A local Mathnasium resource

Understanding math beyond memorizing.

Your child may remember the steps and get the answer right, yet struggle when the question looks different. Asking what a step means can reveal more than asking for another answer.

See two everyday examples

An instructor and student looking at a shape-pattern worksheet at a Mathnasium table — A student and instructor at Mathnasium of Westmere.

The useful distinction

A remembered fact or step is useful. Understanding connects it to what the numbers mean, why the method works and when to use it.

A remembered step: “I multiply both numbers by two.”
An explanation: “The pieces are smaller, so I need twice as many to show the same amount.”
A parent's next question: “Can you show me what you mean?”

From an answer to an idea

Two ways to look beneath a remembered rule.

These are examples for a conversation with your child, not a test of what they should know at a particular grade. Choose something they have already been learning.

Multiplication: what does 6 × 4 mean?

A child might recall that 6 × 4 = 24. Ask them to draw six groups of four dots or show the groups with small objects. The groups give the fact a meaning.

Then ask: “If we add one more group of four, how many will there be?” Seven groups of four make 28. The same idea answers a differently worded question: “There are seven packs with four markers in each. How many markers are there?”

Listen for why the extra group adds four, and how the groups connect to the marker packs.

Fractions: why is 1/2 the same as 2/4?

A child might remember to multiply the top and bottom numbers by two. Ask them to draw two rectangles of the same size. Divide one into two equal parts and shade one; divide the other into four equal parts and shade two.

The shaded amounts are equal. Each fourth is half the size of a half, so it takes two fourths to cover the same amount. Both drawings must represent the same-sized whole for this comparison.

A related question is “What is 1/2 + 1/4?” With the same-sized whole, two fourths plus one fourth make three fourths. The drawing gives a reason to use equal-sized pieces, instead of adding the denominators.

Keep it a conversation

Invite an explanation without adding pressure.

Ask about the idea

“What does that number represent?” or “Why did you choose that step?” Leave room for your child to think.

Offer another way to show it

A drawing, small objects or an example may help your child show an idea that is hard to put into words.

Let them choose the next step

Ask “What could you try?” before supplying a method. Notice whether your child can choose a step and explain it, or needs you to lead each part.

Deciding about support

Bring examples, rather than a label.

One hesitant explanation does not establish a knowledge gap. If your child repeatedly loses track of what a step means, needs the same prompt each time or struggles to apply a familiar idea in a changed question, bring those examples to their teacher or a Center Director.

Ask what support would help your child explain the idea, choose a method and try a related problem independently. That gives the conversation a more specific goal than simply asking for more practice.

At our Mathnasium centers in Clifton Park, Loudonville, Niskayuna and Westmere, an assessment helps identify individual missing skills so a learning plan can start where your child needs support. Generally, it covers material through the end of the previous school year. The purpose is to find gaps, not give a grade.

Read how our assessment finds your child's starting point, or choose a center below to discuss what you are noticing.

Common questions

Questions about remembering and understanding.

Is memorizing math facts a problem?

No. Remembering facts can make calculation easier. Understanding gives those facts meaning and helps a child choose a suitable method when the question changes. Both have a place in learning math.

Does a correct answer mean my child understands?

It tells you they got that question right. Their explanation, a drawing or a related example can show more about how they arrived at it.

What if my child cannot explain in words?

Give them time and invite a drawing or objects instead. Difficulty putting an idea into words is not, by itself, proof that they do not understand it.

Should I keep giving harder questions to find a gap?

You do not need to turn homework into an assessment. Bring a few examples of what your child can do and where they get stuck to their teacher or a Center Director.

Your next step

Let's find out where your child can start.

Choose a local center to schedule an assessment or a conversation with its Center Director.

Select a center to see your booking choices.