Two children have five shells each. One arrangement is a straight row. The other is spread across the table. A child points to the spread-out set and says, “That one has more.”
An adult can correct immediately: “No, they both have five.” Or the adult can turn the mistake into a mathematical comparison. “It looks longer, doesn’t it? Let’s match one shell from this row with one shell from that row.” The children pair the shells. Nothing is left unmatched. The adult asks, “What stayed the same even though we spread them out?”
The lesson is bigger than counting to five. The children are learning that mathematical objects can be compared by properties; that appearance can mislead; that one-to-one matching can test a claim; that same number does not mean same shape; and that a relationship can remain invariant when an arrangement changes.
This kind of learning sits near the centre of early mathematics. Before children manipulate formal symbols fluently, they need repeated opportunities to notice relationships: more and fewer, equal and unequal, longer and shorter, heavier and lighter, before and after, inside and outside, same and different, repeating and growing patterns, whole and part. The Education Endowment Foundation’s Early Years Evidence Store identifies “supporting children to make comparisons and connections” as one of five evidence-informed early-mathematics approaches. It emphasises manipulatives, mathematical language, comparison, pattern, sequence, spatial reasoning, composing and decomposing, and educator thinking aloud.
The evidence needs a careful reading. There is no single “comparison technique” that guarantees a fixed amount of progress. Many studies evaluate combinations of practices inside wider curricula. The useful claim is narrower: early mathematics improves when adults deliberately help children inspect relationships and connections rather than treating number learning as a sequence of isolated facts and counting routines.
This article owns one canonical job on eduKateSG: early mathematical comparison and connection—how children learn to detect, describe, represent and test relationships such as same/different, more/less, order, pattern, spatial relation and part–whole structure before and alongside formal arithmetic. It does not own early number fluency, guided play, mathematical vocabulary as a whole, formal problem-solving instruction, or later algebraic comparison.
The useful question is not, “Can the child name the answer?” It is: can the child see what is being compared, identify the relevant property, justify the relationship and notice when the same idea appears in a different form?
The 50-second answer
Early mathematical comparison works by giving children two or more quantities, objects, arrangements or events that share some features and differ in others. The educator directs attention to the mathematically important property, supplies language such as same, more, fewer, longer, equal, before, after, pattern, or part, and helps the child test the relationship using matching, ordering, counting, measuring, manipulating or representing.
A useful route is:
- Put comparable things into the child’s field of attention.
- Ask what is the same and what is different.
- Name the mathematical property that matters.
- Use action to test the claim. Match, count, line up, weigh, fill, fold or rearrange.
- Change an irrelevant feature. Spread objects out, rotate a shape, change colour or context.
- Ask what stayed the same.
- Represent the relationship. A picture, mark, number line, pattern strip or simple symbol can externalise it.
- Repeat the relationship in another context.
- Invite explanation rather than accepting a guessed label.
- Move from adult comparison toward child-generated comparisons.
The shortest principle is: mathematics grows when children stop seeing isolated things and start seeing relationships among things.
1. Comparison needs a property
“Which is bigger?” can be a bad mathematical question if the adult has not made clear what bigger means.
One object can be taller but narrower. Another can be heavier but shorter. A group can cover more space while containing fewer items.
Early mathematics becomes clearer when comparison is attached to a property: longer, heavier, holds more, has more objects, covers a larger area.
This is not pedantry. It teaches children that mathematical claims have dimensions. “More” of what? “Same” in what respect?
The habit of naming the property protects reasoning from visual shortcuts.
2. Same and different are foundational mathematical categories
Before children compare quantities formally, they constantly classify experience: these two cups match; this block is different; these leaves have the same shape but different colours.
Adults can make the structure explicit.
“These are both triangles because each has three straight sides. This one is larger, but the shape is the same.”
The sentence holds sameness and difference together. Children learn that objects can match on one property and differ on another.
That idea later supports equivalence, classification, geometry, fractions and algebra.
3. One-to-one matching can reveal equality before symbols do
Place four cups beside four plates. Match one plate to each cup. Nothing remains.
The child can experience “same number” without first writing (4 = 4).
One-to-one correspondence is powerful because it gives equality a visible test. If every object has exactly one partner and nothing remains, the sets are equivalent in number.
Later, symbols compress that relationship. Early comparison gives the symbols a conceptual history.
