding Something removedNegative reinforcement: the alarm stops when you get upNegative punishment: losing screen time Two things graduates know. Negative reinforcement is not punishment; it is escape that rewards. And the effects of punishment are weaker and less reliable than people expect: it suppresses behaviour while it is applied and teaches what to avoid, not what to do. Teaching a new behaviour with a reward works better than ending an old one with a penalty, and animal trainers such as the ones in Karen Pryor's books build whole careers on that. Schedules of reinforcement: when the reward comes shapes the behaviour Not every response is rewarded in daily life, and Skinner and Charles Ferster (1957, Schedules of Reinforcement) found that the pattern of rewards matters as much as the amount. The four classic rules: a fixed ratio (every fifth press), a variable ratio (on average every fifth, but unpredictable), a fixed interval (the first press after ten seconds) and a variable interval (the first press after a random wait around ten seconds). In animal records the typical shapes are: fixed ratio gives bursts and a pause after each reward; variable ratio gives a fast, steady rate with almost no pause; fixed interval gives a scallop, slow after a reward and speeding up as the time nears; variable interval gives a steady moderate rate. Try the rules yourself. This is a person tapping, not a pigeon, and you know what is happening, so your pattern will differ from an animal's. What the graph does honestly show is how often the rule paid out. Interactive · A lever, four rules Fixed ratio 5 Variable ratio 5 Fixed interval 10 s Variable interval 10 s No more rewards Press the leverReset record Press the lever to begin. Reward = a tick on the line. Variable ratio draws each next requirement uniformly from 1 to 9 (mean 5); variable interval draws each wait uniformly from 2 to 18 s (mean 10). "No more rewards" is extinction. Slot machines and many app notifications work as variable-ratio schedules, which is one reason they hold behaviour so tightly. The honest limits: that is an analogy from animal behaviour, not proof that any one product causes addiction, and the size of the effect in people is debated. Another fact graduates know is the partial reinforcement extinction effect: behaviour that was rewarded only sometimes lasts longer once rewards stop than behaviour rewarded every time, because "no reward yet" was always part of the deal. Learning is prediction error: the Rescorla–Wagner idea Why does a bell stop teaching once it predicts the food? Leon Kamin showed in 1969 that if an animal has already learned that light predicts shock, then a tone added to the light is barely learned, though it is paired with the shock just as often. This is blocking. The tone adds no surprise, so nothing is left to learn. In 1972 Robert Rescorla and Allan Wagner wrote the idea down. In words: each trial, the change in how strongly a cue predicts the outcome is proportional to the error, the difference between what happened and what all the present cues together predicted. ΔV = α · (λ − ΣV)change in a cue's strength = learning rate × (outcome that happened − total predicted by all cues present) A worked number: with a learning rate of 0.3 and an outcome of 1, a fresh cue A gains 0.3 on trial one, then 0.3 × 0.7 = 0.21 on trial two, and so on, leaving it near 0.99 after ten trials. Now add cue B alongside A, which already predicts 0.99. The error is only about 0.01, so B gets only about 0.003. Compare B learned beside a fresh A: they share the prediction and each reach 0.5. Interactive · Rescorla–Wagner, trial by trial Learn A Blocking Control (A+B from scratch) Extinction Learning rate Blocking: 10 trials of A, then 10 of A+B. Control: 20 trials of A+B. Extinction: 15 trials of A with reward, then 15 without. Outcome strength λ = 1 when rewarded, 0 when not. The model is famous because it is simple and because it was wrong in useful ways. It cannot explain every effect (latent inhibition, for example), and later models added attention and timing. But the big idea survived and moved: learning follows the gap between expectation and outcome. Dopamine is a teaching signal, not the pleasure chemical In the 1990s Wolfram Schultz recorded single dopamine neurons in monkeys. Early in training they fired when an unexpected juice reward arrived. After training, they fired at the cue that predicted the juice and no longer at the juice itself. If the promised juice failed to arrive, their firing dipped below baseline at the moment it was due. Schultz, Dayan and Montague (1997) showed that this matches a reward prediction error, the quantity in temporal-difference learning, an extension of Rescorla–Wagner to time. The toy below uses that model. Each of six steps after the cue carries a value; the signal is how far each step's reward-plus-next-value differs from what was expected. Train it, then look at where the signal sits. Interactive · Where the error signal goes (model) Training trials Reward arrives Reward omitted Temporal-difference model: learning rate 0.3, discount 0.95, reward 1 after the sixth step. Bars above the line are positive error, below are negative. This is a model of the signal, not a recording. At zero trials, the whole error sits at the reward. After enough trials it has moved to the cue (about 0.74 in this setting, which is the discount to the power six) and the reward produces almost none. Omit the reward after training and the error at that moment is strongly negative. This is why dopamine is better described as a signal for learning and wanting than as "the pleasure chemical", the point of Dopamine Is Not the Pleasure Chemical (01/08). It is a strong, influential account, and not the only one: researchers also link dopamine to motivation, effort and salience, and the field argues over how much of its activity a single prediction-error idea explains. Habits: behaviour that no longer asks what it is for With enough repetition in a stable setting, an action stops being a choice made for its result and becomes a response triggered by the setting. Rodent experiments (Adams and Dickinson, 1981) show it when a reward is made unpleasant and the animal keeps pressing anyway. How cleanly that split between goal-directed and habitual control carries over to people is debated. The better-known number is how long it takes. In a 2010 study, Phillippa Lally and colleagues had volunteers choose a simple daily behaviour and rate how automatic it felt over twelve weeks. The time to reach a plateau of automaticity averaged 66 days, ranging from 18 to 254, and missing one day did not noticeably hurt. "It takes 21 days" has no such basis; it traces to a self-help book, Maxwell Maltz's Psycho-Cybernetics (1960), as commonly told. Interactive · How long until it feels automatic? Fast (18 days) Average (66) Slow (254) Day Model: automaticity = 1 − e−3t/D, where D is the days to reach 95% of the plateau (set to 18, 66 or 254 to match the range Lally et al. reported). The shape follows their curve; your numbers will differ with the behaviour and the person. The practical lesson is the cue. A habit attaches to a setting, so the same action in a new place is a new start, and the easiest habits are the ones with a clear, repeated trigger. Observational learning: you don't have to be rewarded yourself People and many animals learn by watching. In the Bobo doll studies (Bandura, Ross and Ross, 1961), nursery-age children who saw an adult hit an inflatable doll were more likely to hit it themselves than those who saw a calm adult. Bandura's later work stressed that watching someone get rewarded or punished matters (vicarious reinforcement), and that beliefs about one's own ability, which he called self-efficacy, shape what people try. The honest caveats: a doll is not a person, children may guess what the experimenter wants, and the studies show imitation in a lab, not that screens cause real-world violence, which later research addresses with mixed and debated results. What holds up is the basic claim that modelling shapes behaviour. What a graduate just sees A learned response is a forecast: the cue became useful because it predicted something. Learning needs surprise. If the outcome was fully expected, nothing changes. Rewards teach what to do better than penalties teach what not to do. Unpredictable rewards produce the most persistent behaviour; "sometimes" holds tighter than "always". Extinction is new learning laid over the old, so old fear or craving can come back. Dopamine is closer to "this was better or worse than expected" than to "pleasure". A habit is attached to a cue and a setting, and takes weeks to months, not a fixed 21 days. People learn from watching, which is why models, not lectures, change behaviour. Where it shows up next Developmental Psychology (35/24): attachment, play and parenting all run through reinforcement and imitation, and so do the arguments over how much experience can shape a child. Clinical Psychology (35/27): exposure therapy is extinction; behavioural activation is reinforcement; the link of prediction error to addiction and depression is an active research area. Machine Learning (34/32): reinforcement learning (Sutton and Barto) uses the same temporal-difference error, which is why computer scientists and neuroscientists read each other's papers. Behavioral Economics (34/46) and Consumer Behavior (34/58): loyalty schemes, gamified apps and "streaks" are schedules of reinforcement. In the world: animal training, classroom management, product design, addiction treatment and parenting advice (and the folk wisdom to be wary of it). If you want to go deeper 📘 Textbook. Michael Domjan, The Principles of Learning and Behavior (Cengage). The standard research-minded text, strong on Pavlovian conditioning. 📘 Textbook. Paul Chance, Learning and Behavior (Cengage). A more readable alternative, with many everyday examples. 📘 Gentler. Karen Pryor, Don't Shoot the Dog! (1984), on training with rewards, and Sutton and Barto's Reinforcement Learning: An Introduction (MIT Press, free online) for the same ideas as computer science. 🌐 Free course. MIT OpenCourseWare 9.00SC Introduction to Psychology (Fall 2011), which covers learning and conditioning, plus the free Noba chapters on conditioning. The takeaway Behaviour is shaped by what predicts what, and by how much the world differs from the forecast. Signals learn to predict, actions are strengthened by their consequences, the timing of rewards sets how stubborn a behaviour is, and dopamine neurons carry the surprise that drives it all. Habits are what a repeated cue leaves behind, and they take months, not weeks. Try this: this week, notice one cue-and-response pair of your own (the notification and the reach for the phone, the smell and the craving). Write down the cue, the action and the reward. Then change just the cue and see what follows. Sources & Further Reading Sources. Pavlov (Nobel Prize in Physiology or Medicine 1904 for work on digestion); Rescorla 1968, Journal of Comparative and Physiological Psychology 66 (contingency); Garcia & Koelling 1966, Psychonomic Science 4; Watson & Rayner 1920 and later critiques (the child's identity and health are disputed; see Wikipedia's summary of Beck, Levinson & Irons 2009 and Digdon et al. 2014 for the competing identifications); Thorndike 1898; Skinner 1938; Ferster & Skinner 1957; Kamin 1969; Rescorla & Wagner 1972; Schultz, Dayan & Montague 1997, Science 275; Adams & Dickinson 1981; Lally et al. 2010, European Journal of Social Psychology 40 (mean 66 days to plateau, range 18 to 254); Maltz 1960 as the usual source of "21 days"; Bandura, Ross & Ross 1961. Schedule shapes are the textbook animal findings. Every number an interactive shows was computed in node: R–W at rate 0.3: A after 20 trials 0.999; blocking leaves B at 0.014 after ten compound trials; control A and B 0.50 each; extinction A 0.005 after 15 unrewarded trials. TD model: cue error 0.735 (0.956) after 50 or more trials; omitted reward, error −1.00. Habit model at day 21: 97% (D = 18), 62% (D = 66), 22% (D = 254). 🌐 MIT OCW 9.00SC Introduction to Psychology 🌐 Noba Project (free psychology textbook chapters) 📘 Domjan, The Principles of Learning and Behavior 📘 Pryor, Don't Shoot the Dog! This describes research, not medical advice. If you are struggling, a doctor or local service can help; findahelpline.com lists free helplines by country. Step 4. Philosophy & History of Education: Big Ideas from Confucius to Freire ----------------------------------------------------------------------------- Why: Big ideas about education, from Confucius to Freire. Every classroom enacts an answer to the question "what is education for?" Seeing the old answers makes the present one visible. Walk into a classroom and you can read a philosophy of education off the room. Desks in rows facing a board say: knowledge flows from the teacher. Desks in clusters and a wall of children's questions say: learners build understanding together. A timetable of exams says: schooling sorts people. A garden, a workshop or a debating circle says something else again. None of these is a neutral fact about teaching; each is an answer, usually inherited and rarely examined, to questions people have argued about for more than two thousand years. The questions are old. What is worth learning? Can virtue be taught? Should a teacher draw things out of a child or put things in? Is school for the individual, for the community, for the economy, or for changing society? This piece walks through the main answers, from China, Greece, the Islamic world, India, Europe, Latin America, South Asia and East Africa, and ends with why the evidence-based turn in education, which is the subject of other pieces in this major, cannot by itself answer them. The course in one box Who takes itEducation majors, usually in the first year, and philosophy and history students; most teacher-training programmes include a "foundations of education" course of this kind. What it is forSeeing the ideas that sit under classroom practice, so that you can tell a practice that has evidence behind it from a belief inherited from a tradition. Comes afterNothing in particular; it is an entry point to the major. Leads toCurriculum & Instructional Design (36/54), Education Systems & Policy Worldwide (36/59), and the sociology of schooling in Stratification & Inequality (35/78). What this piece gives youYou will not know any thinker's whole system. You will recognise the main positions and which classroom habits they sit behind, and you will be able to tell when someone is arguing about evidence and when about aims. Easier first reads: Chinese & Indian Philosophy (36/10), Islamic, African & Latin American Philosophy (36/11), Ancient & Medieval Philosophy (36/08) and How to Learn Anything Faster (17/01). A note on dates. Founding dates for ancient institutions are often traditional or disputed; where they are, this piece says so. The placements in the last interactive are a rough, debatable judgement, not a measurement. Teaching is older than schools, and not only European Societies taught children long before they built schools. Formal teaching shows up wherever writing, ritual or statecraft needed trained people: scribe schools in Mesopotamia and Egypt, Confucius's circle of students in China, Plato's Academy in Athens, Buddhist and Brahmanical centres in India, Islamic study circles and madrasas, and later universities in Bologna and elsewhere. The "first university" is a contest of definitions: the University of al-Qarawiyyin in Fez is dated to the 850s, but historians say it was in effect run as a madrasa until the 20th century, and the story of its woman founder, Fatima al-Fihri, may be partly legendary. Move the slider to see what existed when, and notice how much was going on outside Europe. Interactive · What was happening in education? Year Selected milestones, dates approximate or traditional where marked "c." A small sample, not a full history, and weighted to what this piece discusses. Without JavaScript: Confucius taught in the 5th century BCE; Plato's Academy dates from about 387 BCE; China's civil-service examinations from 605 CE; Nalanda from about the 5th century; the Nizamiyya madrasas from 1065; Rousseau's Émile from 1762; Freire's Pedagogy of the Oppressed from 1968. Confucius: learning as becoming a person Confucius (551 to 479 BCE) is traditionally the first private teacher in China, and his teaching was about character as much as knowledge. In the Analects (a collection of sayings compiled by his followers) he says that "in teaching there should be no distinction of classes" (15.39, in James Legge's 1861 translation), an early and radical claim that a person's origin should not decide who is taught. He wants active students: he will not help one who is not eager, and if he shows one corner of a subject and the student cannot find the other three, he does not repeat it (7.8, paraphrased). And he links the two halves of learning: "Learning without thought is labour lost; thought without learning is perilous" (2.15, Legge). His followers disagreed about human nature, a disagreement that is also a disagreement about teaching. Mencius (4th century BCE) held that we have inborn moral "sprouts" that education should nurture, like a farmer who tends shoots and does not pull on them to make them grow faster. Xunzi (3rd century BCE) held that people's raw tendencies need shaping by teachers and ritual, and began his book on learning with the image that blue is taken from the indigo plant yet is bluer than indigo: education transforms. The two positions echo throughout this piece: is the teacher's job to draw out or to build up? The Confucian tradition also gave the world's longest-running experiment in testing. Examinations for the civil service began under the Sui dynasty in 605 CE, became the main route to office in the Song (960 to 1279), and used the Four Books of the Neo-Confucian canon from the Ming (declared standard in 1370) until they were abolished by edict in 1905. At their peak they offered a chance of rising by merit, in a society that was otherwise rigid, but critics said they narrowed study to approved texts and the eight-legged essay, and in the late Qing about 1% of the two to three million candidates passed. The pros and cons are still the arguments about high-stakes testing today (see Assessment & Measurement, 36/55). Socrates in the Meno: can a teacher draw knowledge out? In Plato's dialogue Meno (c. 380 BCE), a young nobleman asks whether virtue can be taught. Socrates replies by testing a puzzle: how can you search for something you don't know? His answer is recollection (anamnesis): the soul once knew and relearns by being questioned. To prove it he calls over an uneducated slave boy of Meno's household and, only by asking questions, leads him to double the area of a square (Meno 82b to 85d). Here is the puzzle. The square has sides of 2 feet and area 4. How long should the side be to make the area 8? The boy says 4, which gives an area of 16. He then says 3, which gives 9. Both are wrong, and he is puzzled. Socrates then draws the diagonals and the boy sees that the square built on the diagonal of the first square has area 8. The side is the diagonal, about 2.83 feet. Try the boy's guesses. Interactive · Double the square Side of the new square (feet) The boy's first guess: 4Second guess: 3The diagonal Gold: the original square, side 2, area 4. Blue: your square. The target is exactly 8 square feet. Without JavaScript: side 4 gives area 16, side 3 gives 9, and the diagonal of the 2-foot square, about 2.83, gives 8 (its square is exactly 8). What does this show? Plato thought: the boy "knew" it all along. Modern readers see a teacher leading by questions, with a diagram, to a conclusion Socrates already holds, and ask how much was discovered and how much was led. This is the oldest form of an argument still running: discovery and guided instruction (see the evidence in Teaching Reading & Mathematics, 36/56). The Socratic method of persistent, probing questions is still taught in law and philosophy classes, and Aristotle, Plato's student, took a different line in the Nicomachean Ethics: virtue comes by habit, by doing just acts until you are just. The chain of teachers: madrasa, gurukula and monastery In many traditions learning was not a curriculum but a relationship. In the Islamic world, study circles in mosques grew into madrasas. A student read a text with a teacher and received an ijaza, a licence to transmit that text, which linked him or her to a chain of earlier teachers back to the author; a scholar's standing was the chain. The Seljuk vizier Nizam al-Mulk founded the Nizamiyya colleges across the empire; the Baghdad one was established in 1065, and the theologian and philosopher al-Ghazali taught there. The historian Ibn Khaldun, in his Muqaddimah (1377), argued for teaching in gradual stages, starting with the simple, and warned that harsh treatment of pupils does harm. In West Africa, Timbuktu's mosque-schools around Sankore had become renowned centres of Islamic scholarship by the 15th century. In India, learning passed from guru to student, the Vedas by oral recitation of astonishing accuracy and the arts by apprenticeship. The monastic university at Nalanda in Bihar, founded around 427 CE under the Gupta king Kumaragupta I, drew students from across Asia; the Chinese pilgrim Xuanzang studied there in the 630s and 640s and carried 657 texts home. His account gives about 10,000 monks and 1,500 teachers, which modern scholars think exaggerated. The place declined after attack around 1200. These traditions share ideas that modern schools sometimes forget: the teacher's character matters as much as the lesson, memorising is a first step to understanding, not its opposite, and learning is communal. They also share limits: access depended on gender, caste, class or religion, and the authority of the text could discourage questioning, though debate was central to Nalanda and to the Islamic tradition of munazara. Neither the praise nor the dismissal of "rote learning" is simple: Chinese and Japanese learners who memorise often do so as a route to meaning. The child at the centre: Rousseau to Dewey, and the reply In Europe, John Amos Comenius (1592 to 1670) argued that everything should be taught to everyone and published Orbis Pictus (1658), a picture book for children, the first widely used illustrated textbook for the young. Then came a turn toward the child. In Émile (1762) Jean-Jacques Rousseau argued that education should follow the child's natural development and let experience, not lectures, teach. (He placed his own five children in a foundling hospital, an irony critics never let him forget.) Pestalozzi in Switzerland taught through objects and affection, and Friedrich Froebel opened the first "kindergarten" in 1837. In Prussia, a school regulation of 1763 helped establish state schooling, and across the world states took on mass schooling in the 19th century: Japan's education order of 1872, Argentina's Law 1420 of 1884 for free, compulsory, secular schooling under Sarmiento's influence. John Dewey (1859 to 1952) is the best-known "progressive". In Democracy and Education (1916) he argued that school should be a small democratic community in which children learn by doing, with inquiry growing from real problems. Maria Montessori opened her first Casa dei Bambini in Rome in 1907 and built a method around prepared environments and self-directed work. At Reggio Emilia in Italy, parents and the educator Loris Malaguzzi began schools after the Second World War, built on the idea that children have "a hundred languages" of expression. Their ideas are used worldwide. The reply deserves its strongest form. Dewey himself, in Experience and Education (1938), criticised teachers who took "progressive" to mean no structure. In the 1930s the Italian Marxist Antonio Gramsci warned in his prison writings that child-centred reforms could hurt working-class children by denying them the demanding common culture that elites already possessed at home. In the US, Lisa Delpit (1988) argued that withholding explicit teaching of the "codes of power" can hurt Black children while seeming to respect them. E. D. Hirsch (Cultural Literacy, 1987) argued that comprehension needs shared background knowledge that schools must supply. Progressives answer that knowledge without engagement is brittle and that "child-centred" never meant "teacherless". In practice, many classrooms mix both, and the evidence on specific methods (see 36/53 and 36/56) matters more than the label. Freire, Gandhi and Nyerere: education for freedom or self-reliance Paulo Freire (1921 to 1997), a Brazilian educator, taught adults to read in the early 1960s; in one well-known campaign about 300 sugarcane workers learned to read in about 45 days. After the 1964 military coup he was jailed and then exiled, and in Chile he wrote Pedagogy of the Oppressed (first published in 1968; English 1970). His most-quoted idea is the banking concept: a teacher "deposits" facts into students as if they were empty accounts, which trains people to accept the world as given. His alternative is problem-posing education: teacher and students name real problems from the learners' lives and reflect and act on them together, which he called conscientização, or critical consciousness. Critics say the "banking" picture caricatures what good direct teaching is, that critical pedagogy's own claims need evidence, and that (as the feminist scholar Elizabeth Ellsworth argued in 1989) a teacher who claims to empower can still hold unexamined authority. Supporters say it gave literacy teaching a dignity it often lacked, and he served as São Paulo's municipal education secretary from 1989. Elsewhere: Rabindranath Tagore founded his school at Santiniketan in 1901 on open-air learning, art and the unity of humans with nature. Mohandas Gandhi proposed Nai Talim ("new education") at a conference at Wardha in 1937: education through productive craft, in the mother tongue, meant to make schools partly self-supporting. It was hard to apply, and critics said self-financing schools overworked children. Julius Nyerere's Education for Self-Reliance (1967) argued that primary schooling in Tanzania must be complete in itself, tied to farming and community life, not merely a ladder to secondary school for the few. It was adopted partly and criticised for under-funding and for clashing with parents' hopes of social mobility. In Aotearoa New Zealand, the Māori-language kura kaupapa schools, which began in 1985, express the aim of keeping a language and culture alive. And the southern African idea of ubuntu, roughly "a person is a person through other persons", has been used to think about learning as communal. Other thinkers worry about schooling itself. Ivan Illich, in Deschooling Society (1971), argued that institutions confuse being taught with learning. Pierre Bourdieu and Jean-Claude Passeron (1970) argued that schools reproduce inequality by rewarding the cultural capital of the already advantaged, and the sociology of this is the subject of Stratification & Inequality (35/78). What is education for? Evidence cannot answer alone Philosophers of education usually sort the answers into a few families, and most thinkers mix them. Virtue and character (Confucius, Aristotle, the madrasa). Passing on knowledge and culture (the traditionalists, Hirsch). The growth of the child (Rousseau, Montessori, Dewey). Preparing workers and citizens (the examination state, modern economies, Nyerere's self-reliance). Freedom and change (Freire, critical pedagogy). Try sorting some modern claims. Interactive · What is this claim mainly about? Without JavaScript: "School makes people honest and wise" is about virtue; "Every child should meet the best that has been thought and written" is about knowledge and culture; "Follow the child" is about the child's growth; "Schools should supply the skills the economy needs" is about workers and citizens; "Learn to name and challenge injustice" is about freedom and change. Why does this matter in an age of "what works"? The educational theorist Gert Biesta (2007) made the point sharply: evidence can tell you which method gets children to a goal, but a goal is chosen by values, so "what works" is always "what works for what?". Randomised trials of phonics can say whether children learn to decode; they cannot say whether decoding by age six is the goal of a good childhood. The philosophy supplies the "for what" and the evidence the "how well". The rest of this major is mostly about evidence, and this piece is the reminder to ask for the aim. One last toy. Place yourself on two dials and see which thinkers sit nearest. It is not a personality test, and the placements are rough. Interactive · A rough map of thinkers Authority: teacher and tradition (0) to learner and community (100) Aim: pass on an inheritance (0) to change society (100) Placements are a rough, debatable judgement of each thinker's main emphasis; each of them wrote more than a point can hold. Without JavaScript: a teacher-led, tradition-passing view sits near Confucius, the madrasa tradition and Hirsch; a learner-led view that wants to change society sits near Freire and Illich. What a graduate just sees Every classroom layout and timetable embodies an answer to "what is education for?" Formal teaching is global and old: China, India, the Islamic world and West Africa had advanced traditions long before European universities. Confucius, Mencius and Xunzi frame an argument (draw out or build up) that runs through the rest of the history. The Socratic slave-boy demonstration is a question about guided discovery, not just a proof of recollection. Memorising and understanding are not opposites in the great teaching traditions. "Child-centred" and "traditional" both have strong versions and weak versions; the strongest critics came from inside the camp. Freire's "banking" picture is a critique of one way of teaching and a politics of literacy at the same time. Evidence tells you what works; it cannot tell you what to want. Where it shows up next Curriculum & Instructional Design (36/54): choosing what to teach is where these aims become a syllabus. Education Systems & Policy Worldwide (36/59): why Finland, Singapore, Japan and Brazil built different systems from different histories. Stratification & Inequality (35/78): the sociological side of the argument over what schools do to inequality. In the world: curriculum debates, school-choice and testing arguments, teacher training, and the shape of national reforms such as India's National Education Policy 2020. If you want to go deeper 📘 Textbook. Nel Noddings, Philosophy of Education (Westview, 4th ed. 2015), a standard single-author introduction; Randall Curren (ed.), A Companion to the Philosophy of Education (Blackwell, 2003), for the debates. 