Primary 2 Mathematics Diagnostic: Finding the First Broken Number Concept

A Primary 2 learner writes:

302 − 87 = 285.

The obvious response is:

“The child cannot subtract with regrouping.”

That may be true.

It may also be the wrong diagnosis.

The learner might not understand that 302 means 3 hundreds, 0 tens and 2 ones. The child might understand place value but not exchange one hundred for ten tens. The learner might perform the exchange correctly with blocks but lose it in written notation. The child might know the subtraction procedure but copy 87 as 17. The learner might simply have made one calculation slip.

A wrong Primary 2 answer is evidence of failure somewhere in the chain. Diagnosis is the work of finding where the chain first became unreliable.

This is why a useful Mathematics diagnostic is not merely a harder worksheet.

It is a sequence of discriminating questions.

Each question should help separate possible causes.

The goal is not to discover how many questions the learner can fail.

The goal is to find the first broken number concept that later work is being forced to compensate for.

The quick answer: Primary 2 diagnosis should move from foundation to transfer

A strong Primary 2 diagnostic asks four layers of question.

1. Concept: Does the learner understand the mathematical relationship?
2. Representation: Can the learner recognise and rebuild the relationship with objects, diagrams, words and symbols?
3. Procedure: Can the learner execute the required calculation accurately?
4. Transfer: Can the learner select the correct relationship when no worksheet heading announces the method?

These layers should be tested in that order whenever possible.

If the concept is weak, drilling the procedure may only hide the problem.

If the concept is strong and the procedure is weak, rebuilding the entire concept may waste time.

If both are strong but transfer is weak, the learner needs method-selection practice, not more blocked exercises.

Primary 2 is where the number system becomes more demanding

The updated October 2025 Singapore Primary Mathematics syllabus expands several dimensions at once in Primary 2.

• Whole numbers extend to 1000.
• Addition and subtraction use algorithms up to 3 digits.
• Multiplication tables of 2, 3, 4, 5 and 10 become explicit.
• Division notation and the multiplication–division relationship become formalised.
• Fractions become part of a whole, with unit fractions and like fractions compared and ordered.
• Money moves into dollars-and-cents decimal notation.
• Measurement expands to metres, grams, kilograms and litres.
• Time moves to the minute and to hours-and-minutes conversion.
• 3D shapes enter the formal geometry list.
• Picture graphs introduce scales.

The learner is therefore managing more than larger numbers.

Primary 2 increases the number of units, representations, inverse relationships and multi-step decisions that must stay coordinated.

That is why a small weakness from Primary 1 can suddenly become visible.

Primary 2 is often where a hidden misconception stops being cheap.

The first diagnostic question: can the learner still see quantity underneath the numeral?

Show 347.

Ask:

• How many hundreds?
• How many tens?
• How many ones?
• Can you build it with base-ten blocks or drawings?
• Can you rename it another way?

Expected structure:

347 = 3 hundreds + 4 tens + 7 ones.

But it can also be renamed:

2 hundreds + 14 tens + 7 ones.

Or:

3 hundreds + 3 tens + 17 ones.

If the learner treats 347 only as the spoken word “three hundred and forty-seven”, written algorithms will eventually become rule-following without unit meaning.

Renaming is one of the most important diagnostic windows in Primary 2 because regrouping depends on it.

Misconception 1: each digit keeps its face value regardless of place

In 347, the learner says the 3 is worth 3, the 4 is worth 4 and the 7 is worth 7.

This is a place-value failure.

Diagnostic test: compare the value of the digit 4 in 347 and 407.

In 347, 4 is worth 40.

In 407, 4 is worth 400.

The digit is the same.

The place changes.

The value changes.

Do not repair this with more column addition.

Repair positional value first.

Misconception 2: zero means “nothing important” inside a numeral

In 302, the zero records zero tens.

Without the zero, 32 would represent a different number entirely.

Diagnostic test: ask the learner to build 302, 320 and 32 and explain the difference.

If the child treats 302 as “three hundred and two” correctly in speech but cannot represent the empty tens place, written regrouping across zero will become fragile.

Zero can indicate an empty place while still being essential to the numeral’s structure.

Misconception 3: regrouping changes the number

The learner believes:

1 hundred + 2 tens

becomes a different total when one hundred is exchanged for ten tens.

But:

1 hundred = 10 tens.