4. Counting answers “how many”; comparison asks what the count means
A child counts seven bears and five cars accurately. The next mathematical step is not simply counting to eight.
Ask, “Which group has more? How do you know? How many more?”
Now counting values become relational. Seven is not only a recited endpoint. It can be compared with five.
The child begins to use number to describe relationships between sets.
Counting is necessary; comparison makes it useful.
5. Spatial spread can mislead quantity judgement
Young children may judge a spread-out set as “more” because it occupies more space.
Instead of treating this only as an error, create a test. Pair objects one-to-one, count both sets, then spread one set farther apart and repeat.
“What changed? What did not change?”
The child learns that arrangement and quantity are different properties.
This is an early lesson in mathematical invariance: some transformations change appearance without changing the number.
6. Order makes magnitude visible
Give children several sticks of different lengths. Ask them to arrange shortest to longest.
Ordering requires more than pairwise comparison. The child must coordinate a sequence: this is longer than that one but shorter than the next.
Use language deliberately: shorter than, longer than, between, first, last.
Ordering builds a bridge toward number lines and ordered magnitude. A quantity is not merely known; it has a place relative to others.
7. Comparison can be direct or indirect
Two pencils can be placed side by side. Two tables across the room cannot easily be.
Use a string to measure the first table, carry the string and compare it with the second. The string becomes an intermediary.
This introduces a deep mathematical idea: when direct comparison is impossible, a common unit or representation can carry the relationship.
Later measurement systems formalise this. The early child begins with a practical problem: how can we compare things that cannot be moved together?
8. “More” and “fewer” should be connected to actual sets
Children can learn the words more and fewer as vocabulary while still guessing when shown two groups.
Make the relation visible. Build one row of three counters and one row of five. Match them. Point to the unmatched counters.
“Five has two more than three. Three has two fewer than five.”
The paired language helps the child see that more and fewer describe the same relationship from opposite directions.
9. Equality should mean “same value,” not “the answer comes next”
School notation can accidentally teach children that the equals sign means “write the result.”
Early comparison can protect the deeper meaning.
Show two sets with the same number arranged differently. Say, “These are equal in number.” Balance two sides of a simple scale. Say, “The weights are equal.”
Later, (3 + 2 = 4 + 1) has conceptual support. Equality is a relation, not a punctuation mark before an answer.
10. Comparison language is part of the mathematics
EEF’s Evidence Store treats mathematical language as a connected early-maths approach. That makes sense because a child who cannot distinguish more, most, fewer, equal, longer, between, and next has fewer tools for expressing the relationships they may partly perceive.
Language should be tied to objects and actions.
“This ribbon is longer than that ribbon.”
“Both towers are the same height.”
“Which container holds more water?”
The words become usable because they are anchored to comparisons the child can inspect.
11. The adult should model how to compare, not only ask for the answer
Instead of “Which is heavier?” followed by praise or correction, think aloud.
“I’m not sure. They look about the same size. I’m going to put them on the balance. This side went down, so this object is heavier.”
The child sees a reasoning route: uncertainty → test → evidence → claim.
That is more transferable than memorising that one particular object is heavy.
12. Comparison can reveal misleading surface features
A tall narrow container may look as though it holds more than a short wide container. A large shape can have fewer objects inside it. A longer word can represent a smaller quantity.
These contrasts teach children that mathematical properties must be tested, not inferred from one salient visual cue.
Educators should select examples where surface appearance and mathematical structure sometimes align and sometimes do not.
If they always align, children can succeed for the wrong reason.
13. Pattern is comparison across positions
A repeating pattern—red, blue, red, blue—requires the child to compare positions and detect a recurring unit.
“What comes next?” is useful, but “What part keeps repeating?” is deeper.
The child begins to see structure rather than continue by imitation.
EEF’s comparison-and-connections approach includes sequences and patterns because recognising regularity is a major mathematical habit. Pattern detection later supports arithmetic structure, multiplication, functions and algebraic thinking.
14. Copying a pattern is not the same as identifying its unit
A child can copy red-blue-red-blue from a model by matching each item. They may not know that red-blue is the repeat.
Test the concept. Cover part of the pattern. Ask what unit repeats. Start with the same unit but at a different point. Change the objects but preserve the structure.
When the child can transfer ABAB from coloured blocks to claps and taps, the pattern has become more abstract.
