If Not Methods: Fraction Multiplication

Posted on by Denise Gaskins
Father and son doing math homework together

This is the last post (for now, at least) in our If Not Methods series about how to help children figure out tough calculations.

By the time students reach the topic of multiplying fractions, they have become well-practiced at following rules. After some of the complex procedures they’ve learned, a simple rule like “tops times tops, and bottoms times bottoms” comes as a relief.

But we know that relying on rules like that weakens understanding, just as relying on crutches weakens physical muscles.

If we want our students to think, to make sense of math, to figure things out, what can we do with a problem like 5/6 × 21 ?

Continue reading If Not Methods: Fraction Multiplication

If Not Methods: Mixed Numbers

Posted on by Denise Gaskins
A family doing math homework together

Continuing our series on teaching the tough topics of arithmetic…

Our own school math experiences led many of us to think that math is all about memorizing and following specific procedures to get right answers. But that kind of math is obsolete in our modern world.

The math that matters today is our ability to recognize and reason about numbers, shapes, and patterns, and to use the relationships we know to figure out something new.

But what if our children get stumped on a mixed-number calculation like 2 5/12 + 1 3/4?

Continue reading If Not Methods: Mixed Numbers

If Not Methods – Subtracting Fractions

Posted on by Denise Gaskins
Father and daughter doing math homework

We’re continuing our series of posts on how to build robust thinking skills instead of forcing our children to walk with crutches.

When we say, “Use this method, follow these steps,” we teach kids to be mathematical cripples.

If your student’s reasoning is, “I followed the teacher’s or textbook’s steps and out popped this answer,” then they’re not doing real math. Real mathematical thinking says, “I know this and that are both true, and when I put them together, I can figure out the answer.”

But what if our kids get stumped on a fraction calculation like 7/8 − 1/6?

Continue reading If Not Methods – Subtracting Fractions