So:

1 hundred + 2 tens = 12 tens.

The representation changes.

The value does not.

Diagnostic test: use base-ten blocks and ask the learner to exchange one hundred flat for ten ten-rods, then recount total value.

This concept is the load-bearing beam under both addition carrying and subtraction borrowing.

Misconception 4: “carrying” is moving a small 1 because the rule says so

Consider:

48 + 27.

Eight ones + seven ones = fifteen ones.

Fifteen ones can be renamed as:

1 ten + 5 ones.

The “carried 1” is therefore not one extra unit.

It is one ten.

Diagnostic test: ask the learner what the carried digit is worth.

If the answer is “one”, procedure has outrun place value.

Misconception 5: “borrowing” means taking a digit temporarily

Consider 52 − 28.

Two ones cannot remove eight ones within whole-number subtraction.

Rename one ten as ten ones.

52 becomes:

4 tens + 12 ones.

Now:

12 − 8 = 4 ones.

4 tens − 2 tens = 2 tens.

Answer:

24.

The mathematics is exchange, not debt.

Language such as “borrowing” can be retained if familiar, but it should not replace the place-value mechanism.

Misconception 6: column alignment is a handwriting convention

When adding or subtracting 3-digit numbers, digits must align by place value.

For:

326 + 48,

the 8 belongs under the ones digit 6, and the 4 belongs under the tens digit 2.

If a learner writes 48 under 326 beginning at the hundreds column, the calculation becomes a different number problem.

Diagnostic test: ask the learner to label H, T and O before calculating.

Column alignment is positional meaning made visible.

Misconception 7: a correct algorithm proves place value is secure

A child may execute 456 + 278 correctly from memorised steps.

Then ask:

“Why did the 1 move into the hundreds column?”

If the learner cannot explain, the algorithm may be procedural rather than conceptual.

Transfer test: present the same addition with base-ten blocks or expanded form.

The concept should survive the representation change.

Misconception 8: mental calculation means doing the written algorithm in the head

Primary 2 includes mental calculation with 3-digit numbers and ones, tens or hundreds.

A learner should be able to use place-value structure.

Example:

347 + 20.

Twenty is 2 tens.

347 has 4 tens.

4 tens + 2 tens = 6 tens.

Answer:

367.

If the learner mentally runs a full vertical algorithm for every problem, efficiency is limited.

Diagnostic teaching should ask whether place-value units can be manipulated directly.

Misconception 9: multiplication tables are unrelated memory lists

Primary 2 formalises the 2, 3, 4, 5 and 10 multiplication tables.

A child who memorises them as five separate chants carries a larger memory burden than necessary.

Relationships include:

• 4-times facts can be double the 2-times facts;
• 5-times facts can be related to half of 10-times facts;
• 3-times facts can be built from 2-times plus one more group;
• commutativity links reversed factors.

Diagnostic test: ask how the learner would find 4 × 7 if the fact were forgotten.

A learner with structure has a recovery route.

Misconception 10: multiplication means repeated addition with any groups

Multiplication begins from equal groups.

If three baskets contain 2, 4 and 5 apples, one simple multiplication fact does not describe the total.

Diagnostic test: mix equal-group and unequal-group situations and ask which can be represented by one multiplication expression.

The child should identify what quantity repeats.

Misconception 11: division means only sharing

Primary 2 learners need the multiplication–division relationship, and division has two important early meanings.

• sharing — number of groups known, group size unknown;
• grouping — group size known, number of groups unknown.

Diagnostic pair:

“18 sweets shared among 3 children.”

“18 sweets packed 3 per bag.”

Both use 18 ÷ 3 = 6.

The quotient counts different things.

Ask the learner to name the answer unit.

Misconception 12: multiplication and division facts must be memorised separately

If 5 × 6 = 30, then:

• 6 × 5 = 30;
• 30 ÷ 5 = 6;
• 30 ÷ 6 = 5.

Diagnostic test: give one multiplication fact and ask for the related division facts.

If the learner knows the product but cannot reverse it, inverse understanding or reverse-direction retrieval needs work.

Misconception 13: a larger denominator means a larger unit fraction

Compare:

1/3 and 1/5 of the same whole.

A learner may say fifths are larger because 5 is greater than 3.

For unit fractions of the same whole, more equal parts means each part is smaller.

So:

1/3 > 1/5.