📘 Gentler. John Dewey, Experience and Education (1938), short and still fresh; Paulo Freire, Pedagogy of the Oppressed (50th anniversary edition, Bloomsbury, 2018). 🌐 Free text. Stanford Encyclopedia of Philosophy, "Philosophy of Education" (first published 2025), and James Legge's 1861 translation of the Analects (public domain). The takeaway Teaching has been argued over in China, Greece, the Islamic world, India, Europe, Latin America, South Asia and Africa, and each tradition supplies a recognisable answer: shape character, pass on a culture, nurture the child, serve the community, or free people. Real schools mix them. Evidence can tell you how well a method reaches a goal; it cannot say which goal to pick, and a graduate of this subject knows to ask. Try this: look at the room and routine of a classroom you know, in memory or in a photo. Write down three things you see and the answer to "what is education for?" each one implies. Sources & Further Reading Sources. Confucius, Analects 2.15, 7.8, 15.39 (Legge 1861); Mencius 2A2 and 2A6; Xunzi, "Encouraging Learning" (Knoblock). Imperial examinations: Wikipedia "Imperial examination" (605 CE; Song expansion; Four Books standard from 1370; abolished by edict of 2 September 1905; late-Qing figures of two to three million candidates and about 1% passing). Plato, Meno 82b to 85d; Aristotle, Nicomachean Ethics II. University of al-Qarawiyyin: Wikipedia (founded 857 to 859 per the Rawd al-Qirtas, disputed; run as a madrasa until after the Second World War); Nizamiyya: Wikipedia (Baghdad, 1065); Ibn Khaldun, Muqaddimah 1377; Nalanda: Wikipedia (about 427 CE; Xuanzang's visits in 637 and 642 and 657 texts; attack about 1200). Comenius 1658; Rousseau 1762; Froebel 1837; Dewey 1916 and 1938; Montessori 1907; Gramsci, Prison Notebooks; Hirsch 1987; Delpit, Harvard Educational Review 1988. Freire: Wikipedia (Pedagogy of the Oppressed 1968, English 1970; coup 1964; São Paulo secretary of education); Ellsworth, Harvard Educational Review 1989. Tagore 1901; Gandhi, Wardha 1937; Nyerere, Education for Self-Reliance 1967; Illich 1971; Bourdieu and Passeron 1970; Biesta, Educational Theory 2007. Placements and the timeline are illustrative. 📘 Noddings, Philosophy of Education 📘 Freire, Pedagogy of the Oppressed 🌐 Stanford Encyclopedia: Philosophy of Education Step 5. Developmental Psychology: How Minds Are Built, and What Later Research Revised -------------------------------------------------------------------------------------- Why: How minds grow from infancy to adulthood. From Piaget's stages to false beliefs, attachment and the long rebuild of adolescence. What held up, what shifted, and why heritability is not a pie chart. A two-year-old hides her face behind her hands and announces that you can't see her. A four-year-old watches you look for your keys in the wrong drawer and, quietly, knows you are looking in the wrong place. A sixteen-year-old does something spectacularly risky when friends are watching and something sensible when alone. A seventy-year-old forgets a name but explains the situation better than anyone else in the room. These are not separate mysteries. They are four points on one long road, and developmental psychology is the study of the road: what changes, in what order, why, and how much it depends on the child, the family and the century. A graduate of this course stops asking "is it nature or nurture?" and starts asking "which differences, in which population, at which age, under which conditions?". The course in one box Who takes itEvery psychology degree, usually in year 2; education, nursing, social work and paediatrics students take a version. Programmes vary on whether it covers the whole lifespan or mainly childhood. What it is forDescribing how thinking, feeling and relating change from infancy to old age, and testing the explanations. Comes afterCognitive Psychology (35/22) and Learning & Behavior (35/23). Leads toSocial Psychology (35/25), Personality & Individual Differences (35/26) and Clinical Psychology (35/27), and on to teaching, paediatrics and policy. What this piece gives youYou will not be able to assess a child. You will know the big theories, what has been revised, and why children in different places are not interchangeable. Gentler first reads: Attachment: The Blueprint (02/01), How Children Think (02/07), Why Teenagers Aren't Broken (02/03) and Nature, Nurture and You (02/04). This goes further and shows the evidence and its critics. The demos are toys, not studies. Piaget: children think differently, and later research revised the timetable Jean Piaget (1896 to 1980) watched his own children and Swiss schoolchildren and concluded that they are not small adults with less knowledge. They think in a different way, and the way changes in steps. His four stages: sensorimotor (birth to about 2, knowing through action), preoperational (about 2 to 7, symbols and pretend but thinking tied to appearances), concrete operational (about 7 to 11, logic about real things) and formal operational (from about 11 or 12, abstract and hypothetical thought). Two ideas have survived best: children actively build understanding rather than absorbing it, and they can be systematically wrong in ways that make sense from the inside. His best-known test is conservation. Pour water from a short wide glass into a tall thin one and a five-year-old says there is now more. Piaget read this as a lack of the logic of reversibility. Later researchers argued he underestimated young children, because his tasks were hard to follow. In a 1974 study, James McGarrigle and Margaret Donaldson had a "naughty teddy" mess up the arrangement by accident rather than the experimenter doing it on purpose, and many more children then gave the right answer. In the same spirit, Martin Hughes's 1975 police-doll task showed that children as young as three and a half could work out where to hide a doll from a policeman, a task Piaget's "three mountains" test had said they could not do. At the other end, researchers used looking time to ask what babies know. In the 1980s Renée Baillargeon and colleagues reported that infants as young as about three and a half to five months looked longer at an "impossible" event, such as a screen rotating through a hidden box, than at a possible one. They concluded that babies have early knowledge about objects. That claim is contested. Critics point out that looking longer may reflect novelty rather than surprise, that search tasks (reaching for a hidden toy) show later competence, and that some pupil-dilation and replication attempts, especially at 10 months, have not found the expected effect. The honest summary: infants have more early structure than Piaget thought, how much is still argued, and the stage boundaries are softer than the textbook diagram. Interactive · How a looking-time experiment is built (toy model) Tracks hidden objects Does not Does not, but the "impossible" display looks different Familiarisation trials All constants are made up to show the logic. Looking time = 2 + 14·e−0.4n s on trial n. Test events: a possible one (the same as before) and an impossible one, which adds 6 s for an infant who tracks hidden objects, or for one who only notices that it looks different. The toy shows why the debate is hard. Habituation shortens looking at a repeated event; a test that recovers looking is read as "this is surprising". But two different infants, one who understands objects and one who merely finds a new display interesting, can produce the same pattern. Good studies are designed to tell them apart. Vygotsky: the mind grows between people Lev Vygotsky (1896 to 1934) died of tuberculosis at 37, and most of the English-speaking world met him decades later, through Mind in Society (1978). Where Piaget's child is a lone scientist, Vygotsky's child learns thinking tools by using them with others: language first used between people becomes private speech and then inner thought. His best-known idea is the zone of proximal development: the gap between what a child can do alone and what they can do with a little help. Teaching works best inside that gap, not at the level already mastered nor far beyond reach. Wood, Bruner and Ross (1976) called the adult's changing support scaffolding: giving more help when the child struggles and less as they succeed. Vygotsky's work is more a framework than a set of precise predictions, so it has been harder to test than Piaget's. It still shapes teaching practice across the world, from tutoring to the way many early-years programmes use guided play. The cross-cultural point: in many communities learning happens by children joining in adult work rather than in school-style lessons, a pattern Barbara Rogoff and others have documented. Attachment: the first relationships John Bowlby, a British psychiatrist, argued in the 1950s and 60s that infants are built to seek closeness to a caregiver, and that this bond is not just about food. Harry Harlow's 1950s monkey experiments showed baby monkeys preferred a soft cloth surrogate to a wire one that held the milk. Mary Ainsworth, who had observed mothers and babies in Uganda, designed the Strange Situation (1970s): a short lab procedure in which a one-year-old sees a parent leave and return. Babies were sorted by their reaction at reunion: secure (upset perhaps, but comforted and soon back to play), avoidant (little visible distress, avoiding the parent on return), resistant or ambivalent (clingy and angry), and later disorganised. In many studies, most babies are classed secure. But the rest of the picture differs by place. A 1988 meta-analysis by van IJzendoorn and Kroonenberg reported that the patterns shifted across countries; studies in northern Germany found more avoidant babies than American norms, and a study in Sapporo, Japan found more resistant ones. The disagreement is over what that means. One reading is that cultures raise babies differently (a German emphasis on early independence, Japanese babies rarely separated from their mothers, so the procedure stresses them more). Another is that the test, built in the US and the UK, does not measure the same thing everywhere. Both are taken seriously. The strongest evidence about attachment and early care comes from the Romanian orphanages of the 1980s. The Bucharest Early Intervention Project (Nelson, Zeanah, Fox and colleagues, 2007) randomly assigned institutionalised children to foster care or to staying put; those moved earlier, especially before about two, did better on many measures. The English and Romanian Adoptees study (Michael Rutter and others) found that longer deprivation went with longer-lasting difficulties. The lesson is "sensitive period", not "critical window that slams shut": the earlier the good care, the better the recovery, and recovery is still possible later. Another caution: attachment style correlates with later outcomes, but a child's own temperament and the many things that change in life make the link far from destiny. Theory of mind: knowing that others know different things A theory of mind is the understanding that other people have beliefs, desires and knowledge that may differ from yours and from reality. The classic test is the false-belief task (Wimmer and Perner, 1983; the Sally–Anne version by Baron-Cohen, Leslie and Frith, 1985). Try it. Interactive · Predict, then reveal Next sceneStart over In the basketIn the box Press Next scene. Adults answer "the basket" without a thought: Sally believes what she last saw. Many three-year-olds say "the box", because that is where the marble really is. Most children pass around four to five. Wellman, Cross and Watson's 2001 meta-analysis of 178 studies found the same shift from below chance to above chance across the many countries studied, though the age and order of steps differ: in a 2011 study (Shahaeian and colleagues) children in Iran and Australia learned some steps in different orders, an effect linked to how families talk about knowledge. Some experiments report that babies as young as 15 months look longer at scenes that violate a false belief (Onishi and Baillargeon, 2005), but replication attempts have been mixed, and whether this reveals early understanding or something simpler is debated. It is also worth saying that theory-of-mind findings in autistic people are contested: the long-standing claim that autistic people lack a theory of mind has been challenged by researchers who describe a two-way difficulty in understanding across different minds, not a one-way deficit. Adolescence and ageing: change that is neither disorder nor decay Adolescence is a long, normal rebuild. A widely cited 2018 paper (Sawyer and colleagues) argued that it now stretches from about 10 to 24, because puberty comes earlier and adult roles come later. The brain is reorganising: connections are pruned, and the prefrontal regions that help with planning and self-control keep maturing into the twenties. But "the brain isn't mature until 25" is a slogan, not a threshold; there's no age at which a switch flips, and the exact timing varies by region and by person. One well-replicated finding is about when teenagers take risks. In a driving-game study (Gardner and Steinberg, 2005), adolescents took more risks when peers were watching than when alone, while adults did not change nearly as much. The usual reading, Laurence Steinberg's "dual-systems" account, is that a reward system matures before the control system. Critics argue the picture is more nuanced, since adolescents can reason well in calm conditions and risk-taking can also be exploration and learning. For more, see Why Teenagers Aren't Broken (02/03). At the other end, ageing is not simply decline. Psychologists separate fluid abilities (quick reasoning, processing speed, which tend to fall from the twenties) from crystallised ones (vocabulary and knowledge, which keep growing). In 2015, Joshua Hartshorne and Laura Germine analysed large online samples and found that abilities peak at very different ages: processing speed around the late teens and early twenties, working memory in the late twenties to early thirties, and vocabulary much later, into the sixties or seventies. Their result is cross-sectional and from one research programme, so cohort differences blur it. Dementia is a disease, not normal ageing. Interactive · Who is at their peak at this age? Age The bars show approximate peak ranges as summarised from Hartshorne and Germine (2015): speed 18 to 22, working memory 27 to 33, vocabulary 60 to 70. They are simplified ranges, not a curve, and the exact ages vary by task and generation. Nature and nurture, done properly "Is it genes or environment?" is a badly formed question, a bit like asking whether the area of a field comes from its length or its width. The better question is: in this population, how much of the difference between people goes with differences in their genes? That share is the heritability, and it has three properties people forget. It describes a population, not a person; "50% heritable" does not mean half of your height is from genes. It depends on the environment: it is higher where everyone has similar conditions, lower where conditions differ. And it is not fate: a trait can be strongly heritable and still change a lot when the environment changes, as the PKU metabolic disorder does with diet, or as average height has done over the last century (NCD-RisC's 2016 analysis found a gain of about 20 cm for South Korean women born between 1896 and 1996). The numbers are real, though. A 2015 meta-analysis of fifty years of twin studies (Polderman and colleagues, 17,804 traits, about 14.5 million twin pairs) put the average heritability across traits at about 49%, with shared family environment usually small once genes are counted. Eric Turkheimer summarised the pattern as three laws: all human behavioural traits are heritable; the effect of being raised in the same family is smaller than the effect of genes; and a substantial part of the variation is not explained by genes or families. Critics of twin methods argue about their assumptions, and measured DNA often explains less than twin studies imply (the "missing heritability" puzzle). Interactive · Same genes, different heritability Similar environments In between Very different environments Genetic differences (SD) Shared family environment (SD) Individual environment and chance (SD) Simulation of 3,000 identical-twin pairs and 3,000 fraternal pairs (identical twins share all genes, fraternal share half on average). The estimate is Falconer's: heritability = 2 × (identical correlation − fraternal correlation). A model, with the usual twin assumptions. Slide the environment from "similar" to "very different" while leaving the genetic differences untouched. Heritability falls from about 0.9 to about 0.2. The genes did not weaken; the environment simply began to explain more of the gaps. Whose children? The WEIRD problem and cross-cultural findings In 2010 Joseph Henrich, Steven Heine and Ara Norenzayan pointed out that most behavioural science samples come from people who are Western, Educated, Industrialised, Rich and Democratic (WEIRD), a small and unusual slice of humanity. In development this matters a lot. Sleeping alone, school-style questioning, "talking to" babies, and independence as the goal are cultural choices, not universals. Attachment categories vary, theory-of-mind steps vary in order, and the famous "marshmallow test", once thought to predict adult success, was shown in a larger, more diverse sample (Watts, Duncan and Quan, 2018) to be far weaker once family background was accounted for. What does appear widely is the basic outline: infants everywhere form attachments, children everywhere pass false-belief tasks in the preschool years, and adolescents everywhere seek peers. The details are cultural. What a graduate just sees Children are not small adults; their errors have an inside logic, and a task's wording can hide what they know. Timetables of "stages" are rough. Ages for when children can do things move when the test is made fairer. Learning happens in the gap between what a child can do alone and with help; scaffolding means help that fades. A bond with a caregiver is a base for exploring, and the earlier poor care is repaired, the better. Passing the false-belief task means seeing that someone can hold a belief you know is wrong. Adolescent risk-taking depends on the audience, and the brain's rebuild has no fixed finish line. Different abilities peak at different ages; knowledge grows when speed falls. Heritability describes differences in a population and changes with the environment; it never says what one person will become. Ask who was in the sample before generalising to "children". Where it shows up next Social Psychology (35/25): conformity and group identity peak in adolescence, and theory of mind is the base of every social judgement. Personality & Individual Differences (35/26): temperament, the heritability toolkit (twins, adoption) and the stability of traits from childhood on. Clinical Psychology (35/27): attachment-informed therapy, how early adversity affects later health, and how conditions such as autism and ADHD are understood across the lifespan. Education and policy: the early-years evidence behind parental leave, quality childcare and preschool programmes, and the debate over how to teach (guided play, direct instruction, scaffolding). In the world: paediatric care, social work, adoption and foster-care practice, school design and the ageing-population debate. If you want to go deeper 📘 Textbook. Laura Berk, Child Development or Development Through the Lifespan (Pearson). A standard, clear text widely assigned in the US and beyond. 📘 Textbook. Robert Siegler and colleagues, How Children Develop (Worth / Macmillan), strong on cognition and on the evidence behind each claim. 📘 Gentler. Alison Gopnik, The Philosophical Baby (2009), and Margaret Donaldson, Children's Minds (1978), the classic that challenged Piaget with the "naughty teddy" and police-doll tasks. 🌐 Free course. MIT OpenCourseWare 9.85 Infant and Early Childhood Cognition (Fall 2012), and the free Noba developmental chapters. The takeaway Minds are built in steps, but the steps are softer than the diagrams, and they depend on help from others and on the culture around them. Early care matters and later repair is possible. Genes and environment do not split the credit like a pie: heritability is a statement about differences within a population, and it moves when the environment does. Try this: this week, watch a child (or remember being one) solve a problem with a little help. Notice what help worked, and how it faded as they got it. That is a zone of proximal development at work. Sources & Further Reading Sources. Piaget's stages and conservation (standard textbook accounts); McGarrigle & Donaldson 1974, Cognition 3; Hughes 1975 (doctoral thesis, Edinburgh) as reported in Donaldson 1978; Baillargeon, Spelke & Wasserman 1985; replication doubts: Pätzold & Liszkowski 2020 (PLoS ONE, pupillometry, 10-month-olds); Vygotsky 1978 (Mind in Society); Wood, Bruner & Ross 1976; Bowlby (Attachment and Loss, 1969 on); Harlow 1958; Ainsworth et al. 1978; van IJzendoorn & Kroonenberg 1988, Child Development 59; Nelson et al. 2007, Science 318; Rutter and the English and Romanian Adoptees study; Wimmer & Perner 1983; Baron-Cohen, Leslie & Frith 1985; Wellman, Cross & Watson 2001, Child Development 72 (178 studies); Shahaeian et al. 2011, Developmental Psychology 47; Onishi & Baillargeon 2005; Sawyer et al. 2018, Lancet Child & Adolescent Health 2; Gardner & Steinberg 2005, Developmental Psychology 41; Hartshorne & Germine 2015, Psychological Science 26; Polderman et al. 2015, Nature Genetics 47 (17,804 traits, about 14.5 million twin pairs, average heritability 49%); Turkheimer 2000, Current Directions in Psychological Science 9; NCD Risc 2016, eLife 5:e13410 (20.2 cm for South Korean women, 1896 to 1996 birth cohorts); Henrich, Heine & Norenzayan 2010, Behavioral and Brain Sciences 33; Watts, Duncan & Quan 2018, Psychological Science 29. Interactive numbers computed in node: twin simulation with 3,000 pairs each, genetic SD 1: similar environments (individual SD 0.3) gives heritability estimate 0.89 against a true 0.92; very different (SD 2) 0.19 against 0.20; the middle preset 0.44 against 0.44. 