15. Growing patterns introduce change as a rule
One cube, two cubes, three cubes, four cubes.
This is not repetition of a fixed unit. Something changes systematically.
Ask, “What is changing each time?” The child may say, “One more block.”
Growing patterns create an early route toward functional thinking: position and quantity are related by a rule.
Do not rush to algebraic notation. The conceptual job is to notice structured change.
16. Spatial comparison builds geometry before shape names are enough
Children need more than “circle, square, triangle.”
Ask which shapes can roll, stack, tile or fit through an opening. Rotate a triangle and ask whether it is still a triangle. Compare a square and rectangle: what is shared, what differs?
Geometry grows from relations among properties.
A shape category becomes robust when a child can recognise it despite irrelevant changes in size, colour and orientation.
17. Orientation should not change identity
If every triangle presented to a child points upward, a rotated triangle may look “wrong.”
Vary orientation deliberately. “It turned, but did its sides change?”
This teaches invariance: rotation alters position, not geometric identity.
The same principle applies broadly in mathematics. Learners need examples where irrelevant features change so the defining relationship becomes visible.
18. Composing shapes reveals part–whole structure
Two small triangles can form a larger triangle or a square. Several rectangles can form a larger rectangle.
Ask, “What did we make? What parts is it made from? Can we make the same whole another way?”
EEF highlights composing and decomposing as a practice within comparison and connections.
The child learns that a whole can be analysed into parts and parts can be reorganised into wholes—an idea that later appears in number composition, fractions and algebra.
19. Number composition is comparison within a whole
Five can be made from four and one, three and two, five and zero.
Rather than treating these as separate facts, compare them.
“What is the same in all these arrangements? What changed?”
The total stays five while the partition changes.
This is a crucial connection. Arithmetic becomes flexible when the learner sees numbers as structures with multiple decompositions, not fixed strings of counting words.
20. Part–whole reasoning supports subtraction without starting from a rule
Build a group of six objects. Hide two under a cloth. The visible part and hidden part still belong to the whole.
Ask, “We know the whole is six. We can see four. How many must be hidden?”
The child is reasoning about relationships among quantities.
Later, subtraction notation compresses the structure. Early comparison gives the operation meaning before procedures dominate.
21. Balance introduces relational equivalence
A balance scale makes comparison physical. One side descends; the other rises; equal loads balance.
Children can explore heavier/lighter, but the deeper mathematical opportunity is equivalence.
“What could we add to make the sides balance?”
Now comparison becomes transformation: change one side to restore a relation.
This is early equation thinking without formal algebra.
22. Capacity comparisons need controlled conditions
Two containers differ in shape. A child says the taller one holds more.
Use the same small cup as a unit to fill each container. Count how many cups fit.
The activity introduces fair comparison. If the measuring unit changes, the result becomes hard to interpret.
Fairness in measurement is an early form of experimental control: compare one property while keeping the measurement method stable.
23. Weight and size should be deliberately decoupled
Children may assume bigger means heavier. Select a large light object and a small heavy object.
Ask for a prediction, test on the balance, then discuss the surprise.
Counterexamples are educationally valuable because they force the learner to revise an overgeneralised rule.
Use them after the basic concept is understood, not as a trick designed to embarrass.
24. Time comparison grows from sequence before clock notation
Before reading clocks, children compare events: before snack, after story, yesterday, tomorrow, longer wait, shorter wait.
Use routines to stabilise temporal order.
“What happens before we go outside?”
“Which took longer: washing our hands or eating lunch?”
Temporal comparison prepares the conceptual ground for duration and measurement.
Do not confuse knowing clock symbols with understanding time relationships.
25. Everyday routines contain mathematical comparisons
At snack: more cups than children? At tidy-up: which shelf has fewer books? On stairs: who is one step higher? During dressing: which sock is longer?
EEF guidance encourages integrating early mathematics through the day.
The advantage is frequency and meaning. The risk is superficiality. Adults should occasionally pause long enough for children to test or explain the relationship rather than merely hearing a comparison word in passing.
26. Storybooks can carry mathematical relations
A story may include three bears of different sizes, a journey with sequence, sharing, growing objects or repeated events.
The educator can ask mathematical questions without turning every book into a worksheet.
“Which bowl would hold the most?”
“How do you know this bed is longer?”
“What keeps repeating in this story?”
The narrative supplies context; the mathematical comparison supplies structure.
