Teaching Reading & Mathematics: The Two Subjects Every School Must Get Right

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.

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).

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.

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.

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:

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.

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.

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.

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.

Question	Kind	Where things stand
Does systematic phonics help early word reading?	Evidence	Yes, on average; size debated
Do poor readers guess from context?	Evidence	Skilled readers do not; guessing is a weak strategy
Is unassisted discovery as good as explicit teaching?	Evidence	Generally no; guided discovery does better
Is fluency or understanding the point of school maths?	Value	Both, in different proportions
Should teachers choose their own method?	Value	Judgement 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.