🌐 MIT OCW 9.85 Infant and Early Childhood Cognition 🌐 Noba Project 📘 Berk, Child Development 📘 Gopnik, The Philosophical Baby This describes research, not medical or parenting advice. If you are worried about a child's development, talk to a paediatrician or local service; if you are struggling yourself, findahelpline.com lists free helplines by country. Step 6. Language Acquisition: How Children Build a Language ----------------------------------------------------------- Why: How children learn language. Every typical child does something no adult can easily match, and the argument over how is one of the oldest in the cognitive sciences. A two-year-old says "I runned to the door." She has never heard an adult say "runned". Nobody told her the rule for the past tense. She worked it out, from the speech around her, and then applied it a little too widely. Within two years she will say things like "I wonder whether the dog that I saw is still outside", a sentence with a question inside a clause inside a clause, which she has also never been taught. Every typical child, in every country, in every language and in sign, does this. No other animal does, and no adult learner finds it easy to match. The question of how is one of the oldest quarrels in the cognitive sciences, and it is more than a quarrel about children: it is about what a mind starts with and what it takes from the world. This piece goes past the basic timeline in How Children Learn Language (26/06) to the experiments and the arguments. The course in one box Who takes itLinguistics majors in year 4, and psychology, education and speech-language-pathology students, who often meet it earlier; it sits at the border between linguistics and developmental psychology. What it is forUnderstanding how children go from babbling to grammar, what they bring to the job, and what the evidence from deprivation, bilingualism and sign languages says about it. Comes afterSyntax (36/23) and Developmental Psychology (35/24). Leads toPsycholinguistics & the Brain (36/28) and Computational Linguistics (36/30), where learning models meet language models. What this piece gives youYou will not be able to assess a child. You will know the main findings, the two big theories and what each says about the same data, and which famous stories need care. Easier first reads: How Children Learn Language (26/06) and Learning a Language as an Adult (26/07). Not clinical advice. This describes research on typical development. Children vary a great deal. If you are concerned about a child's hearing or speech, a paediatrician or speech-language pathologist is the right person to ask. The first year: statistics before words Speech does not come with spaces. In a continuous stream of sound, a baby has to find where one word ends and the next begins, in a language she does not yet know. In 1996 Jenny Saffran, Richard Aslin and Elissa Newport tested a clever possibility. They played 8-month-old babies about two minutes of a made-up language, a monotone stream built from four nonsense words (tupiro, golabu, bidaku, padoti) in random order, with no pauses and no stress. Within a word, one syllable always follows another (tu is always followed by pi); across a word boundary, the next syllable is one of three possibilities. Afterwards the babies listened longer to new orders that mixed up syllables from different words than to the "words" themselves. They had tracked transitional probabilities: how likely one syllable is to follow another. TP(B | A) = number of times A is followed by B ÷ number of times A occursHigh TP inside a word; a dip at the boundary. The dips are where the words break. This finding has held up well, and it also works for non-speech tones and in other species (Hauser, Newport and Aslin found it in cotton-top tamarins in 2001). It does not mean this is the only cue: real infants also use stress patterns and pauses. Try the learner. Interactive · Find the words without knowing any Words heard in the stream A dip below this probability marks a boundary A simulated stream from the four words used by Saffran et al. (1996), in a fixed pseudo-random order with no word repeated twice in a row. Green bars mark a correct boundary the learner found, red a boundary it hit in the wrong place, grey a boundary it missed. The babies' own results were about listening times, not a count like this. Without JavaScript: inside each word the transitional probability is 100%; at a word boundary it is much lower (in the simulation, roughly a third to two fifths). With enough listening, a rule "break where it dips" finds almost every word. Babies also narrow their ears (the 9-month Mandarin experiment is in 26/06). Sound, rhythm and statistics are the first year's job. The first word usually arrives at around 12 months; by then the child has been learning her language for a year without producing any of it. First words and the rules children invent After the first words (typically around 12 months), vocabulary grows slowly, then faster. By 18 to 24 months many children combine two words ("more milk", "daddy go"). Normal range is wide: a child with 50 words and a child with 300 at two years can both be developing normally, and late talkers often catch up, though not always. Languages differ in what is easy. Turkish words are built by stacking suffixes, as in ev-ler-im-de, and children learning Turkish tend to use these suffixes correctly remarkably early, an observation of Dan Slobin's cross-linguistic work. ev-ler-im-de  (Turkish) house-PL-1SG.POSS-LOC 'in my houses' The error that captured everyone's attention is overregularization. For a while a child says went, then later goed, then went again. The child did not hear "goed"; she extracted the -ed rule (Jean Berko's 1958 "wug test" shows children apply it to new words) and applied it to a verb that breaks it. But the picture is easy to exaggerate. In their 1992 monograph, Gary Marcus and colleagues analysed 11,521 irregular past-tense uses from children's recorded speech and found overregularization in a median of just 2.5% of them. Later analyses give a higher average (4.2% in one dense corpus, with one child at 24%). Maratsos (2000) argued that averages hide the fact that rare verbs are far more error-prone. Children, in short, get irregular verbs right most of the time, and errors cluster on the less common ones. A simple "memory plus rule" model reproduces this pattern. For each irregular verb, the child stores the past form once heard; the more often she hears it, the stronger the memory. If retrieval fails, the rule fills in. Steven Pinker and Alan Prince's "words and rules" account (1988) is built on this idea; connectionist models (Rumelhart and McClelland, 1986) argue that one network can do both jobs. The tool below is a toy of the first kind, with invented frequencies. Interactive · A memory-plus-rule toy Child's age (the rule is learned at 24 months here) Illustrative model, not data. Chance of retrieving a past form = 1 − exp(−hearings ÷ 20); hearings = verb frequency × months of listening since 12. Frequencies are invented. The point is the shape: errors appear when the rule arrives, fall as memories strengthen, and stay highest for rare verbs. Without JavaScript: in the toy, errors begin at the age the rule is learned, fall steadily afterwards, and are highest for the rarest verbs; the overall average is a few per cent, as in the real data. Poverty of the stimulus versus learning from use How can a child learn grammar from input that is messy, incomplete and never labelled? Noam Chomsky's answer (from the late 1950s) is that she cannot do it from experience alone: the data underdetermine the grammar, so children must start with some built-in structure, which he called universal grammar. This is the poverty-of-the-stimulus argument. The standard example is question formation. A child hears "The man is happy" and "Is the man happy?" and could conclude: move the first "is" to the front. That rule fits every simple sentence perfectly and is wrong for "The man who is tall is happy". Interactive · Which rule did the child learn? Simple questions heard Questions with a clause inside the subject heard The two rules are the textbook ones. Hearing counts are for you to play with: how many complex questions real children hear is one of the points in dispute. Without JavaScript: for "The man who is tall is happy", the linear rule gives "Is the man who tall is happy?", which no English speaker says; the structural rule gives "Is the man who is tall happy?". The two rules agree on every simple sentence. The tool shows the argument: with only simple questions the two rules are indistinguishable. The puzzle, said Chomsky, is that children never make the linear error. In 1987 Stephen Crain and Mineharu Nakayama tested children aged three to five by asking them to form questions from sentences like this and found no linear errors. Critics reply in three ways. First, the premise: Geoffrey Pullum and Barbara Scholz (2002) argued that such evidence is more common than claimed, and that "learning from the data" is not hopeless. Second, statistical learners: Florencia Reali and Morten Christiansen (2005) showed simple models trained on child-directed speech get most of these questions right with no built-in syntax. Third, the whole picture: Michael Tomasello and the usage-based school argue that children begin with specific phrases ("Where's the ___?", "I wanna ___") and gradually generalise them into abstract patterns, using general social and pattern-finding skills (reading others' intentions, categorising). The nativists reply that those models learn from far more or differently structured data than a child gets, and that cross-linguistic universals need explaining. The debate is live and has moved. Chomsky's own proposals have shrunk the built-in part to little more than a combining operation (Merge), and Tomasello's side now accepts a rich set of innate learning skills. Language models, trained on enormously more text than any child hears, are now a new kind of evidence; what they show about children is argued by both camps (see Computational Linguistics, 36/30). Daniel Everett's claim that Pirahã in Brazil lacks recursion (2005) was meant to challenge the universal-grammar picture; Andrew Nevins and colleagues (2009) disputed his data. A fair summary: nobody now thinks the child is a blank slate, and nobody agrees about how much of grammar is built in. Critical periods: Genie, Nicaraguan Sign Language and the age curve Is there a window for language learning? The biologist Eric Lenneberg argued in 1967 that language is easily acquired in childhood and, after about puberty, no longer in the same way. Animal studies of imprinting and song learning in birds gave the idea a model. Humans can obviously not be experimented on, so we use accidents of history. The best known is Genie. She was born in 1957 in Los Angeles and from about the age of 20 months was kept confined by her father, mostly alone, with almost no speech around her. She was discovered in November 1970, aged 13 years and 7 months, and linguists including Susan Curtiss studied her for years. Genie learned many words and some structure, but her grammar stayed limited and she never fully acquired a first language. It is tempting to treat this as proof of a critical period. It is not clean evidence: she had suffered severe abuse, malnutrition and trauma, and it is impossible to separate a missing window from everything else; Curtiss argued against a general intellectual impairment, others were less sure. The research itself has been criticised on ethical grounds, since the people studying her were also her carers. The testing ended in 1978, and her later years were hard. Genie is a case to tell with care and without sensationalism. Better evidence comes from people who come to a language late, but without being deprived. Jacqueline Johnson and Elissa Newport (1989) tested Chinese and Korean immigrants to the United States on English grammar: those who arrived before about seven years old matched native speakers, performance fell as the age of arrival rose through adolescence, and after puberty it was scattered. In 2018 Joshua Hartshorne, Joshua Tenenbaum and Steven Pinker analysed an online English grammar quiz taken by roughly two-thirds of a million people. Their results fit a critical period that ends much later than expected: the ability to learn grammar stays high until about 17 or 18, then declines. They suggested cultural and social changes at that age might be partly responsible, in addition to brain maturation. Rachel Mayberry and colleagues found that deaf people who met their first language late (a sign language, for deaf children of hearing parents with limited access) showed lasting effects on grammar, even compared with those who learned a second language later. The effects are about first language exposure. Interactive · Three shapes the age curve could have Age of first exposure to the language Sharp cut-off at 12   Steady decline   High until 17, then falling Schematic shapes, not data. They show how different the three predictions are for, say, a 14-year-old. Real studies measure noisy scores, and the end age and steepness depend on what is measured (accent, grammar, vocabulary). Without JavaScript: a sharp cut-off predicts high scores until the cut-off age, then low; a steady decline predicts a score falling gradually from birth; the 2018 results resemble a plateau into the late teens followed by a decline. The most striking evidence is not a deprivation but a creation. Before 1977 deaf Nicaraguan children mostly lived at home, each with their own family's gestures. When special schools opened in Managua, starting in 1977 with about 50 deaf children and growing to more than 400 pupils in two schools by 1983, the children were together for the first time. They did not receive a sign language from teachers (who used Spanish and fingerspelling). They made one. Judy Kegl, invited by the ministry of education in 1986, and later Ann Senghas and Marie Coppola, documented how each cohort of younger children made the language more systematic. Senghas, Kita and Özyürek (2004) found that younger signers split a rolling-down-a-hill motion into separate signs for manner and path, while the older cohort's signing tended to express both at once, as hearing people's gestures do. A similar story is told for Al-Sayyid Bedouin Sign Language in the Negev, which arose within about three generations (Sandler and colleagues, 2005). What it shows is debated: nativists see children imposing structure; others stress that a community, its needs and its transmission across cohorts matter. Bilingual children: myths and evidence Perhaps half the world's people use more than one language in their daily lives (a common estimate by the psycholinguist François Grosjean). Bilingualism is the normal case, not a puzzle, and the research on bilingual children has gone through a cycle of myth, over-enthusiasm and correction. The old worry, that two languages confuse a child and delay speech, is not supported: bilingual children reach the main milestones in a similar window. What the evidence does show is that vocabulary depends on input. A bilingual toddler usually knows fewer words in each language than a monolingual of the same age, because she hears each for part of the day, but her total across both languages is comparable (Hoff and colleagues, 2012). Mixing languages in a sentence (code-switching) is not a sign of confusion: Shana Poplack's 1980 study of Spanish–English speakers in New York found it follows grammatical constraints and is commonest among the most fluent speakers. The more recent "cognitive advantage" claim, that bilinguals have a stronger executive control, went from headline to dispute: Minna Lehtonen and colleagues (2018) pooled 152 adult studies and found no advantage after correcting for publication bias. Similar disagreement attends the finding that bilinguals show Alzheimer's symptoms about four years later (Bialystok and colleagues, 2007), since later studies with better controls differ. Try your hand at sorting the claims. Interactive · Myth or evidence? Your score is kept in the page only while it is open. Verdicts summarise the studies named in the text. Without JavaScript: bilingualism confusing children is not supported; smaller vocabulary per language but similar totals is supported; code-switching as confusion is not supported; an executive-function advantage and delayed dementia are mixed; most of the world using several languages is supported. Practical points the research does support: amount and quality of input matter more than any one-parent-one-language rule; bilingualism does not cause a language disorder, and a bilingual child with a delay should be assessed in both languages by someone who knows the field. The evidence is about averages; any particular family has its own situation. Sign languages are full languages Until the 1960s many hearing people, including many linguists, treated sign as gesture or pantomime or a broken English on the hands. In 1960 William Stokoe, a professor of English at Gallaudet, published Sign Language Structure, showing that American Sign Language (ASL) signs are built from smaller meaningless units, as spoken words are built from sounds: where the hands are (location), their shape (handshape), the way they move (movement), and later also palm orientation. Change one, and you change the word. Robbin Battison's 1974 minimal pairs are standard examples. Try them. Interactive · Change one part, change the word Pairs follow standard textbook descriptions (Battison 1974, as summarised in references on ASL phonology). Signs are described in words here; a Deaf-led signing course or the free ASL resources linked below are the way to see them. Without JavaScript: APPLE and ONION differ in location; MOTHER and FATHER differ in location (chin or forehead); CAR and WHICH in handshape; PROPOSE and MAYBE in movement; TEMPORARY and TRAIN in palm orientation. Everything else follows. Sign languages have grammar, new vocabulary, poetry, jokes and dialects; they use space and the face for grammar (raised eyebrows can mark a yes/no question) and can express two things at once, which speech cannot. Deaf children of Deaf parents learn them on roughly the spoken timetable, including "babbling" with their hands (Laura-Ann Petitto and Paula Marentette, 1991). Damage to the left hemisphere impairs signing as it impairs speech, and signers with strokes can lose grammar while keeping the ability to gesture (Ursula Bellugi, Howard Poizner and Edward Klima's work on sign aphasia). Sign languages are many and not universal: ASL descends from French Sign Language and is unrelated to British Sign Language, and the two are not mutually intelligible. Counts of sign languages vary widely (from well over a hundred to over three hundred) because it depends on what counts as separate. Most deaf children, about nine in ten by a commonly cited estimate, are born to hearing parents who have never met a sign language. That is why the age-of-exposure research is not abstract: it concerns real children who sometimes reach school with no full language. How best to provide early access to language, through sign, spoken language or both, is discussed in families and Deaf communities, and this piece does not advise on it. What a graduate just sees Babies are statistical learners before they know any word, and "break the stream where predictability dips" is a real strategy. "Goed" is a sign that a rule has been learned; most irregular verbs are produced correctly most of the time. The poverty-of-the-stimulus argument is about what the data can and cannot tell a learner; both camps now accept some innate machinery, and disagree about how much and of what kind. Genie is a hard case with many confounds, not a clean test; the best evidence for a sensitive period comes from late-exposed learners. Deaf children made a language in Nicaragua; languages are made by communities of children. Bilingualism is normal, does not delay children, and its "cognitive benefits" are disputed. Sign languages are languages, with phonology, grammar and a brain. Where it shows up next Psycholinguistics & the Brain (36/28): how an adult brain handles the language the child built. Computational Linguistics (36/30): what language models learn, and how it compares to what children learn from far less. Sociolinguistics (36/26): language shift, heritage speakers and the politics of which languages children are taught in. In the world: early-years teaching, speech-language therapy, deaf education, language policy in schools, and the design of reading programmes. If you want to go deeper 📘 Textbook. Eve Clark, First Language Acquisition (Cambridge University Press, 3rd ed. 2016) is a standard course text; Barbara Lust, Child Language: Acquisition and Growth (Cambridge) is another. 📘 Gentler. Steven Pinker, The Language Instinct (1994) argues the nativist case in an engaging way; Michael Tomasello, Constructing a Language (2003) is the usage-based reply; Susan Curtiss's account of Genie and Russ Rymer's Genie: A Scientific Tragedy (1993) give the case in full. 🌐 Free text. The Noba Project and OpenStax psychology texts have free modules on language development; CHILDES (childes.talkbank.org) is a free archive of recorded child speech. 🌐 Free course. MIT OpenCourseWare 24.900 Introduction to Linguistics (Spring 2022) includes sessions on language acquisition and on language change. The takeaway Children build a language rather than copy one: they find words by tracking statistics, invent rules and over-apply them, and in some conditions create new languages. How much of that rests on innate structure and how much on general learning is the field's great open argument. The age window is real but the best evidence for it is more careful, and later, than the Genie story suggests. Try this: next time you hear a small child say a "wrong" past tense or plural, write it down. Then check whether it follows a rule they have likely learned. Sources & Further Reading Sources. Saffran, Aslin and Newport, Science 1996; Hauser, Newport and Aslin, Cognition 2001. Berko, Word 1958; Marcus et al., Monographs of the SRCD 1992 (11,521 uses; median 2.5%); Maslen et al. 2004 (4.2% mean in a dense corpus); Maratsos 2000; Rumelhart and McClelland 1986; Pinker and Prince 1988; Slobin on Turkish. Chomsky 1959, 1980; Crain and Nakayama, Language 1987; Pullum and Scholz 2002; Reali and Christiansen 2005; Tomasello 2003; Everett 2005; Nevins, Pesetsky and Rodrigues 2009. Lenneberg 1967; Genie: Curtiss 1977, Rymer 1993, Wikipedia "Genie (feral child)" (born 1957, found November 1970 aged 13 years 7 months, confined from about 20 months, testing ended 1978); Johnson and Newport, Cognitive Psychology 1989; Hartshorne, Tenenbaum and Pinker, Cognition 2018; Mayberry and Lock 2003. Nicaraguan Sign Language: Wikipedia "Nicaraguan Sign Language" (1977 school with about 50 children, more than 400 pupils in 1983, Kegl 1986); Senghas, Kita and Özyürek, Science 2004; Sandler et al., PNAS 2005. Grosjean on bilingualism; Hoff et al., Journal of Child Language 2012; Poplack 1980; Lehtonen et al., Psychological Bulletin 2018 (152 studies); Bialystok, Craik and Freedman, Neuropsychologia 2007. Stokoe 1960; Battison 1974; Petitto and Marentette, Science 1991; Poizner, Klima and Bellugi 1987. The numbers the toys display were computed in node; they are illustrative. This piece describes research on children and is not clinical or educational advice. 📘 Clark, First Language Acquisition 📘 Pinker, The Language Instinct 🌐 CHILDES Step 7. Inclusive & Special Education: Teaching Every Child ----------------------------------------------------------- Why: Teaching every child, including those with disabilities. Disability is partly a fact about a body and partly a fact about a building, a lesson and a law. Teachers need to see both. A teacher hands out a worksheet, says "read this and write your answers in two minutes," and puts the video on. A student who is Deaf cannot follow the video. A student who reads slowly runs out of time. A student who writes by hand with difficulty hands in half a page. A student who is still learning the language of the lesson understands the worksheet only in part. Four children, four different barriers, one lesson that was designed for none of them. Nothing in that story required a label. It required noticing that the lesson had barriers, and that some can be removed for everyone at once. That noticing, and the legal and professional machinery around it, is what inclusive and special education is about. It also carries some of the sharpest disagreements in education: about words, about where children are taught, and about who decides. The course in one box Who takes itEducation and teacher-training majors, usually in the second year, often as a required course because nearly every classroom contains students who need adjustments; also psychology, speech and language therapy, and social-work students. What it is forTeaching a class where children differ widely, using adjustments and supports with evidence behind them, and understanding the rights, words and arguments around disability in school. Comes afterDevelopmental Psychology (35/24). Leads toTeaching Reading & Mathematics (36/56), Assessment & Measurement (36/55) and Classroom Practice & Educational Technology (36/60). What this piece gives youYou will not be able to assess or support a particular child; that takes a qualified teacher or specialist and the child's family. You will have the main frameworks, the terms people prefer and why they differ by country, and the live arguments. Easier first reads: the Developmental Psychology pieces (category 02) and How to Learn Anything Faster (17/01). Not diagnosis or advice. This piece describes how education systems and research treat disability. It does not describe how to identify any condition, and the invented students below are illustrations. If you have a concern about a child, start with the class teacher and the school's learning-support or special-needs coordinator, and with the child's family and doctor. Disability is where a person meets a barrier There are two classic ways to think about disability. The medical model locates the problem in the person: a body or mind that differs from a norm and should be treated, trained or cured. The social model locates the problem in the setting: a person who uses a wheelchair is disabled by stairs, a Deaf person by a lecture with no interpreter. The phrase came out of British disabled people's organisations in the 1970s (the Union of the Physically Impaired Against Segregation's 1976 statement) and was named by the academic Mike Oliver in 1983. Most scholars see neither model as the whole story. The World Health Organization's International Classification of Functioning, Disability and Health (2001) combines them: how someone functions depends on the person's body and on their environment and supports. A pair of glasses is a medical fix, a large-print book is a barrier fix, and both can be right. For a teacher the practical question is to ask, for each barrier, "what in the lesson, the room or the test could change?" before asking "what is wrong with the child?" Try it on five common situations. Interactive · Two lenses on one barrier Illustrative scenarios, not cases. In practice the two lenses are combined, and the person's own view comes first. Without JavaScript: for a student who uses a wheelchair and has a class upstairs, the person lens asks how to get the student up the stairs; the setting lens asks why the class is upstairs and whether it can move or a lift can be installed. A slogan from the disability-rights movement sits behind this: nothing about us without us. It was used by activists for years before James Charlton gave it to a 1998 book, and it means that disabled people, and children and families, are consulted in decisions about their schooling, not only informed of them. Words matter, and communities choose them Language about disability changes quickly, differs by country and is sometimes contested within a community. Two patterns are worth knowing. Person-first language ("a student with a disability", "a child with Down syndrome") puts the person before the characteristic; it is the default in much US professional and legal writing. Identity-first language ("a disabled student", "an autistic child", "a Deaf student") treats the characteristic as part of who someone is; it is standard in the UK for "disabled people", and many Autistic and Deaf communities prefer it. In a 2016 survey of 3,470 people in the UK, Lorcan Kenny and colleagues found that "autism" and "on the autism spectrum" were the most widely accepted terms; autistic adults, family members and parents endorsed "autistic" far more than professionals did, and almost half of professionals favoured "person with autism". The authors' advice for anyone unsure was to ask the people concerned. A capital letter marks a similar choice: "Deaf" often refers to a cultural and linguistic community that uses a sign language, while "deaf" describes hearing level (a distinction going back to James Woodward, 1972). Terms also mean different things in different countries, and this trips up readers of international research. The phrase "learning disability" refers to an intellectual disability in the UK, but in the US and Canada it usually means a specific difficulty with reading, writing or mathematics in a student of typical general ability. "Special educational needs" is a legal term in England and Ireland; in the US the legal term is "disability" under the Individuals with Disabilities Education Act. Old words ("retarded", "handicapped", "cripple") are now considered offensive; in 2010 the US passed Rosa's Law to replace "mental retardation" with "intellectual disability" in federal law. Look a few up. Interactive · Same words, different meanings Summaries of common usage, not legal definitions; usage in other countries varies and keeps changing. Without JavaScript: "learning disability" means an intellectual disability in the UK and a specific difficulty such as reading or maths in the US; "Deaf" often marks membership of a sign-language community. A working rule used by many teachers and writers: use the words a person or their community uses about themselves; where you don't know, ask, or use the plain description ("a student who uses a wheelchair") rather than a label. Avoid "suffers from", "confined to", "special" as a euphemism, and "high-functioning" or "low-functioning". Four words the law and the UN use: exclusion, segregation, integration, inclusion Rights to education for disabled children are recent. The US Rehabilitation Act's Section 504 (1973) banned disability discrimination in federally funded programmes; the Education for All Handicapped Children Act (1975), renamed the Individuals with Disabilities Education Act in 1990, promised a "free appropriate public education" in the "least restrictive environment" and