Diagnostic test: partition two equal paper strips into thirds and fifths.

Ask which single part is larger.

The visual model should expose the denominator’s meaning.

Misconception 14: fractions can be compared without checking the whole

Half of a small chocolate bar can be less than one third of a much larger chocolate bar.

Fraction size depends on the reference whole.

Diagnostic test: show 1/2 of a small strip and 1/3 of a large strip.

Ask whether the denominators alone can decide which physical piece is larger.

The learner must first establish a common whole when making the usual same-whole fraction comparison.

Misconception 15: like-fraction addition means add numerator and denominator

A learner writes:

2/7 + 3/7 = 5/14.

The denominator describes the size of the equal parts.

When the parts are already the same size, combining them changes how many parts we have, not the size of each part.

So:

2/7 + 3/7 = 5/7.

Diagnostic test: use a strip divided into sevenths and physically combine two sevenths with three sevenths.

The unit fraction remains one seventh.

Misconception 16: $2.05 and $2.50 are nearly the same because the digits are the same

Money decimal notation is a place-value test.

$2.05 = 205 cents.

$2.50 = 250 cents.

Diagnostic test: convert both amounts to cents and compare.

If conversion succeeds but decimal reading fails, the issue is notation rather than money value.

Misconception 17: change is whatever coins are returned

Change is the difference between payment and price.

Diagnostic test: remove physical coins and use only:

price = $3.70, payment = $5.00.

Ask for the change, then check:

price + change = payment.

This separates monetary representation from subtraction structure.

Misconception 18: a clock numeral gives the minute value directly

Minute hand at 4 does not mean 4 minutes.

It means 20 minutes because each large numeral marks 5 minutes around the 60-minute cycle.

Diagnostic test: label the minute values around a clock face, then remove some labels and ask the learner to reconstruct them.

Misconception 19: time notation behaves like a base-ten number

3:50 to 4:10 is not found by ordinary subtraction of 410 − 350.

One hour is 60 minutes, not 100.

Diagnostic test: ask the learner to bridge:

3:50 → 4:00 = 10 min.

4:00 → 4:10 = 10 min.

Total = 20 min.

The issue is unit structure, not subtraction ability.

Misconception 20: the biggest numeral means the biggest measurement

900 g versus 1 kg.

80 cm versus 1 m.

The units must be aligned before comparing.

Diagnostic test: present several mixed-unit pairs and ask the learner to state the conversion before deciding which is greater.

This reveals whether the child treats units as mathematical information or decorative labels.

Misconception 21: the object determines the unit

A bottle can be measured for:

• height;
• mass;
• liquid volume.

The question determines the attribute.

Diagnostic test: keep one object fixed and ask three different measurement questions.

If the learner always chooses the same unit, attribute selection is weak.

Misconception 22: a tall liquid level means more liquid

The same amount of water can stand higher in a narrow container and lower in a wide container.

Diagnostic test: pour the same measured amount between containers and ask whether volume changed.

This is a conservation task.

Appearance should not override measured quantity.

Misconception 23: picture graphs can be read without checking the scale

Primary 2 picture graphs include scales.

If one symbol represents 2 children, five symbols represent 10 children.

A child who simply counts icons will underread the frequency.

Diagnostic test: show two graphs with identical icon counts but different scale keys.

Ask whether the data totals are the same.

The key is part of the representation.

Misconception 24: 3D shapes are classified by the object they resemble

A child says:

“This is a can shape.”

Everyday analogy is useful.

Mathematics needs properties.

The current Primary 2 syllabus includes cube, cuboid, cone, cylinder and sphere.

Diagnostic test: show unfamiliar objects or idealised solids and ask the learner to classify by faces, curved surfaces, edges and vertices at an appropriate level.

The class should survive a change in colour, size and orientation.

Misconception 25: every wrong word problem is an arithmetic weakness

A learner calculates accurately once an equation is provided but cannot translate the story.

The arithmetic is not the first broken step.

The difficulty may lie in:

• language comprehension;
• quantity identification;
• operation meaning;
• multi-step planning;
• representation choice.

Diagnostic test: read the problem aloud, ask the learner to draw or build it, then provide the equation if necessary.

Observe where performance recovers.

Misconception 26: a keyword chooses the operation

“Each means multiply.”

“Left means subtract.”

“Altogether means add.”