27. Games create natural ordering and equivalence
Board games can require comparing dice values, moving farther, recognising who is ahead, matching quantities or noticing patterns.
Games also create motivation to know the answer because the relation affects the next action.
Adults should ensure the game mechanic actually exercises the target idea. A colourful board is not mathematically useful merely because numbers are printed on it.
28. Comparison should move across representations
Show five counters, a hand with five fingers, the numeral 5 and five dots.
Ask, “What is the same about all of these?”
The surface forms differ. The represented quantity is connected.
Then compare five with six across the same forms.
Representation comparison helps children understand that mathematics can preserve a relation while changing how it is shown.
29. A number line makes order spatial
Place numerals on a line. Five is to the right of four and left of six.
Children can walk along a floor number line, compare distances and discuss “one more” or “two less.”
The number line externalises ordered magnitude.
Later, negative numbers and fractions extend the same representational system. Early work should build the relation rather than turn the number line into decoration.
30. Ask “How do you know?” after the relationship is accessible
If a child is still trying to identify the sets, “Explain your reasoning” can overload the task.
Once the comparison is clear, ask for evidence.
“How do you know these are equal?”
“I matched them and none were left.”
The explanation reveals whether the child used a valid comparison method or guessed from appearance.
Reasoning questions are diagnostic as well as instructional.
31. Children should generate comparisons, not only answer adult comparisons
Give several objects and ask, “What could we compare?”
A child may compare length. Another notices colour. Another counts corners.
The adult can steer toward mathematical properties while preserving agency.
Generating a comparison is cognitively different from selecting an answer. The learner must decide what relation is worth inspecting.
That is a step toward independent mathematical inquiry.
32. Use mistakes to expose the comparison rule
A child says the longest row contains the most counters.
Instead of “wrong,” ask, “How could we test that?”
Matching or counting turns the error into a method.
EEF’s early-maths problem-solving guidance explicitly includes using mistakes as learning opportunities. Comparison makes this concrete: an incorrect judgement is useful when it reveals which property the child relied on.
33. Keep vocabulary precise but developmentally usable
Words such as equal, fewer, heavier, between, pattern, and part are worth teaching explicitly.
But technical vocabulary should not replace the child’s understanding. A child who says “they match exactly” may understand equality before using the word equal reliably.
Name the concept while preserving meaning: “Yes, they match in number. We can say the groups are equal.”
Language expands the concept; it should not become a password.
34. Avoid asking comparison questions where every cue points to the answer
If the larger set is always spread out, darker, and physically bigger, children may learn a visual shortcut.
Vary irrelevant features.
Sometimes the smaller count occupies more space. Sometimes two equal groups use different objects. Sometimes the longer shape is lighter.
Good examples separate the target relationship from accidental cues.
35. Comparison becomes powerful when children transfer the relation
A child learns more/fewer with counters. Later, can they use it with sounds, steps, toy animals and points in a game?
A child notices an AB pattern with beads. Can they find the same structure in clap-stomp-clap-stomp?
Transfer shows the learner has abstracted the relationship from the original materials.
Without transfer, the child may have learned the activity rather than the mathematics.
36. Educators should know when not to compare
Comparison can become socially harmful when applied to children rather than mathematical objects: “Who finished fastest?” “Whose tower is best?” “Who got the most?”
Competition can motivate some situations but also shift attention from mathematical reasoning to status.
Prefer comparisons that illuminate structure. If children’s work is compared, make the instructional purpose clear: two different strategies, two representations, two ways to make six.
The target should be thinking, not ranking children.
37. Mathematical comparison can support inclusion
Concrete materials, gesture and visible relationships can make mathematics more accessible to children who are still developing instructional language.
But manipulatives are not automatically inclusive. The adult must still connect action, language and concept.
A child may successfully match two sets without yet saying equal. That action provides evidence of understanding and a route for language development.
Use multiple response modes without lowering the mathematical idea.
38. The adult should fade the physical support when the relation is stable
Matching counters is useful. Eventually the child should be able to compare some small quantities mentally or through symbols.
Move from objects to drawings to numerals where appropriate, returning to materials when the relation becomes uncertain.
The point is not to “graduate” from manipulatives because concrete is childish. It is to gain flexible choice among representations.
Independence means using the representation that helps, not being trapped in one form.