gave families a role in an individual plan. In the Supreme Court's Endrew F. v. Douglas County School District (2017) the court held that the plan must be reasonably calculated to let a child make progress "appropriately ambitious in light of the child's circumstances". England's Warnock Report (1978) and Education Act 1981 moved toward teaching children in ordinary schools "whenever possible"; the Children and Families Act 2014 created Education, Health and Care plans. Italy's Law 517 of 1977 is usually credited with moving children with disabilities into ordinary classes. The Salamanca Statement (UNESCO, 1994) called on governments to give inclusive education highest priority. And the UN Convention on the Rights of Persons with Disabilities (adopted 13 December 2006; in force 3 May 2008; Article 24 is education) commits states to an inclusive education system at all levels. In 2016 the Convention's committee issued General Comment No. 4 on Article 24, which draws a sharp line between four things. TermIn the Committee's sense ExclusionStudents are directly or indirectly prevented from or denied access to education SegregationEducation in separate settings designed for a particular impairment or several, apart from other students IntegrationPlacing students in existing mainstream schools if they can fit the standard requirements InclusionA system change in content, methods and structures so all students take part The comment's key point is that being in the same building (integration) is not inclusion unless the school itself changes. Not everyone agrees with all of it, as the section on evidence below explains; some Deaf and blind organisations, including the World Federation of the Deaf and the World Blind Union, asked unsuccessfully for an exception for sensory-disability education. Interactive · Which word is it? Without JavaScript: a child refused any school place is excluded; a child sent to a separate school only for children with one kind of impairment is segregated; a child placed in the ordinary class with no change to teaching, tests or room is integrated; a school that redesigns teaching so all can take part is inclusive. Design for the edges and everyone gains The curb cut is the standard picture. Sloped kerbs were campaigned for by disabled activists in 1970s Berkeley, California, and are now used by people pushing prams, wheeling suitcases and riding bikes. The writer Angela Glover Blackwell named this the "curb-cut effect" in 2017: a change made for one group tends to help many. In teaching the matching idea is Universal Design for Learning (UDL), developed from the 1990s by David Rose and colleagues at CAST in the US and now used in many countries. It asks teachers to plan lessons with several routes in from the start: multiple means of engagement (why to learn), representation (what is presented) and action and expression (how to show learning). CAST published version 3.0 of its Guidelines in 2024. Be careful about the claim that follows: reviews describe the research on UDL as a whole framework as limited and hard to separate from other good teaching, and the strongest evidence is for particular practices (captions, explicit instruction, worked examples). UDL is better understood as a planning habit than a proven programme. Two other words teachers must separate: an accommodation changes how a student learns or shows learning (extra time, a reader, speech-to-text) without changing the target; a modification changes what the student is expected to learn. Which one fits is a judgement made with the student, the family and the specialists. Switch options on to see the curb-cut effect. Interactive · Who can take part? Six invented students and a lesson delivered by speaking. Each option opens a route for the students listed. Illustrative: a real class is messier, and each student's own preferences decide. Without JavaScript: switching on captions lets the Deaf student, the student who finds long speech hard to hold, and the student still learning the lesson's language all take part; typed answers help the student who writes slowly; extra time helps the student who needs it. What the evidence says about support, and where educators disagree Evidence in this field is harder to gather than in most of education: children differ, randomising children to schools is rarely possible or ethical, and "inclusion" covers very different practices. A few findings are fairly solid. Explicit, well-structured teaching with practice and feedback helps students who find learning hard, as it helps others. Small-group or one-to-one targeted interventions, especially in early reading and number, have good evidence. The Education Endowment Foundation's 2020 guidance for mainstream schools makes five recommendations, among them high-quality teaching for all, carefully chosen small-group and one-to-one interventions, and working effectively with teaching assistants. Teaching assistants are a good example of method versus deployment: in the large Deployment and Impact of Support Staff study in England (Blatchford and colleagues, 2009), pupils who received more TA support made less progress, which the team attributed to how assistants were used (substituting for teaching) rather than to assistants themselves; the EEF now reports positive effects when assistants deliver trained, structured interventions. On placement the evidence is mixed and the argument is as much about values as data. Reviews of studies on inclusion (for example Ruijs and Peetsma, 2009; Hehir and colleagues, 2016) generally find small positive or neutral effects on students with special needs and little or no harm to classmates, but the studies are mostly observational, so children placed in mainstream classes may differ from those who were not. Here are the positions, in their own terms. Full inclusion. Separate schooling is discrimination in itself; every child belongs in the ordinary school, and the school must change. This is the reading of the UN Committee's General Comment No. 4. A continuum of placements. Some children's needs, they argue, are met best in specialist settings; James Kauffman and others make this case, as did Mary Warnock in 2005, who had led the 1978 report and then wrote that inclusion in practice had been a disastrous legacy of it for some children. Deaf and blind communities. Many argue that for children who use sign language or Braille, a school with peers and teachers who share the language may be the better route to full participation; the World Federation of the Deaf has argued this. Families. Parents disagree among themselves: some campaign for mainstream places, others for specialist ones, and many ask simply that whichever school it is actually delivers what the plan promises. Another contested area is who gets identified. Counts depend on definitions as much as on children. In 2022-23 about 7.5 million students aged 3 to 21 in US public schools, or 15%, were served under IDEA (US National Center for Education Statistics). In England in the 2025/26 school year, 14.8% of pupils received "SEN support" and 6.0% had an EHC plan (Department for Education), about 21% altogether. Neither figure is a measure of how many children "are disabled": each reflects a country's legal categories and funding. In the US, researchers disagree about whether Black and other minority students are over- or under-identified once family income and achievement are taken into account (Morgan and colleagues found under-identification in several categories; Skiba and colleagues documented over-representation in others), and both sides in this literature agree identification should serve the child rather than ration support. What a graduate just sees A barrier is a meeting of a person and a setting; ask what in the lesson could change before asking what is "wrong" with the child. Person-first and identity-first are both legitimate; the best practice is to ask, and to use the words a community or person uses. "Learning disability" does not mean the same thing in the UK and the US; international research needs careful translation. Exclusion, segregation, integration and inclusion are different, and a child in the room is not necessarily included. A lesson with several ways in helps the intended students and many others (the curb-cut effect). Explicit teaching, structured small-group help and well-trained assistants have evidence; doing the same lesson louder does not. Counts of "children with special needs" reflect definitions and funding as much as children. On where to teach, the evidence is mixed and communities disagree; those closest to the child usually know most. Where it shows up next Teaching Reading & Mathematics (36/56): the same code and number instruction, taught in more steps or by other routes, for children who need it. Assessment & Measurement (36/55): when an accommodation makes a test fairer and when it changes what the test measures. Classroom Practice & Educational Technology (36/60): captions, text-to-speech and other tools that serve many students. In the world: learning-support teachers, speech and language therapists, school coordinators, disability-rights lawyers and advocates, and the design of buildings and software. If you want to go deeper 📘 Textbook. James Kauffman and Daniel Hallahan, Handbook of Special Education (Routledge, 2nd ed. 2016); Daniel Hallahan, James Kauffman and Paige Pullen, Exceptional Learners: An Introduction to Special Education (Pearson), a standard US course text. 📘 Gentler. The Education Endowment Foundation's free guidance report on special educational needs in mainstream schools (2020); Mike Oliver, The Politics of Disablement (1990), the classic statement of the social model. 🌐 Free text. The UN's General Comment No. 4 on the right to inclusive education (2016) is on the OHCHR website; CAST's UDL Guidelines are free at udlguidelines.cast.org. The takeaway Disability in school is a relationship between a child and a setting, so teachers get the most leverage by changing lessons, rooms and tests, with the child and family at the centre. Respectful language follows the people it describes; the law now separates being in the building from being included; the evidence supports specific practices more than slogans; and on where to teach, serious people still disagree. Try this: take one lesson, worksheet or video you use or have seen. List three barriers in it, then one change for each. Notice how many of the changes would help other people too. Sources & Further Reading Sources. UPIAS 1976; Oliver 1983 and 1990; WHO ICF 2001; Charlton 1998. Kenny et al., Autism 2016; Woodward 1972; Rosa's Law 2010. Section 504 1973; EHA 1975 and IDEA 1990; Endrew F. v. Douglas County School District (2017); Warnock Report 1978, Education Act 1981, Children and Families Act 2014; Salamanca Statement 1994; UN CRPD (adopted 13 December 2006, in force 3 May 2008) and General Comment No. 4 (2016, paragraph 11). Blackwell, Stanford Social Innovation Review 2017; Rose and Meyer 2002; CAST Guidelines 3.0 (2024). Blatchford et al., Deployment and Impact of Support Staff 2009; Education Endowment Foundation guidance on special educational needs in mainstream schools (2020) and teaching assistants. Ruijs and Peetsma, Educational Research Review 2009; Hehir et al., Abt Associates 2016; Kauffman and Badar on placement; Warnock, Special Educational Needs: A New Look (2005). Morgan et al., Educational Researcher 2015; Skiba et al., Exceptional Children 2008. NCES Condition of Education (students with disabilities, 2022-23); DfE Special educational needs in England (2025/26). The scenario data are illustrative. This is educational information, not advice about a particular child. 📘 Hallahan, Kauffman and Pullen, Exceptional Learners 🌐 CAST UDL Guidelines 📘 Oliver, The Politics of Disablement Step 8. Curriculum & Instructional Design: Planning What to Teach, and in What Order ------------------------------------------------------------------------------------ Why: Planning what to teach and in what order. Every lesson is a bet that this activity, in this order, will leave this knowledge behind. Curriculum design is the craft of making that bet on purpose. Two teachers have the same textbook chapter on the water cycle. One starts at page one: vocabulary list, diagram, worksheet, test on Friday. The other starts by asking what a pupil should be able to do by the end, such as explain why a puddle disappears on a warm day and a cold one lasts, then decides how she will find out whether they can, and only then picks the activities. The first teacher covered the chapter. The second planned for a result. That difference, planning from the outcome backwards instead of from the page forwards, is the first habit of curriculum designers. The second is noticing that topics have an order that is not the order in the book, and the third is knowing how much help a learner needs at each moment. This piece is about those three habits and the long-running argument about the last one. The course in one box Who takes itEducation majors and teacher-preparation students, usually in year 3, and instructional-design and training students. Teacher standards such as the US InTASC model standards (which include planning for instruction) and the UK Core Content Framework (2019) both expect it, and school systems differ in how much of it teachers do themselves and how much the state decides for them. What it is forDeciding what students should learn, in what order, with what activities and what evidence of success, for a lesson, a course or a whole school programme. Comes afterLearning Sciences: How People Learn (36/53). Leads toAssessment & Measurement (36/55), Teaching Reading & Mathematics (36/56) and Classroom Practice & Educational Technology (36/60). What this piece gives youYou will not be able to write a full national curriculum. You will be able to check whether a lesson's goal, activity and test line up, tell Bloom's levels apart, order topics by what they need, and read both sides of the guidance debate. Easier first reads: How to Learn Anything Faster (17/01) and, in this series, 36/53. Start from the end: goal, evidence, then activity In 1949 Ralph Tyler, in Basic Principles of Curriculum and Instruction, asked four questions that are still the skeleton of the field: what purposes should the school try to achieve, what experiences will serve them, how can those experiences be organised, and how will we know the purposes were met? Grant Wiggins and Jay McTighe's Understanding by Design (1998; second edition 2005) turned this into backward design in three stages: identify the desired results, decide what evidence would show them, and only then plan the learning. In higher education John Biggs (1996) called the same principle constructive alignment: the intended outcome, what students do, and how they are assessed must point at the same thing. goal ↔ what students practise ↔ what is testedif any one of the three is a different kind of thing from the others, the course teaches one thing and grades another Misalignment is the commonest design failure and it is easy to miss. A teacher wants pupils to "design a fair test", teaches it by lecture, and gives a multiple-choice quiz. Everything is tidy and nothing connects. The tool below checks the three links. Interactive · Do goal, activity and test line up? Choose one of each. The check compares the kind of thinking each asks for, using Bloom's six levels from the next section. Goal Activity Test Turn on JavaScript to use this tool. Key result: a goal to design an experiment, practised by flashcards and tested by multiple choice, has two broken links; each only lines up when all three ask for the same kind of thinking. Backward design has critics. A plan built entirely from what can be tested may shrink to what is easy to test, and some teachers argue that good lessons find their aims as they go. Wiggins and McTighe reply that the goals can be rich (their "big ideas" and "transfer" tasks) and that unplanned discoveries are welcome inside a planned frame. Objectives and Bloom's taxonomy: a vocabulary, not a ladder A useful objective names something you could watch a learner do. Robert Mager's Preparing Instructional Objectives (1962) pushed the field toward verbs like "solve" and "list" rather than "appreciate" or "understand". In 1956 Benjamin Bloom and colleagues published a taxonomy of cognitive goals from knowledge up through comprehension, application, analysis, synthesis and evaluation. Lorin Anderson and David Krathwohl revised it in 2001 into two dimensions: a cognitive process (remember, understand, apply, analyse, evaluate, create) and a knowledge type (factual, conceptual, procedural, metacognitive). Its great use is to make a teacher ask "what kind of thinking is this question asking for?" Interactive · Which level is this question? Turn on JavaScript to use this tool. Six levels in order: remember, understand, apply, analyse, evaluate, create. Next question Treat the levels with care. They are not a strict staircase: a learner cannot analyse an argument without remembering what the words mean, which is the lesson of Learning Sciences (36/53), that knowledge is what thinking is made from. Calling recall "lower order" can lead to teaching skills in a vacuum. And the same stem can sit at different levels for different learners, since a problem already solved in class is memory the second time. The taxonomy is a tool for asking questions about a lesson, and its authors never claimed more. Sequence: topics have prerequisites, and the order is a graph Some topics need others first. Multiplication needs addition, division needs multiplication, fractions need division. Draw an arrow from each topic to what needs it and you have a graph, and a teacher's choices are the orders consistent with it. The number is much smaller than people expect. Robert Gagné called such maps learning hierarchies in the 1960s, and the practical point is that the expert's order, which follows the logic of the subject, is not always the learner's order. Evidence that foundations matter comes from maths. Robert Siegler and colleagues (2012) used long-term data from the UK and the US and found that a ten-year-old's knowledge of fractions and division predicted algebra and overall maths achievement at sixteen, even after accounting for IQ, family income and other early maths skills. Jerome Bruner (The Process of Education, 1960) added the idea of a spiral curriculum: return to the central ideas again and again at increasing depth, rather than teach each once. Interactive · Build a valid order Tap the topics in the order you would teach them. A topic only goes in when what it needs is already in. Turn on JavaScript to use this tool. Key result: for the eight topics below, only 5 of the 40,320 possible orders respect every prerequisite. Start again Needs: place value needs number sense; addition needs number sense; multiplication needs addition; division needs multiplication; fractions need division; decimals need place value and fractions; percent needs fractions and decimals. The prerequisite map is a simplified teaching example. Real maps are larger and some links are debated. Worked examples, then fading: how help should shrink From Learning Sciences (36/53): a beginner's working memory is swamped by solving a problem from scratch, so studying a solved example teaches more. But an expert needs less help, so help should shrink as skill grows. Fading does this: first a fully worked example, then the same kind of problem with the last step left for the learner, then the last two, and finally the whole problem. Alexander Renkl and Robert Atkinson (2003) found that fading beat both complete examples and plain problem-solving in several studies. Michelene Chi's work (1989) found that students who explained examples to themselves, step by step, learned more. Interactive · Fading in four problems Turn on JavaScript to use this tool. Key result: the same three steps (move the constant, divide, check) appear in every problem; each stage hides one more of them. How much guidance? The argument with two real sides The longest dispute in the field is over how much to tell learners and how much to let them find out. Each side has a strong case. SideIts case Explicit instructionKirschner, Sweller and Clark (2006) argued that unguided or minimally guided teaching ignores the limits of working memory and that decades of evidence favour worked examples and direct explanation for novices. Barak Rosenshine's Principles of Instruction (2012) draws ten practices, such as small steps, checking understanding and many examples, from research on effective teachers. In Project Follow Through (US, 1968 to 1977, the largest experiment in education), the Direct Instruction model scored best on basic skills, though critics questioned how the results were analysed. Inquiry and problem-basedHmelo-Silver, Duncan and Chinn (2007) replied that real problem-based and inquiry lessons are heavily scaffolded, so the critique targets a straw man. Manu Kapur's "productive failure" work has found that struggling on a hard problem before being taught can build deeper understanding than being taught first, at least for some concepts. Montessori schools and Reggio Emilia (founded by Loris Malaguzzi in post-war Italy) are built on child-led exploration with a prepared environment. What the meta-analyses sayAlfieri and colleagues (2011), pooling 164 studies, found that unassisted discovery did worse than explicit instruction, while discovery with guidance (feedback, worked examples, prompts) did better. That supports both camps on their own terms, and shows the live disagreement is about how much and when. A common reading is that novices need more explicit guidance, advanced learners can handle more openness, and "discovery" is only good when carefully designed. This is a summary of the research, and people on both sides would phrase it differently. Where the dispute meets values (what school is for, whether to treat children as explorers or apprentices) the evidence cannot settle it. Who decides the curriculum? Intended, taught and learned International comparisons such as TIMSS distinguish three curricula: the intended one written in law, the implemented one a teacher delivers, and the attained one pupils actually learn. They are never the same, and good design plans for the gaps. PlaceHow the curriculum is set EnglandA national curriculum since the 1988 Education Reform Act, revised in 2014, with schools free to add to it. JapanThe ministry's Courses of Study, revised about every ten years. Teachers also practise jugyō kenkyū (lesson study): small groups plan a lesson, one teaches it while others observe, and they revise it. Stigler and Hiebert's The Teaching Gap (1999) spread the idea abroad. SingaporeA national syllabus from the Ministry of Education; its "Teach Less, Learn More" campaign (from 2005) aimed at less content and more depth. IndiaThe National Education Policy 2020 replaced the 10+2 pattern with 5+3+3+4 stages (foundational, preparatory, middle, secondary) and recommends mother-tongue teaching at least to grade 5. KenyaA competency-based curriculum from 2017, replacing the 8-4-4 system of 1985 with a 2-6-3-3-3 structure; its first cohort moved into junior secondary in 2023, and readiness and cost have been debated. United StatesStandards are set by states. The Common Core (2010) was adopted by most states, and several later revised or replaced it. The structures differ, the problem is the same: what goes in, what comes out, and who has a say. Finland's reforms, like the 2016 national core curriculum asking schools to run multidisciplinary modules, show how a system can set aims and leave method to teachers. What a graduate just sees A plan starts from what students should be able to do, then the evidence, then the activities. Goal, practice and test must ask for the same kind of thinking, or the course teaches one thing and grades another. Bloom's levels are a vocabulary for asking what a question demands, and not a staircase to climb in order. Topics form a graph; few of the possible orders work, and the expert's order is not always the learner's. Help should fade as skill grows: worked examples for beginners, problems for the fluent. "Direct instruction versus inquiry" is mostly a question of how much guidance, for whom, and when. A curriculum exists at three levels: intended, taught and learned. Where it shows up next Assessment & Measurement (36/55): the "evidence" stage of backward design is a test or task, and its quality is the next subject. Teaching Reading & Mathematics (36/56): phonics sequences and number-line progressions are prerequisite graphs. Classroom Practice & Educational Technology (36/60): lesson structure, questioning and adaptive software all depend on sequencing and fading. In the world: corporate training, software tutorials, flight and medical simulators, and every textbook you have used were shaped by these decisions. If you want to go deeper 📘 Textbooks. Grant Wiggins and Jay McTighe, Understanding by Design (ASCD, expanded 2nd edition 2005), the standard backward-design text; and Lorin Anderson and David Krathwohl (eds.), A Taxonomy for Learning, Teaching, and Assessing (Longman, 2001). 📘 Gentler. Barak Rosenshine's short article Principles of Instruction (American Educator, Spring 2012), free at aft.org, and Tom Sherrington, Rosenshine's Principles in Action (John Catt, 2019). 🌐 Free text. The National Research Council's How People Learn (2000), free at nap.nationalacademies.org. 🌐 Free course. MIT OpenCourseWare 11.125 Introduction to Education (Spring 2009), which covers curriculum design and student assessment, and 11.129 Educational Theory and Practice I (Fall 2011) on lesson planning. The takeaway Design a course backward: decide what learners must be able to do, choose evidence for it, then plan the practice, keeping the three aligned. Order topics by what they need, give help to beginners and take it away as they improve, and remember that what is written, what is taught and what is learned are three different curricula. Try this: take any lesson, tutorial or recipe you have used. Write its goal in one sentence with a verb you could watch, then note what was practised and what was tested. Do all three match? Sources & Further Reading Sources. Tyler, Basic Principles of Curriculum and Instruction (1949); Wiggins and McTighe, Understanding by Design (1998; 2005); Biggs, Higher Education 1996; Mager 1962; Bloom et al. 1956; Anderson and Krathwohl 2001; Gagné, The Conditions of Learning (1965); Bruner 1960; Siegler et al., Psychological Science 2012; Renkl and Atkinson, Educational Psychologist 2003; Chi, Bassok, Lewis, Reimann and Glaser, Cognitive Science 1989; Kirschner, Sweller and Clark, Educational Psychologist 2006; Hmelo-Silver, Duncan and Chinn, Educational Psychologist 2007; Alfieri, Brooks, Aldrich and Tenenbaum, Journal of Educational Psychology 2011; Kapur on productive failure (2008 onward); Rosenshine, American Educator 2012; Project Follow Through evaluations (Abt Associates 1977; House et al. 1978); Stigler and Hiebert 1999; IEA TIMSS curriculum model; India NEP 2020 (Union Cabinet, 29 July 2020); Kenya CBC rollout reports (2017 to 2023); Finnish National Agency for Education core curriculum 2014. The prerequisite count and all numbers in the interactives were computed in node. This piece describes research and policy and takes no side on contested values. 