These shortcuts sometimes work and sometimes fail.

Diagnostic test: use matched problem pairs containing similar vocabulary but different quantity structures.

Ask the learner to represent before calculating.

The operation should be chosen from the relationship among quantities.

Misconception 27: if the procedure works on a blocked worksheet, the concept transfers

A page titled “Subtract with Regrouping” removes method selection.

A page titled “5 Times Table” removes fact-family selection.

A section titled “Money” announces the unit system.

Transfer requires mixed conditions.

Diagnostic test: mix one regrouping question, one multiplication fact, one fraction comparison, one money item and one measurement item without headings.

Ask the learner to choose the representation and method.

This reveals whether knowledge can be selected, not merely executed.

The most useful diagnostic principle: change one demand at a time

If a learner fails a question involving unfamiliar language, large numbers, a new diagram and regrouping simultaneously, the error is hard to interpret.

A better diagnostic holds most conditions stable and changes one variable.

• Same number, different place-value representation.
• Same calculation, with and without regrouping.
• Same multiplication fact, bare and inside a story.
• Same fraction values, same whole and different whole.
• Same money value, cents-only and decimal notation.
• Same time interval, clock face and timeline.
• Same measurement attribute, different unit scales.
• Same data, different picture-graph scale.

The first change that causes performance to break gives high-value evidence.

A 30-minute Primary 2 diagnostic sweep

This is not a standardised assessment and should not be treated as one.

It is a teaching diagnostic designed to identify which domain deserves deeper follow-up.

Minutes 1–5: place value and renaming

• Build 347.
• State the value of each digit.
• Rename 347 with one fewer hundred.
• Compare 302, 320 and 32.

If this layer is weak, pause before interpreting later algorithms.

Minutes 6–10: addition and subtraction

• Solve one 3-digit addition without regrouping.
• Solve one with regrouping.
• Explain what the carried unit represents.
• Solve one subtraction with exchange.
• Check with the inverse operation.

Separate execution from unit meaning.

Minutes 11–15: multiplication and division

• Build 4 groups of 6.
• Write the multiplication fact.
• Derive a nearby fact.
• Write the two related division facts.
• Distinguish sharing from grouping.

Observe whether the learner owns equal-group structure or only table chants.

Minutes 16–19: fractions

• Show 1/3 and 1/5 of equal strips.
• Compare them.
• Ask why the whole matters.
• Add like fractions with a visual model.

Observe denominator meaning and part–whole stability.

Minutes 20–22: money

• Read $2.05 and $2.50.
• Convert $1.35 to cents.
• Find change from one simple purchase.

Observe unit alignment and decimal notation.

Minutes 23–25: time

• Read an analogue clock to the minute.
• Find a short duration crossing an hour boundary.
• Convert 1 h 20 min to minutes.

Observe hand roles, 60-minute conversion and interval reasoning.

Minutes 26–28: measurement and geometry

• Choose units for three different attributes.
• Compare 1 m and 85 cm.
• Classify one familiar and one rotated 3D object representation.

Observe unit choice and property-based classification.

Minutes 29–30: scaled picture graph

• Read the key.
• Find one category frequency.
• Find a difference or total.

Observe whether scale is integrated into the representation.

Do not keep testing after the boundary is already clear

Suppose a learner cannot explain 347 as hundreds, tens and ones.

There is little diagnostic value in immediately presenting a page of 3-digit regrouping.

The place-value prerequisite already deserves repair.

Likewise, if the learner understands place value and executes regrouping accurately but fails a word problem, stop repeating calculation questions.

The new diagnostic target is translation or method selection.

A good diagnostic is efficient because it stops once the next useful teaching question becomes visible.

Use a discrimination question, not a vague request to “try again”

If a learner gets 302 − 87 wrong, ask:

“Can you build 302 and exchange one hundred for ten tens?”

If yes, ask the learner to perform the subtraction with blocks.

If that succeeds, move to a place-value chart.

If that succeeds, return to the written algorithm.

Each step removes one possible cause.

“Try again” gives the learner another attempt.

A discrimination question gives the teacher new information.

Record the first incorrect transformation

Consider a multi-step solution.

The final answer may be wrong because of an error in the first line.

Everything after that may be internally consistent with the wrong state.

So diagnostic review should trace backwards until the first unjustified or incorrect transformation appears.

