Help children see the math behind a solution.

“See Math, Not Memorize Steps” begins with a question:

what relationship has the child noticed, and what has the child missed?

An answer tells us what a student wrote.

To help the student grow, we also need to understand what they noticed, what they understood and how they decided what to do.

This applies to a child who is falling behind and to one who is already excelling.

What we look for

Correctness is only one clue.

A child who gets an answer wrong may have understood an important relationship but made an error later. A child who gets it right may be recalling a demonstration without understanding why it works. We observe the child’s explanations, choices and responses when a challenge changes.

This helps us offer a suitable next challenge or support. A strong student may need more room to investigate and adapt, while another may need an experience that makes a foundational idea meaningful.

From experience to understanding

How we develop thinking

01

Explore

The child encounters a purposeful activity or challenge that gives a mathematical idea meaning. Objects and stories are used when they help reveal the relationship, not simply to make a lesson entertaining.

02

Notice

We invite the child to examine what is present, what has changed and what remains possible.

A useful question might be, “What do you have now?” We allow time for the child to investigate.

03

Connect

The child explains the relationship and connects the experience to mathematical language, representations and school questions.

04

Use

We vary the situation. The child has a new opportunity to decide what applies, adapt an idea and explain why.

A successful repeat of one demonstration is a beginning, not the end of learning.

A concrete example

An unfamiliar averages question

A group of boys has an average weight of 39 kg.

Arnold, who weighs 66 kg, joins them.

The new average is 42 kg.

How many boys were there originally?

Rather than begin with a formula, compare everyone with the new average of 42 kg.

The original group is short by 3 kg per boy on average.

Arnold contributes 24 kg above 42 kg.

His excess covers eight 3 kg shortfalls, so there were 8 boys originally.

This does not mean each boy weighed 39 kg.

The relationship is between the group averages and Arnold’s excess.

A child who can explain that distinction has seen more than a calculation.

We would vary the numbers or the situation to see whether the child can use the idea again.

We want children to move from waiting for

“How do I do this?” towards examining a problem:

“What do I have? What can I see? What else can I uncover?”

That shift takes deliberate experiences, practice and opportunities to reason for themselves.

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