📘 Wiggins and McTighe, Understanding by Design 📘 Anderson and Krathwohl, A Taxonomy for Learning, Teaching, and Assessing 🌐 Rosenshine, Principles of Instruction Step 9. Teaching Reading & Mathematics: The Two Subjects Every School Must Get Right ------------------------------------------------------------------------------------ Why: The two subjects every school must get right. Both have had a "war" over how to teach them. In each, some of the argument is about evidence and some is about values, and the skill is knowing which is which. A six-year-old looks at the word ship. Four letters, three sounds: sh, i, p. To read it she has to hear that the spoken word is made of separate sounds (which she has never needed to notice), know that two letters can stand for a single sound, and blend the three into a word she already knows from speech. Then she meets said, which breaks the pattern, and through, which breaks every pattern at once. Next door, a seven-year-old is asked what 47 + 38 is. One child stacks the numbers and "carries the one". Another says 47 plus 3 is 50, and 35 more is 85. A third jumps along a number line. All three are right. Parents, politicians and teachers have argued for decades about which of them the school should teach first, and whether the question even makes sense. These are the two subjects every school is judged on, and the only two where a country's whole system can fail a generation. In 2022 the World Bank and partner agencies estimated that about 70% of 10-year-olds in low- and middle-income countries could not read and understand a simple text (the figure, called "learning poverty", was published in June 2022 and was partly a pandemic effect). This piece is about what teachers of these subjects know, and about how to read the two famous quarrels fairly. The course in one box Who takes itEducation majors and teacher-training students (usually as a methods course in the third year, or within primary-teacher certification), plus anyone who tutors children. What it is forKnowing how children come to read and to understand number, what teaching moves have evidence behind them, and what is still genuinely disputed. Comes afterLearning Sciences: How People Learn (36/53) and Language Acquisition (36/27). Leads toAssessment & Measurement (36/55), Classroom Practice & Educational Technology (36/60) and Inclusive & Special Education (36/57), where the same methods meet children who need more. What this piece gives youYou will not be able to run a reading programme. You will see why a child who "can read every word" may not understand, why 3/4 > 5/8 surprises many children, and how to tell an evidence claim from a values claim in a headline. Easier first reads: How Children Learn Language (26/06), How to Learn Anything Faster (17/01) and Math Is Not Arithmetic (12/01). Not advice about a particular child. This describes how teaching works and what research found, mostly in English-speaking countries. If you are worried about a child's reading or number skills, talk to the class teacher and the school's learning-support staff. Reading is two jobs, and a child can lack either Spoken language is old and almost free: nearly every child learns it from being spoken to. Writing is a recent invention, devised independently in only a few places, and nobody learns it by simply being around it. So reading has to be taught, and it helps to know what, exactly, is being built. In 1986 Philip Gough and William Tunmer proposed the Simple View of Reading: understanding a text is the product of two things, decoding (turning print into the spoken words) and language comprehension (understanding those words once they are spoken to you). Reading comprehension = decoding × language comprehensionA product, not a sum: if either is zero, so is the result. The multiplication is the point. A child who can decode perfectly but has little vocabulary for the topic understands little. A child who understands every spoken story but cannot yet decode cannot read the same story. They need different help. Hollis Scarborough's 2001 "reading rope" draws the same idea with more strands: word recognition (phonological awareness, decoding, sight words) braided with language comprehension (vocabulary, grammar, background knowledge, verbal reasoning). Critics note that the Simple View is a useful organiser rather than a full model of how reading develops (Castles, Rastle and Nation, 2018). Try it. Interactive · The Simple View Decoding (print to speech) Language comprehension (understanding speech) Illustrative scales from 0 to 100, not test scores. The four corners are profiles of teaching need, not diagnoses; a real picture of one child needs a teacher or specialist and proper assessment. Without JavaScript: with decoding at 80% and language comprehension at 40%, comprehension of the text is 0.8 × 0.4 = 32%. Strong decoding cannot make up for thin language, and the reverse. Letters are a code, and some codes are harder Writing systems differ in how faithfully letters map to sounds. Finnish, Italian and Spanish are close to "one letter, one sound". English spelling carries centuries of history: ough is pronounced seven different ways in though, through, tough, cough, bough, thought, thorough. In a 2003 study across thirteen European languages, Philip Seymour, Mikko Aro and Jane Erskine found that children in most of them were reading accurately by the end of first grade, with exceptions including French, Portuguese, Danish and especially English, where development was more than twice as slow. The explanation they gave was the depth of the spelling system and the complexity of syllables, not the age at which school starts. This matters for what research can tell a teacher: most reading studies are in English, the hardest case, and findings do not transfer automatically to Spanish or Hindi, whose scripts work differently, or to Chinese, where characters stand for syllables and meanings and children learn the sounds first through the pinyin alphabet. Teaching the code is called phonics. The distinction that matters is systematic (a planned order, from simple to complex, with practice) versus incidental (teaching a letter-sound link when a word happens to come up). Within systematic phonics there are synthetic programmes (sound out each letter, then blend) and analytic ones (start from whole words and break them down). Because each pattern builds on the last, a teacher always asks: with the patterns taught so far, which words can the child decode? Move the slider. Interactive · What can a child read after each step? Phonics patterns taught A sample set of 34 common words, each tagged by the highest pattern each needs. Real programmes differ in order and in the words they choose; this shows the logic, not a curriculum. Words in bold can be decoded with the patterns taught so far. The five "tricky" words (said, was, one, two, who) are never fully decodable by simple rules, but even they are partly regular (the s and d in said behave) and are taught explicitly. Without JavaScript: with only single-letter sounds taught, about 15% of the sample set (5 of 34 words) is readable; with all six patterns, about 85% (29 of 34). The rest are the tricky words. The reading wars: what the evidence says, and what it cannot say The quarrel is old. In 1955 Rudolf Flesch's Why Johnny Can't Read demanded a return to phonics. In 1967 Kenneth Goodman described reading as a "psycholinguistic guessing game", and with Frank Smith and others built the whole-language view: children learn to read much as they learn to talk, through meaningful use of real texts, with letter-sound teaching in context if at all. Its practical form in many schools was "balanced literacy", and a classroom habit called three-cueing (prompting a child stuck on a word to use meaning, sentence structure and the first letter, which includes looking at the picture). Its defenders point to motivation, to reading for meaning from day one, and to a long tradition of teacher expertise. The opposing case is that written English is an alphabetic code that most children will not crack by exposure alone. Here is the evidence, stated narrowly. The US National Reading Panel (2000) reviewed experiments and concluded that systematic phonics instruction improves early reading more than unsystematic or no phonics; its overall effect size was about 0.41 (Ehri and colleagues' 2001 analysis of the same studies). Re-analyses estimated it lower: Camilli, Vargas and Yurecko (2003) got about 0.24 once they weighted studies differently, and the effect on comprehension is smaller than on word reading. England's Rose Review (2006) came down for systematic synthetic phonics; a school-based trial in Clackmannanshire, Scotland (Johnston and Watson), was influential, a classroom comparison of synthetic phonics with other approaches in one Scottish council. The Education Endowment Foundation's Toolkit rates phonics at about five additional months of progress, with very extensive evidence and the biggest benefit for the youngest readers. By October 2025, 40 US states and the District of Columbia had passed laws or policies on evidence-based reading instruction. Eye-tracking research finds that skilled readers fixate nearly every word rather than skipping predictable ones, which is why guessing from context is not how fluent reading works (Rayner and colleagues' reviews). And here is what that evidence does not settle. It does not say joy matters less than skill, or the reverse. It does not say how many weeks a school should spend on the code, how to teach a Year 3 child who missed it, or what to do when the child is learning in a second language. It does not say teachers should have no say in method. Those are values and judgements about what a school is for. Sort some real-sounding claims: Interactive · Evidence, value, or both? Without JavaScript: "Systematic phonics improves early word reading on average" is an evidence claim (supported). "Children should read stories they love from day one" is a values claim. "A school should spend scarce hours on what raises test scores" mixes the two. Fair summary: nearly everyone in the debate now accepts that children need to learn the code and need rich language and books. The live disagreements are about sequence, emphasis, the role of cueing, how to train teachers, and who decides. Comprehension is mostly knowledge, not a trick Once a child decodes fluently, understanding depends on language and on what the child already knows. In a classic 1988 experiment, Donna Recht and Lauren Leslie gave junior-high students a passage about a baseball game. Poor readers who knew a lot about baseball remembered and explained the game better than good readers who knew little. Knowledge of the world is a strand of the rope. That is why many researchers (E. D. Hirsch is the best-known advocate in the US) argue that schools should build a broad, coherent curriculum of content, so that a child hearing about a river delta in Year 4 has met rivers, maps and farming in Years 1 to 3. Others stress that comprehension strategies (summarising, questioning, monitoring) help too when taught briefly and explicitly, and that overlong "skill drills" on generic strategies add little. The values question sits underneath: whose knowledge goes in the curriculum, and who chooses? Teachers in Kenya, India and Brazil face a second layer, because the language of the textbook may not be the language the child speaks at home, and a child can decode a language she does not understand. Number sense: the picture that makes arithmetic make sense Children arrive at school with a rough sense of "more" and "less" and the ability to count. The job of the early years is to connect number words, quantities and written symbols until they are one idea. Teachers of maths in Singapore use three steps from the psychologist Jerome Bruner's work: handle real objects, draw a picture, then write symbols (concrete, pictorial, abstract). The picture used most is the bar model, which turns a word problem into rectangles whose lengths you can compare. A worked example. Two children share 64 stickers in the ratio 3 to 5. Draw one bar of 3 equal units and one of 5. That is 8 units, so one unit is 64 ÷ 8 = 8 stickers. The children get 24 and 40. No algebra, and a seven-year-old can see why. Interactive · A bar model Total First share (parts) Second share (parts) Without JavaScript: sharing 64 in the ratio 3 : 5 gives 8 units of 8, so 24 and 40. Fractions: where the number line earns its keep Fractions are the first place many children find that numbers do not behave like counting numbers. In whole numbers a bigger digit means a bigger number; with fractions, a bigger denominator means smaller pieces. The habit of reading 1/8 as bigger than 1/4 has a name, the whole-number bias (Ni and Zhou, 2005). The fix is to see a fraction as a point on the number line, not as two numbers stacked. This is not a niche worry. In studies with US and UK samples, Robert Siegler and colleagues (2012) found that knowledge of fractions and division at age 10 predicted algebra and overall mathematics achievement in secondary school years later, even after accounting for other skills such as IQ and family income. a/b = the point where b equal pieces of the unit, a of them, end3/4 = 0.75; 5/8 = 0.625. Same unit, so compare the endpoints. Interactive · Which is bigger? First fraction, denominator First fraction, numerator Second fraction, denominator Second fraction, numerator Without JavaScript: 3/4 is 0.75 and 5/8 is 0.625, so 3/4 is larger even though 8 > 4. The maths wars: procedures, understanding, and what each side argues In the United States the arguments flared after the National Council of Teachers of Mathematics published its Standards in 1989, which stressed reasoning and problem-solving, and after California adopted reform-minded frameworks and then, in 1997, more traditional standards. "Traditional" supporters (many of them mathematicians and parents) argue that without fast, accurate recall of facts and procedures, thinking is swamped; "reform" supporters (many education researchers and teachers) argue that procedures learned without meaning are fragile and joyless and that children should explore. Similar quarrels ran in Britain, Australia and elsewhere, and returned with the US Common Core (2010). The evidence, narrowly: a 2001 report of the US National Research Council, Adding It Up, said mathematical proficiency has five intertwined strands: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and a productive disposition. The National Mathematics Advisory Panel (March 2008) said that to prepare students for algebra, the curriculum must develop conceptual understanding, computational fluency and problem-solving simultaneously, and it called for children to recall basic facts quickly and effortlessly. On method, Alfieri and colleagues' 2011 meta-analysis found that unassisted discovery learning is less effective than explicit teaching, while guided discovery (with feedback and scaffolds) does better than both. The large US experiment Project Follow Through (1968 to the late 1970s) found that Direct Instruction produced the strongest results on basic skills; defenders cite a 2018 meta-analysis (Stockard and colleagues) of a half-century of studies, while critics note that Follow Through's sites and measures varied and that the basic-skills measures favoured what that model taught. In Japan, "lesson study", teachers planning and observing one lesson together, and structured problem-solving lessons are central, as the 1990s TIMSS video studies (Stigler and Hiebert, The Teaching Gap, 1999) described. From 2014 England's Maths Hubs brought Shanghai teachers and Singapore-style textbooks into primary schools as "teaching for mastery". The values questions: Is the aim of school maths to give every child reliable tools, or to let every child experience thinking mathematically? Should the standard written algorithm be taught early and well, or after children understand place value? How much should an anxious child be protected from timed tests? Evidence can say which sequences of teaching raise which scores; it cannot say which aim a society should choose. See where the three methods for 47 + 38 differ in what they ask of memory. Interactive · Three honest ways to add First number Second number All three routes give the same sum; they differ in the steps and what a child must hold in mind. Which to teach first, and whether to teach all, is the contested part. Without JavaScript: for 47 + 38 the column method adds 7 + 8 = 15, writes 5 and carries 10; the make-ten method moves 3 to reach 50 then adds 35; the number line adds 30 then 8. All give 85. QuestionKindWhere things stand Does systematic phonics help early word reading?EvidenceYes, on average; size debated Do poor readers guess from context?EvidenceSkilled readers do not; guessing is a weak strategy Is unassisted discovery as good as explicit teaching?EvidenceGenerally no; guided discovery does better Is fluency or understanding the point of school maths?ValueBoth, in different proportions Should teachers choose their own method?ValueJudgement about trust and standardisation What a graduate just sees Reading is decoding times language comprehension; a child can be weak in either, and the cure differs. A list of "words a child can read" depends entirely on which spelling patterns have been taught so far. English is a hard writing system; evidence from English does not transfer automatically to Spanish, Hindi or Chinese. Systematic phonics has good evidence for early word reading; that is not a verdict on the whole of literacy teaching. Comprehension grows with knowledge of the world, so the curriculum matters as much as the comprehension lesson. A bar model or number line makes a ratio or a fraction visible before it is symbolic. "Bigger denominator, bigger fraction" is the most predictable error in primary maths, and a number line cures it. In both wars, ask: is this an evidence claim or a values claim? The answers need different kinds of argument. Where it shows up next Assessment & Measurement (36/55): the phonics screening check in England (since 2012) and fluency probes show how reading is measured, and why one test cannot settle a war. Inclusive & Special Education (36/57): children for whom the usual route is blocked need the same code taught in a different way, with the same goal. Classroom Practice & Educational Technology (36/60): how a teacher paces, checks and corrects a reading or number lesson. In the world: primary teaching, tutoring, textbook publishers, national literacy and numeracy strategies, and parents helping with homework. If you want to go deeper 📘 Textbook (reading). Louisa Moats, Speech to Print: Language Essentials for Teachers (Brookes, 3rd ed. 2020), a standard teacher-training text on the sounds and structure of English; Kilpatrick, Essentials of Assessing, Preventing, and Overcoming Reading Difficulties (Wiley, 2015). 📘 Textbook (maths). National Research Council, Adding It Up: Helping Children Learn Mathematics (National Academies Press, 2001), free to read online; John Van de Walle and colleagues, Elementary and Middle School Mathematics: Teaching Developmentally (Pearson), a methods-course staple. 📘 Gentler. Stanislas Dehaene, Reading in the Brain (2009) and The Number Sense (1997), neuroscience for the general reader; Daniel Willingham, Why Don't Students Like School? (2009). 🌐 Free text. Adding It Up can be read free on the National Academies Press site (nap.edu), and the Education Endowment Foundation publishes free guidance reports on primary literacy and maths. The takeaway Reading needs both a decoded word and an understood sentence, and a child can lack either; maths needs both fluent procedures and the picture that makes them mean something. Each "war" mixes questions the evidence can answer (does systematic phonics help? is unassisted discovery enough?) with questions it cannot (what is school for, and who decides?). A good teacher uses the first kind of answer and argues openly about the second. Try this: next time you read a headline about "the science of reading" or "new maths", underline each claim and mark E (testable with evidence) or V (a statement about what we should value). Count how many of each. Sources & Further Reading Sources. Gough and Tunmer, Remedial and Special Education 1986; Scarborough 2001; Castles, Rastle and Nation, Psychological Science in the Public Interest 2018. Seymour, Aro and Erskine, British Journal of Psychology 2003. Flesch 1955; Goodman 1967. National Reading Panel 2000; Ehri et al., Review of Educational Research 2001; Camilli, Vargas and Yurecko, Education Policy Analysis Archives 2003. Rose Review 2006; Education Endowment Foundation Teaching and Learning Toolkit (phonics). Wikipedia "Reading wars" for the count of US states (40 and DC, 2013 to October 2025). Rayner et al., Psychological Science in the Public Interest 2001. Recht and Leslie, Journal of Educational Psychology 1988. World Bank, State of Global Learning Poverty: 2022 Update. NCTM 1989; National Research Council 2001; National Mathematics Advisory Panel 2008. Alfieri et al., Journal of Educational Psychology 2011; Stockard et al., Review of Educational Research 2018. Ni and Zhou, Educational Psychologist 2005; Siegler et al., Psychological Science 2012. Stigler and Hiebert 1999. The numbers the toys display were computed in node; the word list and the stickers example are illustrative. This is educational information, not advice about a particular child. 📘 Moats, Speech to Print 📘 National Research Council, Adding It Up 📘 Dehaene, Reading in the Brain Step 10. Classroom Practice & Educational Technology: Attention First, Screens Second ------------------------------------------------------------------------------------- Why: Running a classroom, and what technology helps or doesn't. A lesson is a fifty-minute attention budget. Teachers who run it well share a few habits that evidence backs. Technology has a patchier record: some uses work, many do not, and the loudest claims on both sides outrun what has been measured. Watch a good teacher open a lesson and you can miss what they are doing. Pupils walk in, pick up a sheet, and begin a short task before anyone has been told to. Nothing dramatic happens. But three minutes of the fifty have been saved, and the tone is set. Now watch a lesson in which the teacher asks for books out, waits for quiet, repeats the instruction, and hands out materials one desk at a time. Same room, same pupils, and ten minutes are gone. Education technology walks into these rooms with big promises. A laptop for every child. Software that adapts to each pupil. A tutor chatbot that never tires. In 2023 and 2024, governments from the Netherlands to France moved the other way and restricted phones in schools, and UNESCO's monitoring reported that about 40% of education systems had some school phone ban by 2024. Both movements claim to be about learning. What does the evidence say about each? This piece grades it. Part one covers what a classroom runs on, with evidence that does not need a screen. Part two grades each kind of technology use separately, because one number for "technology" hides everything that matters. Where the evidence is thin, it says so. The course in one box Who takes itTeacher-education and education students, usually in the third year, alongside placements in schools. Teacher-standards frameworks such as the US InTASC standards and the UK Department for Education's Core Content Framework (2019) both cover behaviour, instruction and the use of evidence; the Education Endowment Foundation's guidance reports are widely used in teacher training. What it is forRunning a room of learners so that attention goes to the thing being learned, and judging which tools earn their place in it. Comes afterCurriculum & Instructional Design (36/54). Leads toAssessment & Measurement (36/55) and, for the wider view of schooling, Education Systems & Policy Worldwide (36/59). What this piece gives youYou will not be able to manage a real class from this. You will see why routines buy time, how a teacher sees what a whole room understands, how to read an effect size and a trial, and which technology claims have evidence. Easier first reads: the memory pieces in 17 Thinking & Learning, and Learning Sciences (36/53). Attention is the first thing a classroom runs on In 1970 the researcher Jacob Kounin filmed classrooms and asked what separated teachers whose pupils stayed on task from those whose pupils drifted. The answer was not how teachers punished misbehaviour. It was how they ran the lesson. His four labels still turn up in training: withitness (the teacher visibly knows what is happening everywhere in the room), overlapping (dealing with an interruption without stopping the lesson), momentum (no dead stretches) and smoothness (no abrupt jumps in direction). A teacher who is withit stops a small problem before it has an audience. The practical form of this is routines: the same way of entering, handing out, asking for attention and finishing, taught early and practised until it is automatic. A routine costs minutes to teach and returns them every lesson. The interactive counts the minutes. It is plain arithmetic on your own numbers. minutes lost per year = transitions × seconds each ÷ 60 × lessons a day × school daysthis is time lost per class; it is time no pupil gets back Interactive · The transition budget Transitions in one lesson (entering, handing out, switching tasks) Seconds each takes Lessons per day for this class Illustrative arithmetic: a 50-minute lesson and 180 school days. Real transitions vary; the point is the size of the total. Without JavaScript: six transitions of 90 seconds in a 50-minute lesson cost 9 minutes, 18% of the lesson, and about 135 hours over a year at five lessons a day. Good routines are not about control for its own sake. They free the minutes in which pupils can think, and they let a teacher spend attention on the pupil who is stuck, not the pupil who is loud. Ask, wait, check: seeing what the whole room thinks A teacher explains, asks "does that make sense?", sees a few nods and a raised hand, and moves on. Half the class is lost. The nods are not evidence. Barak Rosenshine's 2012 summary of the research on effective teaching, Principles of Instruction, puts it as a short list: review prior learning, present new material in small steps, ask many questions and check the responses of all pupils, give models and worked examples, guide practice, and keep practising until the skill is automatic. The checking step is what turns teaching into a loop. A second finding is about silence. Mary Budd Rowe's studies in the 1970s found that teachers typically wait only about a second after asking a question. When they were trained to wait three seconds or more, answers got longer and more pupils took part. A pause feels long to the one holding it. chance of spotting a misunderstanding = 1 − (1 − p)kp = share of the class that is confused, k = pupils whose thinking you actually see Interactive · How many minds can you see? Share of the class confused Pupils whose answers you see Computed for a class of 30, assuming the pupils you see are a fair sample. A volunteer is usually someone who knows, so the real chance for "ask a volunteer" is lower than this. Without JavaScript: if a quarter of the class is confused, asking one fair-sampled pupil spots it 25% of the time, three pupils 58%, ten pupils 94%. Mini-whiteboards show all 30. That is why teachers use cold-calling (anyone might be asked) and all-pupil responses such as mini-whiteboards or hands-up voting on a multiple-choice question: they raise k from one volunteer towards the whole room. Doug Lemov's Teach Like a Champion catalogues these moves. Reading an effect size, and why one trial cannot settle it Most of the research in this piece is reported as an effect size: how many standard deviations the average treated pupil moved compared with the comparison group. A value of 0.2 means the typical treated pupil ends up where the 58th percentile of the comparison group would be. John Hattie's Visible Learning (2009) pooled thousands of such numbers and suggested 0.40 as a "hinge point" for what is worth doing. Critics including Terry Wrigley and Robert Slavin answer that studies differ in design, age and the outcome measured, so pooling them into one league table mixes unlike things. Matthew Kraft (2020) proposed benchmarks calibrated to rigorous education trials: under 0.05 is small, 0.05 to 0.20 medium, 0.20 and above large. Seen that way, many real interventions are "large" at 0.2. Interactive · What does an effect size mean? Effect size (standard deviations) Normal distributions assumed. Percentile = Φ(d). Chance a random treated pupil beats a random comparison pupil = Φ(d/√2). Labels follow Kraft (2020). Without JavaScript: d = 0.2 puts the typical treated pupil at the 58th percentile of the comparison group; a random treated pupil beats a random comparison pupil 56% of the time. Now the other half: whether one trial can even see such an effect. A small study often cannot. If the true effect is 0.2 and you compare two groups of 25 pupils, you will find a clear result only about one time in nine, and you will see a difference in the wrong direction about one time in four. When whole classrooms are assigned to a method, the effective sample is the number of classrooms, which is smaller still. That is why a single enthusiastic school pilot proves little, and why large randomised trials and reviews carry the weight. Interactive · Can this trial see the effect? True effect (standard deviations) Pupils in each group Two groups of equal size, pupils assigned individually, a two-sided test at the 5% level. Power = Φ(d√(n/2) − 1.96) + Φ(−d√(n/2) − 1.96). Without JavaScript: with a true effect of 0.2 and 25 pupils per group, power is about 11%; with 400 per group it is about 81%. Technology, graded use by use "Does technology help learning?" is like asking whether paper helps learning. It depends what is written on it. The EEF's Teaching and Learning Toolkit puts digital technology at about four months of extra progress on average, but the reviews behind that average range from about two months to more than a year, and the strand lost a padlock of confidence for that reason. A 2020 review of randomised trials by Escueta, Quan, Nickow and Oreopoulos reached the same shape: simply giving pupils access to devices did not reliably raise achievement, while software that changed what pupils practised, mostly in maths, often did. Grade five uses before you read the verdicts. Interactive · Grade the evidence Grade five uses. Each verdict summarises the best-known studies at the time of writing, not every study. Grades: Promising, Little or no effect, Mixed or too early. Without JavaScript: adaptive maths software, promising; a laptop for every pupil with no change in teaching, little or no effect; typed versus handwritten notes, mixed; unguarded AI chat for practice, early evidence of harm; school phone restrictions, mixed or too early. The AI case deserves a sentence of its own because it is new. In a field experiment with nearly 1,000 high-school maths pupils in Turkey (Bastani and colleagues, PNAS, 2025), pupils who practised with a chatbot that simply answered like a general assistant did better on the practice problems and then scored 17% lower on an exam taken without it, compared with pupils who never had access. A version built to give hints without giving answers largely removed that harm. It was one school in one semester, so it is a caution about design, not a ruling on AI. Practising is how people learn; a tool that does the practising for them can remove the learning. Adaptive practice: the screen use with the best record Where technology does well, the mechanism is usually the same. A class has pupils who are two years behind and pupils who are two years ahead, and one worksheet at grade level wastes the time of both. Adaptive software gives each pupil items just beyond what they can already do. In a well-known Indian trial of the Mindspark programme (Muralidharan, Singh and Ganimian, 2019), pupils in after-school centres gained about a third of a standard deviation in maths over a few months. The reason is not the screen. It is that the software did what one teacher with 40 pupils cannot: matched the task to the child, again and again. Educational psychologists describe the target as the zone just beyond current skill, the idea behind Vygotsky's "zone of proximal development". The toy below encodes that assumption: a pupil gains most from items near their level and almost nothing from items far above it. It is a model of the mechanism, not a measurement, but the pattern it shows is the argument behind adaptive tools and behind a teacher who groups flexibly. Interactive · Fixed worksheet or matched practice? How far behind grade level the pupil starts Practice items completed Adaptive target above current skill Matched Grade-level worksheet Easy review Illustrative model in made-up "grade-level" units: gain per item = 0.002 × exp(−((difficulty − skill)/0.8)²). The pupil's grade is 6. The shape of the curve is an assumption, not data. Without JavaScript: a pupil two grade levels behind who works 300 grade-level items gains almost nothing in this model; with matched items the same pupil gains about half a grade level. The model's lesson cuts both ways. Matched practice helps the pupil who is far behind; it also depends on the software choosing well, on pupils actually using it, and on a teacher who connects it to the lesson. Reviews find that programmes fail more often than their sales pages say. Phones, wellbeing and the argument Phones are the most argued-over technology in school, partly because two questions get tangled. The first is about attention in lessons: do phones in a classroom, in a pocket or on a desk, cost learning? The second is about wellbeing: has smartphone use harmed young people's mental health, and should schools act on that? On the first, the case for restriction is plain. A phone is built to pull attention, and its owner is not the only one affected: the OECD's PISA 2022 reported that many pupils were distracted by their own or others' devices in maths lessons. A study of English schools by Beland and Murphy (2016) found test scores rose after phone bans, most for the lowest-attaining pupils. A ban is cheap to run and easy to explain. The cautious reply is that most of the evidence is observational, that schools which ban phones differ in other ways, and that a ban does not teach pupils to manage their attention elsewhere. On the second, the sides are further apart. Jonathan Haidt (The Anxious Generation, 2024) argues that a phone-based childhood, spreading from about 2010, is a main cause of rising teen anxiety and depression, and that schools are the easiest place to take phones out of children's days. Critics such as Candice Odgers and Amy Orben answer that the evidence is mostly correlational and effect sizes are small: Orben and Przybylski (2019), analysing large datasets, found that digital technology use explained at most about 0.4% of the variation in adolescent wellbeing. Haidt's side replies that average screen time is a poor measure of what harm looks like. Each is a position held by researchers who have read the same studies. Evidence of harm to wellbeing has not been settled, and nor has evidence of safety. This piece describes research and is not medical or mental-health advice. If a young person you know is struggling, a doctor or a local service can help; findahelpline.com lists free helplines by country. A fair reading separates the claims. Restricting phones during lessons is a modest, plausible attention measure with some supporting evidence. Claims that bans will fix teen mental health go well beyond what has been shown. Claims that phones are harmless to learning go beyond it the other way. What a graduate just sees Lessons run on attention, and routines are an investment: minutes taught once are returned every day. Nods and a volunteer are not evidence; checking many pupils' thinking is what turns teaching into a loop. A pause after a question is not dead air, and it is longer than it feels. An effect size means little until you know the design, the age and the outcome, and 0.2 can be a large effect. A small trial can miss a real effect, and a single pilot proves less than a large randomised trial. "Technology" is not one thing: graded by use, adaptive practice has the best record and handing out devices alone the weakest. A tool that does the practising for a pupil can remove the learning. Phones in lessons and phones in mental health are separate questions with different amounts of evidence. Where it shows up next Assessment & Measurement (36/55): the checking step and the reliability of any score you use to decide who needs help. Education Systems & Policy Worldwide (36/59): national phone rules, device programmes and testing policy are the same arguments at the scale of a country. Learning Sciences (36/53): retrieval, spacing and worked examples are what a good routine and a good check are made of. Inclusive & Special Education (36/57): adaptive tools and assistive technology serve pupils for whom the one-size lesson fails. In the world: teacher training, school leaders deciding on a phone policy, and anyone buying software for a school. If you want to go deeper 📘 Textbook. Carolyn Evertson and Edmund Emmer, Classroom Management for Elementary Teachers (Pearson), with the matching secondary text, the standard classroom-management course books; and Richard Mayer, Multimedia Learning (Cambridge University Press), the research behind how to design screen-based explanations. Check for the current editions. 📘 Gentler. Doug Lemov, Teach Like a Champion (3rd edition, 2021), a catalogue of classroom techniques; Daniel Willingham, Why Don't Students Like School?; and Justin Reich, Failure to Disrupt (Harvard University Press, 2020), a sober history of why ed-tech promises fall short. 🌐 Free text. Barak Rosenshine, "Principles of Instruction" (American Educator, 2012), free from the American Federation of Teachers, and the Education Endowment Foundation's guidance reports at educationendowmentfoundation.org.uk. 🌐 Free course. MIT OpenCourseWare CMS.595 Learning, Media, and Technology (Spring 2024, taught by Justin Reich). The takeaway A classroom runs on attention, and the best-supported habits cost nothing: routines, small steps, and checking what every pupil thinks. Technology earns its place when it changes what a pupil practises or how a teacher sees thinking, and not when it only puts a screen in front of them. Ask of any claim: which use, compared with what, in how big a trial, measuring which outcome. Try this: in your next meeting, class or study session, count how many minutes go to getting started. Then find one place where you could see what everyone in the room thinks, not only the one who speaks first. Sources & Further Reading Sources. Kounin, Discipline and Group Management in Classrooms, 1970; Rosenshine, "Principles of Instruction", American Educator, 2012; Rowe, "Wait time and rewards as instructional variables", Journal of Research in Science Teaching, 1974; Hattie, Visible Learning, 2009, and critiques by Wrigley and Slavin; Kraft, "Interpreting effect sizes of education interventions", Educational Researcher, 2020; the Education Endowment Foundation Teaching and Learning Toolkit, digital technology strand (EEF blog, "Updating the Toolkit"); Escueta, Quan, Nickow and Oreopoulos, "Upgrading education with technology", Journal of Economic Literature, 2020; Cueto and colleagues' ten-year randomised study of One Laptop per Child in rural Peru (2025); Muralidharan, Singh and Ganimian, American Economic Review, 2019; Mueller and Oppenheimer, Psychological Science, 2014, and Urry and colleagues' 2021 replication; Bastani, Bastani, Sungu, Ge, Kabakcı and Mariman, PNAS, 2025; Beland and Murphy, Labour Economics, 2016; Orben and Przybylski, Nature Human Behaviour, 2019; Haidt, The Anxious Generation, 2024; UNESCO Global Education Monitoring Report on technology in education (2023) and its 2024 update; the Dutch government's school phone ban from January 2024. All interactive outputs were computed in node. This piece reports evidence and takes no side in disputes the field has not settled. 📘 Mayer, Multimedia Learning 📘 Reich, Failure to Disrupt 🌐 MIT OCW CMS.595 Step 11. Assessment & Measurement: How to Tell What Someone Has Learned ----------------------------------------------------------------------- Why: How to tell what someone has learned. A test score looks like a fact about a student. It is really an estimate, with a margin of error, of something you cannot see directly. Measurement is the craft of knowing how good that estimate is. A student scores 74 on Tuesday's test. The pass mark is 75. She fails, misses a place on a programme, and her teacher feels the grade was fair because the number is the number. But suppose she had sat a different version of the same test on Wednesday. Would she have scored 74 again? Probably not: perhaps 71, perhaps 78. The first score was a single draw from a spread of scores she might have got. Almost everyone treats test scores as exact. People who have studied measurement treat them as estimates with a width. That change of habit shows up everywhere, from exam boards to school league tables, and from hiring tests to the AI benchmarks of the past few years. This piece is about the width, the question of whether the test measures the right thing at all, and what happens when a number gets high stakes attached. The course in one box Who takes itEducation majors, usually in year 3, as classroom assessment; psychology and statistics students meet its deeper form as psychometrics. The US Standards for Educational and Psychological Testing (AERA, APA and NCME, 2014) are the field's shared reference, and teacher-standards documents such as InTASC expect trainee teachers to know formative and summative assessment. What it is forDesigning and judging ways of finding out what people have learned, and understanding what the resulting numbers can and cannot say. Comes afterProbability & Statistics (34/05) and Curriculum & Instructional Design (36/54). Leads toEducation Systems & Policy Worldwide (36/59) and Classroom Practice & Educational Technology (36/60), both of which use test results and feedback. Its methods are also the base of Research Methods in Psychology (35/19). What this piece gives youYou will not be able to build a certified exam. You will be able to say how wide a score's error is, why a longer test is steadier, what makes a test valid, how adaptive tests work, and why league tables need caution. Easier first reads: How to Spot Bullshit (17/03) and, in this series, Probability & Statistics (34/05). The data in the toys are invented. A score is a true score plus error The oldest model in measurement, classical test theory, goes back to Charles Spearman's work in 1904 and was set out fully by Frederic Lord and Melvin Novick in 1968. It says an observed score is the sum of two parts: a true score, the average you would get over endless equivalent versions of the test, and a random error. Errors come from the particular questions chosen, the student's mood and sleep, a lucky guess, a marker's mood. observed score = true score + errorthe spread of the error is the standard error of measurement: SEM = SD × √(1 − reliability) Reliability, written r, is a number from 0 to 1: the share of the differences between students that reflects real differences and not noise. A test with reliability 0.85 and a spread (standard deviation) of 10 points has an SEM of about 3.9 points, so about 95 times in 100 a student's observed score falls within roughly ±7.6 points of her true score. A pass mark inside that band decides some students by luck. Interactive · One student, retaken many times (invented numbers) A student has a true score of 70. The test has a spread of 10 points and the pass mark is 75. Set the reliability, then sit the test again. Reliability r0.85 Sit the test againClear Turn on JavaScript to use this tool. Key result: at reliability 0.85 the SEM is about 3.9 points, and a student whose true score is 70 clears a pass mark of 75 on about 10 sittings in 100. The simulated scores use a fixed pseudo-random sequence, so they repeat every time you reload. The chance of passing is computed from the normal distribution. Reliability: more good items, less noise Reliability can be estimated several ways. Test–retest compares scores on two occasions. Parallel forms compares two versions. Internal consistency, most often Cronbach's alpha (1951), asks whether the items hang together. For essays, inter-rater reliability asks whether two markers agree; it is often much lower than people assume until markers are trained and use a scoring guide. The practical rule is the Spearman–Brown formula (1910): lengthening a test with items of the same quality raises its reliability. If a test with reliability r is made k times longer, the new reliability is k × r ÷ (1 + (k − 1) × r). Starting at 0.60, doubling gives 0.75, and a six-fold length gets to 0.90. The gains shrink as the test grows, which is why a 200-item exam is not twice as good as a 100-item one. One more fact: reliability caps validity. A noisy test cannot track anything well, though a steady test can still track the wrong thing. Interactive · How long a test do you need? A 10-item test has reliability 0.60 (invented). Change the number of similar items. Items10 Turn on JavaScript to use this tool. Key result: 10 items give 0.60; 20 give 0.75; 60 give 0.90. Validity: is it measuring the right thing? A bathroom scale that is always 2 kilograms off is reliable and not valid. Validity is whether the scores support the interpretation you want to draw from them. Samuel Messick (1989) argued that validity is not a property of a test but of the use of its scores, built from evidence about content, response processes, internal structure, relation to other measures and consequences. Michael Kane's argument-based approach (2006) asks for an explicit chain from the task to the claim and a test of its weakest link. Two threats do most damage. Construct underrepresentation is a test too narrow for what you claim: a "writing" score from a grammar quiz. Construct-irrelevant variance is something else moving the score: a maths word-problem test that a pupil fails because the English is hard. Both can leave reliability high. The classic old example of reliable and invalid is measuring skull size to the millimetre to estimate intelligence. Interactive · Name the problem Turn on JavaScript to use this tool. Five labels: unreliable, reliable but invalid, too narrow, irrelevant factor, sound. Next case Items have difficulty and discrimination, so tests can adapt Classical theory treats a test as a whole. Item response theory (IRT) models each question. Georg Rasch (1960) and Frederic Lord worked out that the chance of a correct answer can be written as a curve against the student's ability. Each item has a difficulty (b: the ability at which you have even odds) and a discrimination (a: how sharply the curve rises there). In the two-parameter model, P(correct) = 1 ÷ (1 + e−a(θ − b)), where θ is ability. The payoff is the adaptive test. Pick the next item near your current estimate of ability: a question far too easy or too hard tells you little. After about a dozen well-chosen items the estimate can be as good as a much longer fixed test. Computer-adaptive testing has been used for professional and admissions tests such as the GMAT since the 1990s. A guard on the other side is differential item functioning: an item that behaves differently for two groups of equal ability is flagged for review. Interactive · An item curve, and an adaptive test (simulated) Difficulty b0.0 Discrimination a1.2 Turn on JavaScript to use this tool. Key result: a student whose ability equals the item's difficulty has a 50% chance of getting it right. True ability of a simulated student0.5 Run a 10-item adaptive test All items in the adaptive run have a = 1.2 and a bank of difficulties from −3 to 3 in steps of 0.5. Ability is estimated after each answer as the mean of the plausible values on a grid, starting from a standard normal prior. Answers are random draws, so each run differs. Grades compare to a standard, or to each other Robert Glaser (1963) separated two meanings of a grade. A criterion-referenced grade says what you can do: an A means you met the standard, and everyone can get one. A norm-referenced grade says where you stand: an A goes to, say, the top fifth, however well everyone did. Grading "on a curve" is the second. It fits selection (choose the best twenty) and fits poorly with teaching, since a strong class still produces failures and a weak one produces undeserved As. Interactive · The same scores, two grading rules (invented classes) Standard: score needed for an A85 Turn on JavaScript to use this tool. Key result: a curve that gives As to the top 20% hands out 4 of 20 whether the class is strong or weak; a fixed standard of 85 gives 10 As in the strong class and none in the weak one. The sharpest recent lesson came in England in 2020. With exams cancelled in the pandemic, the regulator Ofqual used a statistical model that adjusted teachers' predicted grades using each school's past results, to hold national results steady. About 39 percent of A-level grades came out lower than the teachers' predictions, small classes were treated less fairly, and after protests the government and Ofqual reverted to teacher-assessed grades on 17 August 2020. The model delivered a stable national distribution and an unfair result for individuals, which is what a norm-style fix does when the aim shifts. Grading scales differ around the world and are not directly comparable: Germany uses 1 to 6 with 1 best, Finland's schools use 4 to 10, Mexico 0 to 10 with 6 as a pass, and many US schools use letters. Formative assessment: tests that change what happens next A summative assessment sums up learning at the end: a final exam. A formative one is used while learning is under way to change teaching. Paul Black and Dylan Wiliam's 1998 review, with its short companion Inside the Black Box, argued that classroom assessment used this way produced substantial learning gains. Later reviewers, such as Randy Bennett (2011), have said the evidence was weaker and less specific than the headlines. A kind of agreement remains: the useful thing is the loop of finding out what students understand and doing something about it, not any single technique. Feedback is the part to handle with care. Avraham Kluger and Angelo DeNisi's 1996 meta-analysis found that, on average, feedback helped, but more than a third of the interventions made performance worse, especially when feedback drew attention to the person and not the task. John Hattie and Helen Timperley (2007) sorted feedback by whether it addressed the task, the process, self-regulation or the self. The Education Endowment Foundation's Toolkit rates feedback as a high-impact approach on average, with wide variation. Low-stakes quizzes join this and Learning Sciences (36/53): retrieval is both a measurement and a way of learning. League tables, PISA and what happens when a number has stakes International studies turn school results into rankings. PISA (OECD) tests 15-year-olds every three years; the 2022 results, published in December 2023, covered about 690,000 students in 81 countries and economies. The OECD average in mathematics fell to 472 from 489 in 2018, a 15-point drop, the largest between two cycles, and Singapore led with 575. TIMSS (IEA) tests grades 4 and 8; in its 2023 cycle Singapore led grade 8 mathematics with 605, ahead of Chinese Taipei (602), Korea (596) and Japan (595). The pandemic is one likely contributor to the declines, and researchers disagree about how much. A published rank hides the error. Each country's score is an estimate from a sample of students and questions with a standard error, and two countries a few points apart may not differ. Comparisons across countries add further problems: different populations of 15-year-olds in school, translation of items, and motivation on a test that counts for nothing. Interactive · How stable is a ranking? (invented countries) Standard error of each score6 Turn on JavaScript to use this tool. Key result: with a standard error of 6, the country ranked 4th on the published scores lands anywhere from about 2nd to 7th once the error is allowed for. Then there are the stakes. Donald Campbell stated in 1976 that the more a quantitative indicator is used for decisions, the more it is subject to corruption pressures and the more it distorts what it measures; Charles Goodhart made a similar point about monetary targets. In education that looks like teaching to the test, narrowing the curriculum to what is examined, coaching, and sometimes cheating. Systems respond differently. High-stakes selection exams are central in China (the gaokao, taken by about 13 million candidates in recent years), South Korea (the CSAT) and India (JEE and NEET); France has the baccalauréat; Finland has had little standardised testing until the upper-secondary matriculation exam. Defenders of high-stakes testing argue that it gives objective, comparable and fair criteria; critics argue that it distorts teaching and rewards test-taking skill. Evidence and values both come in, and neither settles it alone. What a graduate just sees A score is an estimate: true score plus error, and the error has a width you can compute. A pass mark inside the error band decides some people by luck. Longer tests of good items are steadier, with diminishing returns. Reliable is not valid; ask what is being measured and what else moves the number. Good items are neither too easy nor too hard for the person, which is why adaptive tests work. A grade is either against a standard or against other people; know which. Feedback can help or hurt, and the loop matters more than the technique. A ranking is a sample with error; stakes bend what is measured. Where it shows up next Education Systems & Policy Worldwide (36/59): PISA, TIMSS and national exams are how systems compare themselves. Classroom Practice & Educational Technology (36/60): quiz platforms and adaptive tutors rest on item response models, and AI changes what a take-home essay can show. Research Methods in Psychology (35/19): reliability and validity are the same ideas as in every questionnaire study. In the world: driving tests, medical licensing, hiring tests, credit scores and AI benchmarks all depend on error, validity and what happens when people target the number. If you want to go deeper 📘 Textbooks. W. James Popham, Classroom Assessment: What Teachers Need to Know (Pearson, recent edition), the common teacher-education text; and Cecil Reynolds, Ronald Livingston and Victor Willson, Measurement and Assessment in Education (Pearson, recent edition) for more on reliability and validity. Check for the current edition. 📘 Gentler. Dylan Wiliam, Embedded Formative Assessment (Solution Tree, second edition 2018), and Daniel Koretz, The Testing Charade (University of Chicago Press, 2017), on high-stakes testing. 🌐 Free text. The OECD's PISA reports at oecd.org/pisa explain how the sampling and scaling are done. 🌐 Free course. MIT OpenCourseWare 11.125 Introduction to Education (Spring 2009), which includes student assessment, and 5.95J Teaching College-Level Science and Engineering (Fall 2015) on designing exams. The takeaway A test score is an estimate of something hidden, with an error you can calculate and a validity you must argue for. Steady tests need enough good items, adaptive tests choose them well, grades need a stated standard, feedback is useful when it changes what happens next, and any number given high stakes will be bent toward. Try this: next time you see a ranking or a test score, ask three questions. How wide is its error? Does it measure what people say it does? What would someone do to raise it? Sources & Further Reading Sources. Spearman 1904 and 1910; Lord and Novick, Statistical Theories of Mental Test Scores (1968); Cronbach, Psychometrika 1951; Messick, in Educational Measurement (3rd ed., 1989); Kane, in Educational Measurement (4th ed., 2006); AERA, APA and NCME, Standards for Educational and Psychological Testing (2014); Rasch 1960; Lord, Applications of Item Response Theory (1980); Glaser, American Psychologist 1963; Black and Wiliam, Assessment in Education 1998; Bennett, Assessment in Education 2011; Kluger and DeNisi, Psychological Bulletin 1996; Hattie and Timperley, Review of Educational Research 2007; Campbell, 1976 (Western Michigan University occasional paper); Goodhart 1975; OECD, PISA 2022 Results (December 2023); IEA, TIMSS 2023; Ofqual and press reports on the August 2020 A-level grading (17 August 2020 reversal); Education Endowment Foundation Toolkit. Every computed number in the interactives was checked in node. The classes, countries and scores in the toys are invented. 