39. Comparison is one route into generalisation
After several examples, ask, “What do you notice?”
If adding one object always makes the count one more, the child is approaching a general relation.
If a square remains a square after rotation, the child is distinguishing defining from non-defining features.
Generalisation begins when comparisons across examples reveal a pattern that extends beyond one case.
This is the seed of mathematical theory.
40. The educator should compare strategies as well as answers
Two children solve a sharing problem differently. One deals objects one at a time; another makes equal piles quickly.
Put the strategies side by side.
“What is the same? What is different? How did both make the groups fair?”
Children learn that mathematics contains methods that can be compared for correctness, clarity and efficiency.
This develops metacognitive awareness without requiring formal terminology.
41. Home mathematics can move beyond counting practice
Families often receive the message “count everything.” Counting is useful, but comparison creates richer conversation.
Which bag is heavier? Which route is shorter? Do we have enough plates? Which container will hold all the rice? What pattern do the floor tiles make?
These questions connect number, measurement, space and reasoning.
The home does not need special equipment. It needs attention to relationships.
42. Assessment should test relational understanding, not only labels
A child may correctly answer “more” on familiar picture cards but fail when arrangement changes.
Use varied tasks: matching, ordering, explaining, constructing an equal set, continuing a pattern, finding a counterexample.
Assessment should ask whether the child can operate the relation.
A vocabulary answer is useful evidence, but not sufficient evidence of mathematical structure.
Worked case 1 — Five still means five
A child correctly counts five counters in a tight row. The teacher spreads them across the table. The child says, “Now more.”
The teacher places a second set of five in a tight row and matches each spread counter to one in the row. “Did we add any counters?” The child says no. They count again.
The teacher repeats later with toy animals and then with dots on cards. Eventually the child says, “It only looks more because it’s spread.”
The learning is not simply conservation vocabulary. The child has learned to distinguish spatial extent from quantity and to use a test when appearance conflicts with number.
Worked case 2 — The triangle that “stopped being a triangle”
A child identifies upright triangles but rejects one rotated onto its point.
The educator places several triangles of different sizes and orientations together. They trace sides and count corners. “What stayed the same when I turned it?”
The child rotates the shapes personally. Later, during a block activity, she identifies a sideways triangular piece without prompting.
Variation made the defining property more visible than the familiar orientation.
Worked case 3 — Pattern copying without pattern knowledge
A child copies red-blue-red-blue accurately from a strip. The teacher removes the model and asks what repeats. The child cannot answer and produces red-blue-blue-red.
The teacher builds the pattern slowly: “This little unit is red-blue. We do the same unit again.” They clap-stomp using the same AB structure and return to blocks.
Several days later the child creates spoon-fork-spoon-fork and says, “It repeats two.”
The child moved from positional copying toward structural recognition.
Worked case 4 — Comparing capacity fairly
Two children argue about which bottle holds more. One is tall and thin; the other short and wide.
The educator asks how they could find out. Children suggest pouring one into the other, but the bottles have narrow openings. They agree to use the same small cup as a unit.
The tall bottle takes six cups; the wide bottle takes seven. The children had predicted the opposite.
The important learning is not “wide bottles hold more.” It is that appearance can mislead and a common measurement procedure can test a comparison.
Practical route for teachers and early-years educators
Plan comparisons around properties, not just answer labels. Put examples side by side, make the relevant dimension visible and vary irrelevant features. Use manipulatives when direct action clarifies the relationship. Think aloud about how you test a claim. Teach comparison language explicitly and connect it to action.
Across the week, revisit the same relation in different contexts. More/fewer can appear at snack, in stories, on a number line and in a game. Same/different can appear in shape, quantity and pattern. Invite children to create examples and counterexamples.
Observe whether a child can explain or demonstrate the relationship when surface features change. That is more informative than success on a repeated worksheet format.
Practical route for learners
When you compare, ask what property matters. Are you comparing number, length, weight, size, time or shape?
Do not trust appearance immediately. Match, count, measure, order or represent if you need evidence. Ask what changed and what stayed the same.
Try showing the same relationship in another way: objects, drawing, numbers, words. If your idea survives the change, you probably understand more than one example.
Practical route for parents and families
Use everyday decisions as mathematics. “Do we have the same number of forks and people?” “Which bag feels heavier?” “Which queue is shorter?” “Can you make the same pattern with spoons and cups?”