Examples:

• wrong number copied;
• wrong operation selected;
• unit converted incorrectly;
• place-value exchange misapplied;
• fraction whole changed;
• graph scale ignored.

The first broken step is more useful than the last wrong answer.

Confidence can help prioritise repairs

Ask after selected answers:

“Did you know, work it out, or guess?”

High-confidence wrong answers can indicate stable misconceptions.

Hesitant correct answers may indicate emerging but fragile knowledge.

Confident correct answers that survive a representation change provide stronger evidence.

Confidence should never replace mathematical evidence.

It can help decide what to investigate first.

Immediate repair is not proof of durable learning

A learner receives help and answers the next question correctly.

Good.

But what has been demonstrated?

Possibly only supported performance.

Retest:

• later in the lesson;
• on another day;
• with a changed representation;
• inside a mixed problem set;
• without the prompt that triggered the repair.

Durable learning should survive reduced assistance.

Transfer should survive a changed surface.

A diagnostic should eventually observe both.

The repair cycle: reveal, discriminate, rebuild, fade, retest

1. Reveal the current idea

Ask for explanation, drawing or model before correction.

2. Discriminate among causes

Use the smallest question that separates competing explanations.

3. Rebuild the missing relationship

Connect concrete, pictorial, verbal and symbolic forms.

4. Fade unnecessary support

Move from blocks to diagrams to mental reasoning when the learner is ready.

5. Retest later and differently

Check whether the repair survives delay and transfer.

This cycle is more reliable than correction followed immediately by another nearly identical question.

What parents should ask after a Primary 2 mistake

• What does each number refer to?
• Can you show the number with hundreds, tens and ones?
• What unit are we using?
• Can you draw the equal groups?
• What does the denominator tell us?
• What does the answer count?
• Can you solve it another way?
• How can you check using the inverse operation?
• What stayed the same when we changed the representation?

These questions are more useful than:

“Why were you careless?”

Carelessness is sometimes real.

It should be a conclusion supported by evidence, not the default explanation for any wrong answer.

What tutors should record

• the exact task;
• the learner’s response;
• the representation available;
• the first wrong or unsupported step;
• the learner’s explanation;
• the competing hypotheses;
• the discriminating question used;
• which support restored performance;
• whether the learner could repeat independently;
• what should be retested later.

A note such as:

“Subtracts correctly with blocks after exchange but loses the exchange when recording across a zero tens place”

is far more useful than:

“Weak in subtraction.”

The first note suggests a targeted next lesson.

The second is only a label.

What a Primary 2 diagnostic cannot prove

Educational tasks can reveal patterns in mathematical performance.

They do not diagnose dyscalculia, dyslexia, ADHD, anxiety, memory disorders or other clinical conditions.

Performance can vary with fatigue, language, familiarity, attention, teaching history and the supports available.

A persistent and broad difficulty may warrant appropriate professional discussion.

The Mathematics diagnostic should remain within its scope:

What mathematical relationship is secure, what is not yet secure, and what evidence would change that conclusion?

How this fits Singapore Primary 2 Mathematics

The MOE Primary Mathematics framework places problem solving at the centre, supported by concepts, skills, processes, metacognition and attitudes.

That matters for diagnosis because a learner can possess one component without the others.

A child may know a concept but lack fluency.

A child may execute a procedure but fail to select it.

A child may read a representation but fail to explain it.

A child may solve a familiar example but fail a near-transfer version.

Primary 2 content across number, fractions, money, measurement, geometry, time and data should therefore be diagnosed as a connected system rather than as a set of chapter scores.

How do we know developmental progressions matter?

Evidence-informed early-mathematics guidance from the Institute of Education Sciences and the Education Endowment Foundation describes learning in terms of developmental progressions, connected representations and deliberate movement from concrete experiences toward increasingly abstract reasoning.

These progressions are not rigid ladders that every child climbs identically.

They are useful because they identify prerequisite relationships.

If a learner cannot rename 302 across hundreds, tens and ones, regrouping has no stable base.

If equal groups are not understood, multiplication tables become detached memory.

If the whole is not fixed, fraction comparison becomes unsafe.

If units are not aligned, money and measurement comparisons become meaningless.

Diagnosis is the practical use of those dependency relationships.

The Primary 2 dependency map

A simplified map looks like this:

Primary 1 quantity and tens/ones → hundreds/tens/ones → renaming → regrouping → reliable 3-digit algorithms.