📘 Popham, Classroom Assessment 📘 Wiliam, Embedded Formative Assessment 🌐 OECD PISA Step 12. Research Methods in Psychology: How to Not Fool Yourself ----------------------------------------------------------------- Why: How to read the research. Psychology asks questions that cannot be put on a scale, answers them with small noisy samples, and then discovered that many famous answers did not repeat. The methods course is how the field learned to check itself. .chips button{min-width:0} .row2{display:flex;gap:8px;flex-wrap:wrap} .row2 button{flex:1 1 90px;min-width:0} .item{border-top:1px solid var(--line);padding:10px 0;font-family:-apple-system,sans-serif;font-size:.93rem} .item b.nm{display:block;margin-bottom:6px} .item .ans{margin-top:6px;color:var(--ink);background:var(--hi);border-radius:8px;padding:8px 10px;display:none} .item.done .ans{display:block} .legend{font-family:-apple-system,sans-serif;font-size:.8rem;color:var(--muted)} A headline says that people who stand like a superhero for two minutes feel braver and take more risks. It was published in a good journal in 2010, taught in business schools, and watched by tens of millions in a talk. Then bigger studies tried it and the hormone and risk results did not appear. The problem was not a villain. It was a method: small groups, many ways to analyse the numbers, and a system that printed only the exciting result. Every psychology graduate has this story somewhere in their head, and it changes how they read every claim about the mind. They do not ask "is it true?" first. They ask: how was it measured, who was in it, was anyone assigned at random, how big was the effect, and would it happen again? That habit is what a methods course sells. The course in one box Who takes itEvery psychology major, usually in year 1 or 2, alongside statistics. The APA's undergraduate guidelines and the British Psychological Society's accreditation both make research methods a core strand, and neuroscience, nursing, education and sociology programmes teach a version of it. What it is forTurning a question about minds into a measurement, and telling a result worth believing from one that merely happened. Comes afterProbability and Statistics: Reasoning With Uncertainty (34/05). Leads toSocial Psychology (35/25) and Personality & Individual Differences (35/26), where most of the famous disputed findings live. Its cousins are Research Methods in Political Science (35/18), Econometrics (34/44) and Marketing Research and Analytics (34/59). What this piece gives youYou will not be able to design a publishable study. You will be able to see why a small, flexible study can "find" nothing at all, and what the field now does about it. Easier first reads: The Biases That Fool Everyone (17/02) and How to Spot Bullshit (17/03). The statistics here are the ones in 34/05; this piece goes further into what they do in a lab. Measuring what you cannot see: operationalising, reliability and validity You cannot put "stress", "intelligence" or "attachment" on a scale. So the first move of any study is to operationalise: to pick something you can count that stands for the idea. Stress becomes cortisol in saliva, or a score on a questionnaire. Intelligence becomes the score on a set of puzzles. Every such choice is a bet that the number captures the thing, and the bet can be wrong. Two words judge the bet. Reliability is whether you get the same number again: the same person, the same scale, a week later. Validity is whether the number measures what you meant. A bathroom scale that always reads 3 kg too heavy is perfectly reliable and not valid for weight. Reliability is necessary but not enough, and without it nothing else works, because noise in a measure shrinks every relationship you try to find with it. observed correlation ≈ true correlation × √(reliability of X × reliability of Y)called attenuation: noisy measures hide real links Interactive · Noise hides real links Reliability of the measure True link between the two traits Illustrative simulation: 400 invented people, each measured twice with noise; the plot shows 60. Both traits are measured with the reliability you chose. With reliability 0.7 on both measures, a real link of 0.6 shows up as about 0.42. A study of a shaky questionnaire can fail to find a true effect simply because its ruler is made of rubber. Experiments and correlations: only random assignment breaks the confounder People who exercise report better wellbeing. Does exercise cause it? Maybe. Or people with more free time, better health and less money stress both exercise more and feel better: a confounder. A correlational study records what people already do, and cannot tell these stories apart however large it is. An experiment does one thing differently: the researcher decides who gets the treatment, by chance. A coin flip cannot be related to free time, health or anything else, so on average the groups differ in nothing except the treatment. That is why randomised experiments sit at the top of the evidence ladder, and why a study that merely compares people who chose different things should say "associated with", not "causes". Interactive · A link with no cause Observe what people do Assign by coin flip True effect of exercise on wellbeing How strongly free time drives both Invented data, 400 people, standardised scores. Observing: exercise = confounder × c + chance. Coin flip: exercise = chance alone. The plot shows 80 people. With a true effect of zero and a confounder of 0.6, the observed link is about 0.35, and a naive reading says exercise helps. Flip the switch to coin-flip assignment and it falls to roughly zero, which is the truth. Experiments are not always possible (you cannot assign people to grief or to poverty), so psychologists also use careful natural comparisons, but they say so when they have not randomised. Effect size and power: how big, and could this study even see it? "Statistically significant" says only that a result would be unlikely if nothing were going on. It says nothing about size. A huge study can make a trivial difference significant; a small one can miss a large one. So papers now report an effect size. The common one for two groups is Cohen's d: the gap between the group averages, measured in standard deviations. d = (mean of group B − mean of group A) ÷ standard deviationd = 0.5 means the average person in B sits half a standard deviation above the average in A Interactive · What an effect size looks like d = 0.2d = 0.5d = 0.8 Effect size d Two normal distributions with equal spread. Probability of superiority = Φ(d/√2); share above the other group's average = Φ(d). At d = 0.5 the curves overlap by about 80%, and if you pick one person from each group at random the one from the higher group is ahead only about 64% of the time. Cohen suggested 0.2, 0.5 and 0.8 as small, medium and large, and he meant them as a last resort when you know nothing better about your field. A tiny effect can matter when it is applied to millions of people; a medium one can be useless for one person. Power is the chance a study detects an effect that is really there. It depends on the true effect, the sample size and the cut-off. Try it. Below, thousands of invented studies are run on the same true effect; significant ones are shaded. Interactive · Run 1,500 studies True effect d People per group Each study: two groups of n, normal data, two-sided t-test at p < .05, fixed random seed so the numbers repeat. Dark bars are significant studies. With d = 0.5 and 20 people per group, power is only about a third. With 64 per group it is about 80%, the usual target. Now notice the second number. When the true effect is small and the study is small, the few studies that reach significance are the ones that overshot: at d = 0.2 and 20 per group, power is about 10% and the "winners" average an effect around four times the truth. Journals that print only the winners print inflated effects. This is one reason replications so often come back smaller. P-hacking: the forking paths A p-value below .05 is meant to happen by luck one time in twenty when nothing is going on. That promise holds only if you decide what to test before you look. A researcher with ten outcome measures, four ways to exclude "bad" participants, and the freedom to stop when the result looks good has dozens of tests to choose from, and reports the one that worked. Simmons, Nelson and Simonsohn showed in 2011 that such ordinary flexibility could make almost anything "significant". Andrew Gelman called it the garden of forking paths: nobody has to cheat, because each fork seems reasonable at the time. Interactive · Nothing is going on. How often does something "work"? Many outcome measures Peek and stop early Outcomes measured 1,000 simulated studies per setting; both groups drawn from the same distribution, so every significant result is a false alarm. Outcomes: 20 per group, independent outcomes. Peeking: test after every 10 per group. With ten independent outcomes the chance that at least one is "significant" is 1 − 0.9510, about 40%. With twenty it is about 64%. Peeking at the data after every ten participants and stopping the moment p dips under .05 gives a false-alarm rate of about one in five (18% in the simulation) across ten looks. Real outcomes are correlated, so the real numbers are a little lower, but the lesson stands. The cure is not more careful people. It is committing to the plan first. The replication crisis, and the reforms that followed Around 2011 several things collided. Daryl Bem published nine experiments in a leading journal claiming evidence of precognition, using ordinary methods, which suggested ordinary methods could prove the impossible. The Dutch social psychologist Diederik Stapel was found to have fabricated data. And the false-positive paper appeared. Then people began to re-run studies. In 2015 the Open Science Collaboration, led by Brian Nosek, repeated 100 published experiments: 97 of the originals had significant results, while only about 36% of the replications did, and replication effects averaged about half the original size. Cognitive studies fared better than social ones. That does not say 64% of psychology is false, since a failed replication can itself be underpowered, and studies differ in how hard they are to repeat. It does say published effects are routinely inflated. The Many Labs projects asked a different question: do the same results appear across many sites? In the first, in 2014, 10 of 13 effects replicated consistently across 36 samples, one weakly, and two, flag priming and currency priming, did not. Test your own sense of what held up. Interactive · Held up, shrank, or failed? Guess, then reveal Guess each one. Your tally appears here. The reforms are practical. Preregistration means writing down hypotheses and the analysis plan before data arrive, which removes the forks. Registered reports go further: a journal reviews the question and method first and promises to publish whatever comes out, which removes the pull to print only winners; the Center for Open Science counts over 300 journals offering the format. Open data and materials let others check and reuse your work. Larger samples, shared multi-lab studies and reporting every effect size with its uncertainty are now common advice. Not everyone agrees on how far to go: some argue that strict rules suit confirmatory tests and fit badly with exploratory or qualitative work, and that fixing the incentives matters more than any checklist. Few dispute that the field is better checked than a decade ago. Who is in the study? WEIRD samples Most experiments recruit whoever is nearest: university students. In 2010 Joseph Henrich, Steven Heine and Ara Norenzayan reviewed the evidence in The Weirdest People in the World? and pointed out that the participants were overwhelmingly from societies that are Western, Educated, Industrialised, Rich and Democratic, a small slice of humanity, and that on several measures such people were outliers. The classic example is a visual illusion (the Müller-Lyer, in Sensation & Perception, 35/21), which fools people in industrial societies more than it fools people in some small-scale societies. Results about fairness games, moral reasoning and self-concept differ across cultures too. The remedy is plain: say who was studied, write the claim to match, recruit more widely, and be wary of "humans do X" from a campus sample. Some effects are universal, some are local, and without other samples you cannot tell which. What a graduate just sees A study is only as good as its ruler: a noisy or invalid measure hides real effects or measures something else. "Linked to" is not "caused by". Only random assignment removes a hidden third factor. Significant is not important. Ask how big the effect is, and how uncertain. Small studies are noisy, and the ones that reach print overshoot. Treat a lone small result as a hint. Flexibility in analysis quietly raises false alarms. The question is what was decided before the data. One result is a starting point; a result that repeats across labs is evidence. Who was studied limits who the finding is about. A failed replication is information, not an accusation. Where it shows up next Social Psychology (35/25): obedience, priming and group studies are where the replication story is most dramatic, and the tools above decide what you can still trust. Personality & Individual Differences (35/26): reliability and validity are the whole business of a test, and heritability claims depend on design. Econometrics (34/44) and Marketing Research and Analytics (34/59): the same logic of confounders, A/B tests and natural experiments in other disciplines. In the world: reading a news story about a "new study", judging a health claim, running a product experiment, or deciding whether a therapy has evidence. If you want to go deeper 📘 Textbook. Beth Morling, Research Methods in Psychology: Evaluating a World of Information (W. W. Norton, 5th edition). Widely used; built around judging claims in the news as well as designing studies. 📘 Textbook. Frederick Gravetter and Lori-Ann Forzano, Research Methods for the Behavioral Sciences (Cengage). The other standard syllabus text. 📘 Gentler. Stuart Ritchie, Science Fictions (2020). A readable account of fraud, bias, hype and the reforms. 🌐 Free text. Daniël Lakens, Improving Your Statistical Inferences: a free online book on effect sizes, power and open practices. 🌐 Free course. MIT OpenCourseWare 9.00SC Introduction to Psychology (Fall 2011, John Gabrieli), a full introductory course. The takeaway Psychology is hard to measure and easy to fool yourself about. The defences are the ones in this piece: measure reliably, assign at random when you can, report how big, run studies large enough to see the effect, and decide the analysis before you look. When a field applied them, a lot of famous results shrank or vanished, and that is the method working. Try this: the next time you read "a new study shows", find three things: how many people, whether they were assigned at random, and how big the effect was. Most headlines leave out at least two. Sources & Further Reading Sources. Reliability, validity, attenuation, Cohen's d and power are standard textbook methods (Morling; Cohen 1988). Open Science Collaboration, Estimating the reproducibility of psychological science, Science 349 (2015): 100 studies; 97 originals significant; about 36% of replications significant; effect sizes about half. Klein et al., Investigating variation in replicability, Social Psychology 45 (2014): 13 effects, 36 samples. Simmons, Nelson & Simonsohn, False-positive psychology, Psychological Science (2011). Hagger et al., multilab ego-depletion replication, Perspectives on Psychological Science (2016): 23 labs, d = 0.04, 95% CI −0.07 to 0.15. Ranehill et al. (2015) on power posing; Watts, Duncan & Quan (2018) on the marshmallow test. Henrich, Heine & Norenzayan, The weirdest people in the world?, Behavioral and Brain Sciences 33 (2010). Registered Reports: Center for Open Science (over 300 journals). All simulated numbers are invented illustrations computed live, and a one-person demo is not a study. 🌐 Lakens, Improving Your Statistical Inferences 🌐 MIT OCW 9.00SC Introduction to Psychology 🌐 Center for Open Science: Registered Reports 📘 Morling, Research Methods in Psychology Step 13. Education Systems & Policy Worldwide: The League Table and the Arguments Behind It ------------------------------------------------------------------------------------------- Why: How countries organise schooling, and what comparisons show. Every country runs the same experiment on its children and publishes a different design. The comparisons are real evidence and badly over-read. This piece teaches both halves, and lets each side of the three big fights speak in its own words. On 8 September 2026 the OECD released the results of PISA 2025. More than 760,000 fifteen-year-olds in 91 countries and economies had sat the tests, standing in for about 33 million of their age. Within hours the headlines had a winner (Singapore topped reading; four Chinese provinces and cities combined, Beijing, Shanghai, Jiangsu and Zhejiang, topped maths and science), a loser, and a verdict on every minister. The OECD itself reported that its member countries had reached the lowest average levels it has observed in science, reading and mathematics. Look at the same table another way. Kenya and Rwanda took part, with maths scores of 326 and 312 against an OECD average of 463. Is that a verdict on their teachers? On their wealth? On how many 15-year-olds are in school to be tested at all? The table cannot say. Someone who has studied comparative education reads a league table the way a doctor reads one blood test: as a number worth having, with a long list of things it does not settle. The second half of the subject is the argument. Should children be sorted into different schools early? Should families be able to choose, with public money? How much should be tested, and what should the results cost the people being tested? Serious people hold every side of these, and the evidence is real but narrower than anyone's slogans. The course in one box Who takes itEducation and public-policy students, usually in the final year of a four-year course, and in master's programmes in comparative and international education. Syllabi lean on OECD and UNESCO comparative work (the OECD's Education at a Glance and the PISA reports, UNESCO's Global Education Monitoring Report) beside case studies of individual countries. What it is forUnderstanding how countries organise schooling, what international comparisons can and cannot show, and how to argue about school policy without confusing evidence with values. Comes afterPublic Policy (35/16) and Stratification & Inequality (35/78). Leads toIt closes the Education major. It draws on Assessment & Measurement (36/55), Philosophy & History of Education (36/58), Inclusive & Special Education (36/57) and Classroom Practice & Educational Technology (36/60). What this piece gives youYou will not be able to design a country's school law. You will be able to read a PISA table with its caveats, say what tracking, vouchers and high-stakes testing are meant to do, and state each side's best case. Easier first reads: Social Mobility in 30 Society & Sociology, and the biases in 17 Thinking & Learning. Every system answers the same five questions Schooling looks different everywhere, but the differences come from five choices every government makes. Who runs the schools: the state, local authorities, churches, private operators. Who pays: taxes, fees, or both. Who chooses: the family, or a catchment line on a map. When children are sorted: by 10, 12, 15 or never. How learning is checked: a national exam, school-based judgement, a sample survey. Two systems that look alike on three of these can differ sharply on the other two. SystemA few facts that mark its design FinlandComprehensive schools phased in 1972–77; compulsory schooling starts at 7; teachers hold a master's degree; no high-stakes tests in basic education; the first split, academic or vocational, comes after about age 15. SingaporePrimary national exam (PSLE) after six years. From 2024 the old Express and Normal streams gave way to Subject-Based Banding, with pupils in levels G1, G2 and G3 that can differ by subject. Japan6-3-3-4 structure; nine compulsory years; secondary entry by school admissions exams; roughly six in ten pupils attend private cram schools (juku). NetherlandsA 1917 settlement made religious and other private schools publicly funded; in 1997 more than 70% of pupils were in privately run, publicly funded schools. Tracking is early and has strengthened since the late 1990s. ChileA universal voucher system from 1981; in 2008 a law gave 50% higher vouchers for priority (poorer) students. IndiaThe National Education Policy 2020, approved 29 July 2020, replaced the 10+2 shape with 5+3+3+4 and set mother-tongue teaching through grade 5; the three-language rule is contested, especially in the south. It aims at public spending of 6% of GDP. KenyaFree primary schooling returned in 2003; the 8-4-4 structure (1985) gave way to a competency-based 2-6-3-3-3 curriculum from 2017; exams close primary (KCPE) and secondary (KCSE). Sources in the list at the end. The Singapore, Japan, Finland, India, Kenya and Netherlands entries are dated descriptions of design, not rankings. A league table is a measurement with error bars PISA tests 15-year-olds who are in school, using a sample of schools and pupils in each place. A score is an estimate from that sample, so two neighbours in the ranking a few points apart are, statistically, often tied. The test is also a particular choice: it asks students to apply what they know to unfamiliar problems, not to repeat a national curriculum. TIMSS, which tests 4th and 8th graders on curriculum-linked maths and science, asks something different, and rankings can shift between them. And PISA says nothing about children who are not in school at 15, which matters most where enrolment is lowest. Interactive · PISA 2025 explorer Treat gaps smaller than this as a tie Scores from the OECD's PISA 2025 results (released 8 Sept 2026) as reproduced in the public tables. The tie threshold is your own choice, a stand-in for the margin of error, which differs by country. A * on the United States means a sampling standard was not met. Without JavaScript: PISA 2025 mathematics, OECD average 463: B-S-J-Z 612, Singapore 563, Japan 525, Estonia 508, United States 463, Brazil 377, Kenya 326, Rwanda 312. Notice what the bars do and do not carry. B-S-J-Z is four rich, urban Chinese jurisdictions, not China. Estonia sits near the top of Europe in all three domains. Finland, first in reading and science and second in maths in 2003, scored 474 in reading, 469 in maths and 504 in science in 2025: still above the OECD average in all three, but no longer in the top tier. Compared with 2022, science held broadly steady, but among the 23 OECD countries that took part in both rounds the average fell by 16 points in reading, 11 in maths and 5 in science. What top systems share is less clear than the headlines Every ministry wants to copy a winner. The honest reading is that top performers differ more than they agree. Finland has almost no high-stakes testing before 16 and a master's-level teaching force. Singapore has a national exam at the end of primary school, at about 12. Japan has a tradition of teachers studying lessons together (lesson study) and a large private tutoring industry beside the schools. Estonia, a small country, scores near the top in Europe. Shared features are modest: a well-prepared teaching profession, a coherent curriculum, high expectations. Even those are descriptions of correlation, not tested causes. Comparative scholars warn against "policy borrowing": lifting a feature out of a system whose parts depend on each other. A national exam works differently in a country with strong teacher trust than in one without. The question to ask of any success story is what else was true of that country, and whether the result also appeared before the policy. Tracking: when to sort children, and who sorts them Tracking means separating children into different schools or classes by measured ability. Germany assigns pupils to a secondary school type after about grade 4; the Netherlands and Switzerland sort around the end of primary; Finland waits until about 15; the United States keeps secondary schools comprehensive but sorts inside them with advanced classes. The cross-country evidence that early tracking increases inequality in outcomes is among the stronger findings in the field (Hanushek and Woessmann, 2006), while its effect on the average is unclear. Economists who re-examined that work have questioned how robust the statistical result is. One reason the debate does not settle is that sorting at 10 is a noisy act. The next toy shows how noisy, for a given test reliability. It assumes ability is fixed and that a single test decides, both simplifications: real systems use grades, teacher opinion and parents' choices, and a child's ability changes. Interactive · Sorting with a noisy test Test reliability Share placed in the academic track Computed live from 20,000 simulated pupils with normally distributed ability; observed score = true ability plus test noise. Illustrative reliabilities, not any real exam's. Without JavaScript: with reliability 0.80 and 30% of places academic, about a fifth of the truly top 30% land in the lower track. School choice: vouchers, charters and catchment lines All systems ration places somehow. A catchment line rations by address, which means by house price. School choice rations by family preference: public money follows the child (vouchers), or independent state-funded schools compete with the local ones (charter schools in the US, free schools in Sweden and England, the Dutch system of private schools funded by the state). Defenders and critics both point to evidence, and the evidence differs by country. Predict each result before you reveal it. These are lottery-based or large-scale studies, chosen because they are the best-known tests of the idea. Interactive · Predict, then reveal Make four predictions. Each result is one study in one place and time. Programme design, the quality of the private schools available and the comparison group all matter. Without JavaScript: Colombia (PACES lottery): gains of about 0.2 standard deviations after three years. Chile (1981 vouchers): no clear average gain, more sorting. Louisiana (scholarship lottery): worse test results for winners. Milwaukee: higher graduation and college-going in a 2013 study. Sweden is the most-watched middle case. Its 1992 reform allowed independent schools with public funding; by 2008 over 10% of pupils attended them. One study found competition improved results in nearby public schools; critics, including the researcher Susanne Wiborg, argue the system increased social and ethnic segregation. Both claims can be partly true: a benefit for the average and a cost for the mix. Testing and accountability: what a score can carry Exams do two jobs that pull against each other. They give pupils, parents and governments information; and, when stakes are attached, they steer behaviour. Campbell's law says that the more a number is used for decisions, the more it bends the thing it measures: teaching to the test, narrowed subjects, schools shedding hard-to-teach pupils. Yet the information is valuable. Disaggregated results show which groups are being left behind, and in the US, studies of the 2002 No Child Left Behind law (Dee and Jacob, 2011) found maths gains in the middle grades but not in reading. A single score is also noisy for an individual. If a test has a standard error of measurement of 4 marks and the pass mark is 50, a pupil whose true level is 52 passes only about 69% of the time. A cut score turns a smooth scale into a cliff. Interactive · The cliff at the cut score Test reliability (score spread 10) Each bar: chance a pupil whose true level sits that far from the cut passes on one sitting. SEM = 10 × √(1 − reliability). Normal errors assumed. Without JavaScript: reliability 0.90 gives SEM about 3.2; a pupil 3 marks above the cut passes about 83% of the time. Finland's answer is to hold no high-stakes tests in basic education and to rely on teacher judgement and sample-based checks, concentrating the one big exam (the matriculation exam) at the end of the academic upper secondary track. Singapore, Korea, Japan and China (the gaokao) use exams as gates and have large private tutoring industries around them. These are different bets about whether the information is worth the pressure. Argue it from inside each side A good test of understanding is to state a view you do not hold so its holders agree you got it right. Pick a topic and a side. The tool shows the position as its defenders put it, the evidence they rely on, and what would count against them. Note which parts are about facts and which are about values. Interactive · Both sides, in their own terms Tracking, for: teaching can be pitched to the level; strong pupils are not held back; vocational routes carry dignity. Against: early sorting is noisy and follows family background. Choice, for: families know their children and exit pressure improves schools. Against: skimming and segregation. Testing, for: information makes gaps visible. Against: stakes distort what is measured. What a graduate just sees Every system answers who runs, who pays, who chooses, when to sort and how to check; the answers are linked, so features do not transplant cleanly. A league table is a sample-based estimate: neighbours are often tied, and the table only covers children who are in school and sampled. A top-ranked system is a bundle of choices; ask what else was true of that country, and whether the result predates the policy. Early tracking has a noisy sorter and a family-background tilt; its defenders answer with better-pitched teaching and respected vocational routes. School-choice evidence is genuinely mixed, and the sign depends on the programme, the schools on offer and what the comparison is. A cut score is a cliff on a smooth scale; the more stakes, the more the measure bends. What a test shows (a gap) and what to do about it (a policy) are separate questions; the first is evidence, the second also involves values. Where it shows up next Assessment & Measurement (36/55): reliability, standard error and validity are what sit under every PISA bar and every cut score here. Philosophy & History of Education (36/58): the purposes behind each system, from civic schooling to examination for office, came from earlier ideas about what school is for. Inclusive & Special Education (36/57): tracking and choice rules decide where children with disabilities are taught. Classroom Practice & Educational Technology (36/60): the same comparisons are used in arguments over phones and screens in school. In the world: ministries of education, think tanks and the OECD, UNESCO and World Bank education teams; journalists covering PISA day; school-board debates about enrolment lotteries and exam reform. If you want to go deeper 📘 Textbook. Mark Bray, Bob Adamson and Mark Mason (eds.), Comparative Education Research: Approaches and Methods (Springer, 2nd edition 2014), the standard guide to how comparison is done; and the OECD's annual Education at a Glance, which most comparative-policy syllabi use for the numbers. Check for the current edition. 