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.
‘Cause even if they know that 7 times 8 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, if they have to do that every time to get to 56, they have to add 8 plus 8 plus 8 plus 8 plus 8 plus 8, or even the doubling trick, you know, 7 times 2, then double it again, then double it again, even if they can do this reasonably quickly, it still takes a lot of mental effort.
And if you put that 7 times 8 inside of a long division problem.
Which is hard enough as it is with all these other computations going on.
You know, 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 ‘cause all their focus is on the multiplication ‘cause they haven’t memorized it, ‘cause they have to go through these procedures every time.
It’s mentally exhausting, so no wonder they get tired, they get overwhelmed, they wanna quit.
In order to keep learning these new levels of math, kids should not have to just stop and solve 7 times 8 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.
This teaser is distilled from the following posts, if you want to dive deeper:
- Cognitive Science of Learning: Developing Automaticity
- If You Want to Learn Algebra, You Need to Have Automaticity on Basic Arithmetic
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