Why Understanding Multiplication Isn’t Enough

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Students have to understand conceptually what multiplication is, and they gotta know how to compute.

But even if they have these two things, the understanding and the computation, that doesn’t mean that the practice is done.

They also gotta have it memorized.

Even if they know that 7x8 means add together 7 equal groups of 8, even if they know the procedure to get to the answer and they can carry it out, even if they can do the doubling trick, you know, take 7, then double it, then double it again, then double it one more time…

Even if they can do this reasonably quickly, it still takes a lot of mental effort.

And if you put that 7x8 inside of a long division problem – which is hard enough as it is with all these other computations going on, and now they’re trying to learn long division while multiplying numbers over and over again in their head.

They can’t focus on the long division. Why? Because all their focus is on the multiplication. Why? Because they haven’t memorized it.

It’s mentally exhausting, so no wonder they get tired, they get overwhelmed, they want to quit.

In order to keep learning these new levels of math, kids should not have to just stop and solve 7x8 by recomputing it every single time it shows up.

At some point, 56 should just be there, so their attention can focus on the new material.

Further reading:

• Cognitive Science of Learning: Developing Automaticity
• If You Want to Learn Algebra, You Need to Have Automaticity on Basic Arithmetic

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