📘 Gentler. Amanda Ripley, The Smartest Kids in the World (2013), three American exchange students in Finland, Korea and Poland; and Pasi Sahlberg, Finnish Lessons 3.0 (2021), the insider case for the Finnish model. 🌐 Free text. The OECD's PISA results and Education at a Glance are free to read at oecd.org/pisa; the UNESCO Global Education Monitoring Report is at unesco.org/gem-report. 🌐 Free course. The best free substitute is reading country notes side by side: the OECD's PISA 2025 country notes and the UNESCO Global Education Monitoring Report's country profiles, both free online. The takeaway Comparing countries is the only way to see that the way we school children is a choice, and it is a weak way to learn which choice is best. Read a league table as a measurement with error bars, ask what else was true of a winning country, and keep apart what the evidence shows from what a society wants its schools to be for. Try this: take any education headline that cites a ranking and find the actual scores. How far apart are the countries it contrasts, and are they close enough to be tied? Then write the strongest argument against the policy it recommends. Sources & Further Reading Sources. OECD, PISA 2025 Results (Volume I), released 8 September 2026, and the OECD Secretary-General's launch statement of that date; the PISA 2025 country tables as reproduced in public references, retrieved November 2026; Hanushek and Woessmann, "Does educational tracking affect performance and inequality?", Economic Journal, 2006; Duflo, Dupas and Kremer, "Peer effects, teacher incentives and the impact of tracking", American Economic Review, 2011; Oakes, Keeping Track, 1985; Friedman, "The role of government in education", 1955; Hsieh and Urquiola, Journal of Public Economics, 2006; Angrist et al., on Colombia's PACES vouchers, American Economic Review, 2002; Abdulkadiroğlu, Pathak and Walters on the Louisiana Scholarship Program, American Economic Journal: Applied Economics, 2018; Wiborg on Sweden's free schools; Dee and Jacob, Journal of Policy Analysis and Management, 2011; Campbell, 1979; national structure facts from the Finnish, Singaporean, Indian (National Education Policy 2020) and Kenyan government and reference descriptions. Every figure in the interactives was computed in node. This piece reports evidence and takes no side on the policies it describes; a ranking's difference in score is not a measure of how good a teacher or school is. 📘 Bray, Adamson and Mason, Comparative Education Research 📘 Ripley, The Smartest Kids in the World 🌐 OECD PISA Step 14. Stratification & Inequality: Measuring Who Gets What ------------------------------------------------------------- Why: Who gets ahead, and the part schools play. A single number can describe a whole society’s inequality, and hide most of what matters. The skill is knowing what each measure shows, what it leaves out, and where the measuring stops and the arguing begins. Line up every adult on Earth by income, poorest at the left and richest at the right. The World Inequality Report 2022 did exactly that with data for 2021 and found that the poorest half of humanity received about 8.5% of the world's income, while the richest tenth received about 52%. The same line-up for wealth is starker still: the bottom half owned about 2%, the top tenth about 76%. Those two sentences are the whole subject in miniature. They are a measurement: someone had to decide what counts as income, which people to count, and how to compare a Brazilian real with an Indian rupee. They are also a starting point for argument, because people who agree on every digit still disagree about whether such a line-up is a problem, whose fault it is, and what to do. This piece teaches the measuring, and keeps the arguing clearly labelled as arguing. Throughout, the figures carry their year and source. Survey-based inequality statistics are not interchangeable across countries, and the biggest mistake a newcomer makes is to read a table of Gini numbers as if every row were measured the same way. The course in one box Who takes itSociology majors, usually in year 2 or 3. US programmes following the American Sociological Association's guidance on the major, and UK programmes built on the QAA benchmark statement, treat stratification as a core area; economics and public-policy students meet the same data in labour and public economics courses. What it is forDescribing how resources, status and opportunity are spread across people and groups, measuring that spread, and testing explanations for it. Comes afterClassical Social Theory (35/75) and Sociological Research Methods (35/76), with Statistics (34/05) underneath. Leads toRace, Ethnicity & Migration (35/79) directly, and it feeds Public Policy (35/16) and Political Economy (35/17). What this piece gives youYou will not run a household survey. You will be able to read a Lorenz curve and a Gini, say what they hide, tell income from wealth, read a mobility matrix, and compare caste and class. Easier first reads, which this piece does not repeat: Class, Status and Power (30/02), Castes, Estates and Classes (30/03) and Climbing the Ladder (30/04, which covers Chetty's mobility results and the Great Gatsby curve in depth). The Lorenz curve and the Gini: one number for a whole shape Picture the population lined up from poorest to richest. Now plot, for each point along that line, the share of all income held by everyone up to that point. At the left, almost nothing; at the right, 100%. If everyone had the same income the plot would be a straight diagonal. Real societies sag below it. That sagging curve is the Lorenz curve, drawn by the American statistician Max Lorenz in 1905. The Italian statistician Corrado Gini turned the sag into one number in 1912. The Gini coefficient is the area between the diagonal and the Lorenz curve, divided by the whole triangle under the diagonal. Zero means perfect equality; one means one person holds everything. A Gini of 0.30 is not "30% unequal"; it is a way of saying how far the curve bows. Gini = (area between diagonal and Lorenz curve) ÷ (area under the diagonal)0 = everyone equal · 1 = one person has it all · many sources print it ×100, as 41.8 The tool below builds a Lorenz curve from four real-looking points: what the poorest fifth gets, what the richest fifth gets, and what the richest tenth gets. Pick a country preset or drag the sliders yourself. The page computes the curve's Gini from those points; a real national figure uses the whole survey, so the two differ a little. Interactive · Build a Lorenz curve Poorest fifth receives Richest fifth receives Of which, the richest tenth Presets use World Bank Poverty and Inequality Platform shares, latest year available (shown on each button). The curve joins your points with straight lines, so it cuts corners and the estimated Gini comes out several points lower than the official one (which uses the whole survey); the official figure is shown for comparison. Without JavaScript: the US in 2024 (World Bank) had a Gini of 41.8, with the poorest fifth receiving 5.1% of income or consumption and the richest fifth 47.1%. Slovenia in 2023 had 24.7, with 10.0% and 34.8%. Two warnings travel with every Gini. First, it is blind to where on the curve the inequality sits: very different distributions can share the same value. Second, what is being measured matters as much as the arithmetic. Income before or after taxes and transfers, household or per person, income or consumption: each choice moves the number. What the Gini hides: tops, bottoms and the shape between A country can have the same Gini as another and a very different top. This is why researchers also report shares: how much goes to the bottom tenth or fifth, and how much to the top tenth or one per cent. José Gabriel Palma's ratio, the top tenth's share divided by the bottom forty per cent's, was proposed because he found that the middle half of most distributions looks surprisingly alike and the real differences sit in the tails. Surveys have a second problem: the very rich rarely answer them, and when they do they under-report. Researchers at the World Inequality Database (Thomas Piketty, Emmanuel Saez, Gabriel Zucman and colleagues) therefore combine surveys with tax records and national accounts to estimate the top. Their figures for the top are higher than survey-only figures, and the two approaches are an active methodological dispute, not a settled matter. For India, the World Bank's 2023 survey-based Gini of 23.0 is built on consumption, which is much more equal than income; the WID estimates that the top 10% held about 56% of national income in 2014 (Chancel and Piketty, 2019). Both numbers are "right" about different things. Explore a dozen countries below. Switch the measure and see how the order changes. Interactive · Same countries, four measures World Bank Poverty and Inequality Platform, latest survey year per country (year in brackets). Surveys differ: consumption-based for India; income-based for most others. Not strictly comparable. The ratio is the richest fifth's share divided by the poorest fifth's. Without JavaScript: Gini 54.1 (South Africa, 2022), 50.3 (Brazil, 2024), 41.8 (US, 2024), 33.7 (Germany, 2022), 24.7 (Slovenia, 2023). Income is one thing, wealth is another Income is a flow: wages, profits, benefits arriving over a year. Wealth is a stock: houses, savings, shares, pensions, minus debts. Wealth is always more concentrated than income, because it accumulates, it is inherited, and people with spare income can buy assets that grow. Households with big mortgages can have negative net wealth while earning a decent salary, which is why the bottom half's wealth share is near zero. Interactive · Who gets what, income against wealth World Inequality Report 2022 executive summary: global figures for 2021, using market exchange rates adjusted for purchasing power. "Middle 40%" is what remains after the top 10% and bottom 50%. Without JavaScript: global income 2021, top 10% about 52%, bottom 50% about 8.5%; global wealth, top 10% about 76%, bottom 50% about 2% (World Inequality Report 2022). Evidence and argument separate here. The evidence is the distribution. The arguments begin with why: Thomas Piketty's Capital in the Twenty-First Century (2013, English 2014) argued that when the return on capital exceeds economic growth, wealth concentrates. Critics have disputed the data (the Financial Times questioned some of his series in 2014), the law-like claim, and whether returns behave as the theory needs. Defenders replied with revised data and extended series. Economists who study the same figures still disagree on how much comes from technology, trade, taxes, institutions, market power or inheritance. Mobility: the same ladder seen as a matrix A snapshot of inequality does not say how people move within it. If a society is very unequal but everyone's children shuffle freely, a lifetime perspective looks fairer than the snapshot. If the same families stay at the same rungs, the snapshot understates the problem. Sociologists measure movement with a mobility matrix: sort families into fifths by income, sort their grown children the same way, and tabulate where children from each parental fifth end up. Without any movement the matrix would have 100% on the diagonal. If rank were inherited not at all, every cell would show 20%, because each child lands in a random fifth. Real countries sit between. The key parameter is the rank-rank correlation between parents' and children's positions. In Raj Chetty and colleagues' 2014 study of US tax records, it was about 0.34; Chetty et al. also reported that a child born in the bottom fifth had about a 7.5% chance of reaching the top fifth, against 20% under random shuffling. The simple model below, set to 0.34, gives about 8%, close to that observed figure. Interactive · A mobility matrix you can tune Rank-rank correlation (how much rank is inherited) Computed live from a bivariate-normal model of parent and child rank; real matrices are not exactly this shape, and the presets other than 0.34 are illustrative, not measurements. Rows are the parents' fifth (1 = poorest); columns are the child's fifth. Without JavaScript: with a rank correlation of 0.34, a child of the poorest fifth in this model has about an 8% chance of reaching the richest fifth and about 35% of staying in the poorest fifth, against 20% for each under pure shuffling. What the matrix does not tell you is why. Chetty's team found large differences across US places, and the strongest correlates of upward mobility were less segregation, better schools, more two-parent households, and more social ties across class lines. Those are correlates; sociologists and economists debate how far each is cause. And the matrix measures rank, not welfare: a society where everyone is richer can have the same matrix as a stagnant one. The Great Gatsby curve, and why it is a clue and not a verdict Plot countries' inequality against how strongly parental income predicts children's income and you get an upward slope: more unequal countries tend to be less mobile. Alan Krueger named it the Great Gatsby curve in 2012, using Miles Corak's data. Climbing the Ladder (30/04) tells that story and tabulates the numbers; here is what the measurement lens adds. The curve is built from perhaps a couple of dozen rich countries, with inequality measured years before mobility, and with mobility estimates that depend on how each national study defined income and age. The OECD's 2018 report, A Broken Social Elevator?, reported that families at the bottom tenth needed about two generations to reach average income in Denmark, five in the United Kingdom, seven in China and India, nine in Brazil and eleven in Colombia (as reported by secondary summaries of the OECD figures; the OECD's own average across member countries was about four to five). Those are projections from a simple model, not forecasts. The causal reading: when the gaps between rungs are wide, advantaged parents have more to invest and more to lose, so advantage is passed on. Inequality causes immobility. The sceptical reading: a handful of countries is a small sample; a third factor (education systems, labour-market rules, immigration, family structure) could shape both. The correlation may survive without the causal story. Caste and class: two ways to lock a ladder Class is a position you hold; caste is a category you belong to. In the sociological sense, a caste system fixes membership at birth, restricts marriage to within the group (endogamy), links rank to ideas of purity or worth, and in its strict forms limits the occupations open to each group. A class system has none of these formal locks: in principle anyone may move, and the ladder is made of money, schooling and connections. Real societies are mixtures, and every comparison is partial. SystemFixed at birth?MarriageLegal status today Modern class (most countries)No, but parents' position predicts stronglyFree, with class homogamy in practiceFormally equal citizens Caste in India (jati, within the four varna)YesMostly within the group (endogamous)Untouchability abolished by Article 17 of the 1950 Constitution; affirmative-action quotas for Scheduled Castes and Tribes Estates (France before 1789)Yes, with limited ennoblementRank-matched in practiceAbolished 1789 Burakumin in JapanDescent-based stigmaDiscrimination in marriage documentedStatus abolished 1871; remedial laws 1969 to 2002; Act to promote elimination of discrimination, 2016 Race as "caste" (US, apartheid South Africa)Yes, by law in the pastBanned across lines, now struck down or repealedLegal bars removed (US 1960s, South Africa 1991); gaps persist Take India, where the evidence is richest. In the 2011 census Scheduled Castes were 16.6% of the population and Scheduled Tribes 8.6%. India has not published a full caste census since 1931; Bihar's state survey (published October 2023) counted about 63% of its people as Other Backward Classes or Extremely Backward Classes and about 19.7% as Scheduled Castes, and in April 2025 the national government announced that caste would be enumerated in the next census. Research on mobility finds both change and persistence. Hnatkovska, Lahiri and Paul (2013) found that gaps in education and wages between Scheduled Castes and Tribes and others narrowed between 1983 and 2005; a correspondence study by Thorat and Attewell (2007) sent matched job applications with names signalling caste or religion and found that employers called back applicants with Dalit or Muslim names less often. The tool below shows the arithmetic that makes group inequality persist even when within-group variation is huge. It is a pure statistical illustration of how a gap in group averages turns into over- and under-representation at the top and bottom. It does not say what causes any real gap. Interactive · A gap in averages, a gap at the extremes Group B's share of the population Gap in average position (in standard deviations) Illustrative model: both groups have normally distributed outcomes with the same spread, and Group B's average is lower. No real dataset; it shows how averages and tails relate. Without JavaScript: with a 20% group whose average sits half a standard deviation lower, that group makes up about 32% of the poorest fifth and about 10% of the richest fifth. Does the quota system answer the problem it addresses? Here the evidence and the positions come apart. Defenders of caste-based reservations argue that exclusion was by group, so remedy must be by group; that representation in universities, government and politics matters in itself; and that Scheduled Caste graduates still face discrimination in hiring. Critics offer several different objections: that class-based criteria would target need better, that a "creamy layer" within backward groups captures the benefits (the Supreme Court's 1992 Indra Sawhney ruling excludes it for OBC quotas and capped reservations at about 50%), or that a merit principle should govern selection. India added a 10% quota for economically weaker sections of the unreserved categories in 2019; the Supreme Court upheld it by a 3 to 2 majority in November 2022. These are arguments about justice, and the data in this section can inform each side without deciding between them. B. R. Ambedkar's Annihilation of Caste (1936, written for a conference that cancelled his speech) argued that caste could not be treated as a mere economic layer, because it divides labourers from one another and is sustained by belief; many Marxist writers in India held that class struggle was primary and caste a form of it. The disagreement is still live in the field: is caste a status order, a class order, or both? Measuring is not deciding The facts above are compatible with several philosophies of what, if anything, to do. A graduate keeps them separate and can state each one fairly: Egalitarian. Inequalities that come from luck, birth or circumstance are unjust (luck egalitarians such as G. A. Cohen and Ronald Dworkin), or large gaps corrode equal standing among citizens (relational egalitarians such as Elizabeth Anderson). Look at the gaps and at how they arose. Prioritarian and Rawlsian. Benefits to the worst off count for more; for John Rawls (1971), inequalities are justified only if they improve the position of the least advantaged. Look at the bottom. Sufficientarian. Harry Frankfurt argued that what matters morally is that everyone has enough, not that everyone has the same. Look at whether anyone falls below the line. Entitlement (libertarian). For Robert Nozick (1974), a distribution is just if it came about through just acquisition and voluntary transfer, whatever pattern results. Look at the process, not the shape. Desert and meritocratic. Rewards should track effort and contribution; the target is unfair barriers, not unequal outcomes. Michael Young, who coined "meritocracy" in 1958, meant it as a warning that a society which believes its ranking is earned will treat the bottom harshly. Each position has serious critics, and each looks at different statistics. A top-share figure speaks most to the egalitarian; a poverty line to the sufficientarian; a mobility matrix to the meritocrat. When a speaker moves from "the gap is X" to "so we must Y" without saying which philosophy carries the step, the second part is not a finding. What a graduate just sees A Gini is one number for a whole curve; two countries can share it and differ at the top or the bottom. Before comparing two inequality figures, ask: income or consumption, before or after tax, household or person, which year, which survey. Surveys miss the very rich; tax-based estimates of top shares are higher, and that method dispute is real. Wealth is much more concentrated than income, worldwide: about 76% of it sits with the top tenth, against about 52% of income (2021). Mobility is a matrix, not a slogan: ask where children of the poorest fifth end up, and compare that with 20% under pure shuffling. A gap between group averages produces big gaps in the tails, even with huge overlap. Caste and class overlap but differ: one is a category fixed at birth and marriage, the other a position. "The gap is this" and "so we should do that" are different sentences, and the second always needs a value premise. Where it shows up next Race, Ethnicity & Migration (35/79): the group gaps here are measured with categories that were themselves made, which is the next piece's subject. Public Policy (35/16) and Political Economy (35/17): tax and transfer design, minimum wages and affirmative action all come from this evidence plus a value judgement. Statistics (34/05): the survey weights, confidence intervals and rank correlation behind every table above. In the world: the World Bank's inequality tables, the OECD's Society at a Glance, an economist's wealth-tax proposal, an Indian court case on quotas. If you want to go deeper 📘 Textbook. David Grusky (ed.), Social Stratification: Class, Race, and Gender in Sociological Perspective (Routledge/Westview, several editions), the standard reader; and the free OpenStax Introduction to Sociology (3rd ed.), chapters on global and US stratification. 📘 Textbook for the numbers. Anthony Atkinson, Inequality: What Can Be Done? (Harvard University Press, 2015), a careful economist's account with proposals clearly marked as proposals. 📘 Gentler. Branko Milanovic, Global Inequality: A New Approach for the Age of Globalization (Harvard University Press, 2016), which explains the elephant chart and the world's income ladder. 🌐 Free data. World Inequality Database, Our World in Data on economic inequality, and Opportunity Insights for US mobility atlases. 🌐 Free course. MIT OpenCourseWare 14.74 Foundations of Development Policy (Spring 2009) for how poverty and inequality are measured in developing countries. The takeaway Inequality is measured with curves, shares and matrices, and each hides something: the Gini hides the shape, surveys hide the very rich, snapshots hide movement. The same figures sit under several moral philosophies, so a good sociologist reports the gap, says how it was measured, and labels the step to "should" as a different kind of claim. Try this: pick one inequality statistic you have seen in the news and find out its year, its unit (income, consumption or wealth), its source and what it leaves out. Sources & Further Reading Sources. World Bank Poverty and Inequality Platform, indicators SI.POV.GINI and SI.DST.* (latest survey year per country, retrieved November 2026). World Inequality Report 2022 (Chancel, Piketty, Saez, Zucman), executive summary: global income and wealth shares for 2021. Chancel and Piketty, "Indian income inequality, 1922–2015" (2019). Chetty, Hendren, Kline and Saez, Quarterly Journal of Economics 2014 (rank-rank 0.34; 7.5%). Krueger 2012 and Corak 2013 on the Great Gatsby curve. OECD, A Broken Social Elevator? (2018). Hnatkovska, Lahiri and Paul, Journal of Human Resources 2013. Thorat and Attewell, Economic and Political Weekly 2007. Census of India 2011; Bihar caste-based survey (October 2023); Government of India decision of 30 April 2025. Indra Sawhney v. Union of India (1992); Janhit Abhiyan v. Union of India (2022). Ambedkar, Annihilation of Caste (1936). Rawls 1971; Nozick 1974; Frankfurt 1987; Young 1958. 📘 Grusky (ed.), Social Stratification 📘 Milanovic, Global Inequality 🌐 World Inequality Database