Another branch:

equal groups → repeated addition and arrays → multiplication tables → division sharing/grouping → multiplication–division inverse fluency.

Another:

part–whole reasoning → unit fractions → same-whole comparison → like-fraction addition and subtraction.

Another:

unit value → dollars and cents → decimal money notation → comparison and change.

Another:

attribute → unit → instrument → measurement → comparison → reasonableness.

Another:

clock reading → minute resolution → hours/minutes conversion → duration.

And:

one-picture-one-object graph → scale key → scaled frequency → comparison and total.

These branches interact.

A money problem may require subtraction and unit conversion.

A graph question may require multiplication by the scale and subtraction as difference.

A word problem may require multiplication but fail because equal-group language was not recognised.

This is why the first broken concept can live several steps away from the final worksheet topic.

A Primary 2 readiness checkpoint before moving on

• Can numbers to 1000 be read, built and renamed?
• Can the learner explain the value of each digit?
• Can regrouping be explained as exchange?
• Can 3-digit addition and subtraction be executed accurately?
• Can mental calculation use place-value units directly?
• Can multiplication be represented as equal groups and arrays?
• Can tables of 2, 3, 4, 5 and 10 be retrieved or reconstructed?
• Can sharing and grouping division be distinguished?
• Can multiplication and division facts be used as inverses?
• Can unit fractions be compared for the same whole?
• Can like fractions be added and subtracted without changing the denominator unit?
• Can dollars and cents be read in decimal notation and converted to cents?
• Can simple change be found and checked?
• Can time be read to the minute and durations found across an hour boundary?
• Can hours and minutes be converted appropriately?
• Can length, mass and liquid volume be distinguished?
• Can sensible units and instruments be selected?
• Can 3D shapes be classified by properties rather than appearance?
• Can picture-graph scales be read and applied?
• Can mixed word problems be solved without keyword hunting?

No learner needs perfect speed on every item before progressing.

The question is whether the dependency network is strong enough that Primary 3 can extend it rather than continually rebuild it.

The deeper lesson: diagnosis protects later learning from hidden debt

A learner can compensate for a weak concept for surprisingly long.

Count every multiplication fact from repeated addition.

Memorise regrouping marks without understanding exchange.

Guess fraction size from denominator numerals.

Ignore units until the last line.

These workarounds can survive easy worksheets.

Then later mathematics increases scale, combines topics and removes familiar cues.

The workaround collapses.

That is why Primary 2 diagnosis is valuable even when marks are acceptable.

It checks whether the learner is building real mathematical assets or accumulating hidden conceptual debt.

The best time to repair a broken number concept is before a later procedure learns how to hide it.

Where this leads next

Primary 3 extends the number system again.

Whole numbers grow to 10,000.

Multiplication and division become more demanding.

Fractions and decimals expand.

Time problems become more complex.

Area, perimeter, angles and bar graphs introduce new representations.

The learner who enters Primary 3 with dependable place value, multiplicative structure, unit discipline and representation transfer will have a very different experience from a learner carrying memorised procedures over unstable concepts.

The next diagnostic question is therefore:

Which Primary 2 relationships can this learner still reconstruct when the familiar cue, diagram or chapter heading disappears?

That is the knowledge worth carrying forward.

For the wider Primary Mathematics map, see eduKateSG’s How Mathematics Works resources.

Final thought

A Primary 2 test can tell us that a child scored 72%.

That number is useful.

It does not tell us whether the missing 28% came from one deep misconception or seven unrelated slips.

It does not tell us whether regrouping is understood or merely performed.

It does not tell us whether a table fact is known directly, reconstructible, or guessed.

It does not tell us whether a money error is arithmetic or unit confusion.

Diagnosis asks for that missing resolution.

And once the first broken concept is found, “weak at Primary 2 Mathematics” becomes something smaller, more precise and more teachable.

The purpose of diagnosis is not to describe the child with a score. It is to identify the earliest mathematical relationship that must become dependable next.

Sources and further reading

• Singapore Ministry of Education — Primary Mathematics Syllabus, updated October 2025
• Institute of Education Sciences — Teaching Math to Young Children
• Education Endowment Foundation — How Children Learn Maths
• Education Endowment Foundation — Use Manipulatives and Representations to Develop Understanding