Ask, “How could we check?” instead of supplying the answer.
Avoid turning every comparison into a contest between children. Compare objects, routes, quantities and strategies. Let the child explain what property they used.
Common failure modes
- Asking “which is bigger?” without specifying the property.
- Teaching comparison words as labels without testing actual relationships.
- Letting visual spread stand in for number.
- Presenting shapes only in one familiar orientation.
- Using patterns that children can copy position by position without identifying the repeat.
- Treating manipulatives as self-explanatory.
- Asking for explanations before the child has enough access to the comparison.
- Keeping examples so similar that children learn a superficial cue.
- Changing too many features at once so the mathematical relationship disappears.
- Ranking children instead of comparing mathematical objects or strategies.
- Counting endlessly without connecting counts to relationships.
- Moving to symbols before children understand what the symbols compare.
- Keeping children on concrete materials after they can reason flexibly without them.
- Assuming a correct vocabulary word proves conceptual understanding.
- Correcting a misconception without showing a method for testing it.
- Treating early maths as number alone and neglecting space, pattern, measurement and part–whole relations.
Frequently asked questions
Is comparison really mathematics, or just language?
It is both conceptual and linguistic. The relation exists mathematically, but children need language and representations to identify, discuss and generalise it.
Why does EEF treat comparisons and connections as a distinct early-maths approach?
Because mathematical understanding depends on relationships. EEF’s Evidence Store highlights comparison, connection, sequence, pattern, spatial reasoning and composing/decomposing as practices that help children build those relationships.
Should children count before comparing?
Sometimes counting is the best comparison method; sometimes direct matching, weighing or ordering is more appropriate. The method should fit the property.
What is the difference between “same” and “equal”?
Same is broad and can refer to many properties. Equal is more precise: two quantities or measures have the same value in the relevant dimension.
Why vary colour, size and orientation?
Variation helps children separate defining mathematical properties from irrelevant surface features.
Are patterns important before formal algebra?
Yes. Recognising repetition and systematic change develops attention to structure, which later mathematics uses extensively.
How do manipulatives help?
They let children act on quantities and relations: match, group, order, compose, decompose and measure. Their value depends on the adult connecting the action to the mathematical idea.
Can storybooks support comparison?
Yes. Stories create contexts for size, number, sequence, pattern and part–whole questions, especially when the adult keeps the mathematical relationship visible.
What should parents do if a child guesses?
Ask how they could check. Turn the guess into a test using matching, counting, measuring or arranging.
How do we know a child has transferred the idea?
They recognise or construct the same relationship with new materials, representations or contexts without needing the original prompt.
Sources and further reading
- Education Endowment Foundation, Supporting children to make comparisons and connections, Early Years Evidence Store: https://educationendowmentfoundation.org.uk/early-years/evidence-store/early-mathematics/supporting-children-to-make-comparisons-and-connections
- Education Endowment Foundation, Developing mathematical language, Early Years Evidence Store: https://educationendowmentfoundation.org.uk/early-years/evidence-store/early-mathematics/developing-mathematical-language
- Education Endowment Foundation, Developing mathematical problem-solving, Early Years Evidence Store: https://educationendowmentfoundation.org.uk/early-years/evidence-store/early-mathematics/developing-mathematical-problem-solving
- Education Endowment Foundation, Early mathematics, Early Years Evidence Store: https://educationendowmentfoundation.org.uk/early-years/evidence-store/early-mathematics
- Education Endowment Foundation, Improving Mathematics in the Early Years and Key Stage 1, guidance report: https://educationendowmentfoundation.org.uk/education-evidence/guidance-reports/early-maths
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The final idea
Early mathematics is not a collection of isolated facts waiting to be memorised. It is a network of relationships.
Five is larger than four, equal to another five, one less than six, composed of two and three, positioned between four and six, and representable by objects, fingers, dots, a numeral and movements on a number line. A square remains a square when rotated. A repeating unit can be carried from colours into sounds. A quantity can stay constant while its arrangement changes.
Children build this relational world through repeated comparison. Adults help by choosing examples, naming properties, making tests available and asking what changed or stayed the same.
The endpoint is not a child who answers “more” faster. It is a child who knows what is being compared, can justify the relation, can see it through different surface forms and can use that relation as a building block for new mathematics.
When children learn to see connections, mathematics stops being a pile of answers and starts becoming a system.