Building Long-Term Math Mastery

Have you ever stopped and asked yourself, “Why does one plus one equal two?” Most people who find themselves faced with this math question will probably say something along the lines of “it just does.” But if you thought about it, you could probably come up with a more articulate answer. For example, if you have one marker, then buy another one, and count how many markers you have, you will have two. That’s why one plus one equals two.

What did I have to do in order to answer the question? For most adults, connecting number problems to familiar objects is automatic. That’s because, as children, we learned number sense by working with objects that we could count and move around. You know that manipulatives are key to developing math comprehension. But are there other keys to math comprehension that are essential for long-term mastery?

Yes. Our Math 2 student worktext constantly asks your child questions about the processes he used and how he found his answer.

Students must learn to think about and explain the processes and formulas they use in order for math to have any lasting purpose for them.

For example, in high school, I was at the top of my class in math, but not because I had any idea of what all those numbers meant. It was simply because I could put numbers in the right places in a formula. In fact, I always loved the quadratic equation, and I still remember x equals negative b plus or minus the square root of b-squared minus 4ac all over 2a. But when I got to geometric proofs, I was hopelessly lost. My high school math textbooks never reminded me that the formulas and numbers I loved playing with actually meant something. It was like putting together a puzzle with edge pieces but no middle.

A child’s ability to solve equations doesn’t mean he gets it.

So how do you ensure that your child will be able to make sense of math as he moves into more and more complex ideas?

• Ask him to explain his process. What would the equation he’s solving look like in real life?
• Ask him for observations about the concepts he’s learning. Does he see any new patterns? Do other math concepts apply to the new one? Does the new math concept apply to old ones?
• Incorporate common objects as manipulatives. As he begins learning about area and surface area, can he find the surface area of a tissue box? How would that information be useful to the person designing the box or putting it together?

Look through the thought bubbles in Math 2 student worktext for more ideas of questions to ask your child.

When math has meaning, it also has purpose. If you can create a strong connection between your child and the meanings of the numbers and formulas, you might also connect him to a future career.