FAQ: Doing Math His Own Way

Isn’t it fun when children surprise us with their understanding?

All my children have figured out ways to do things in math that I would never have expected, and I’ve learned quite a bit from listening to their explanations.

But what if the child’s creative method makes it hard for them to learn what our textbook wants to teach?

A Reader Asks

My seven year old son is learning how to subtract with “regrouping.” We used base-ten blocks to learn the traditional method, but today, he showed me how he works the problems.

Instead of regrouping, he subtracts the ones column and gets a negative number. Then he subtracts the rest of the numbers (tens and hundreds columns), and then he adds the negative number back in.

So for 342 − 225, he does:

2 − 5 = −3,

then 340 − 220 = 120,

and adding back the −3 is 117.

I know this method works and I’m blown away that he came up with it. (Not sure how he knows about negative numbers!)

But what do I do — do I continue reviewing the regrouping method? Do I let him do his own thing and eventually go back to the traditional method? Do I leave it alone and see what happens? Do I try to combine the two methods in his learning?

Great Questions

And congratulations to your son for developing such a solid understanding of numbers!

There is nothing magic in the standard algorithms (the rules for pencil-and-paper arithmetic). Your son’s method is perfectly fine and logical — and also much better suited for working in his head on the fly, which is how we often do math in real life.

The main thing you want to teach your son is that math makes sense. That it’s logical, something he can figure out on his own, not just “rules from on high.”

So let him use the method that makes sense to him.

There may come a day (maybe in third or fourth grade) when the numbers get too big for him to handle with his method. At that point, he may adapt his own algorithm to include written notes about the negative numbers in each place value column, or he may be ready to learn the standard algorithm.

Either way, if you follow his lead, you will strengthen his ability to reason things through.

Develop Mathematical Thinking

In adult life, when we have big numbers to deal with, we have calculators on our phones and computers, and we do our accounting in spreadsheets that do the calculations for us.

The standard pencil-and-paper algorithms were designed for a different world, a place where clerks had to do hundreds of manual calculations every day with as little thought as possible because thinking about the numbers slowed them down.

But cognitive scientists tell us that children only learn what they think about, and the deeper they think, the more the concept links itself to other ideas in their mind. That means we want our children to think about the numbers, not just follow rules to get answers.

The math that was perfect for Bob Cratchit really doesn’t help our kids today. Because the thinking is what’s valuable — it’s the thing computers and phones can’t do for us.

So enjoy your son’s insight, and continue your adventure of exploring the mathematical world together.