I got a little angry the other day when watching the video below.
The new math is the old math.
A method in math is a “trick.” And tricks are fine and dandy – IF you created them yourself and you’re using them yourself.
When you create a trick or method to do something, you enhance your own learning. You build on things that you previously learned about and bridge it to the new learning.
But if you’re given a trick, your learning could be skewed. Your understanding could be distracted.
And you’ll be deprived of the freedom to create your own method.
Teach the definition, let the rest follow.
Math is based on two things: definitions and assumptions. From those two, we create all the rest.
From some basic definitions and assumptions, we’ve created addition of real numbers as well as multiplication of real numbers.
Those are what we all know and love as plain old non-italicized addition and multiplication.
So what’s with the lattice method?
The example in the video (at 0:49 – 2:15) is 46 x 59. How about we do it according to the definition of the distributive property:
If Alicia, Brian and Carl are real numbers, then Alicia x (Brian + Carl) = (Alicia x Brian) + (Alicia x Carl), and vice versa when needed.
Note: the distributive property is the only way we can integrate addition and multiplication.
So first we rewrite the second number in a nice way in alignment with our place value system:
The multiplication can distribute over the addition:
And we can do it again inside each bundle:
Which gives us:
Now watch that part of the video again and keep your eyes peeled for the similarities:
Are the tricks useful?
Indeed many students will jump in, see the pattern and do the lattice method. It might even be fun.
And if they get the hang of it and feel confident with it, they’ll know how to multiply two digit numbers.
But it’s a trick. And it’s a trick that can’t be extended to other algebraic uses like
Starting with a pixie-dust-magic lattice method kills the hope that children will understand the distributive property.
And if they can’t understand the distributive property, they’re dead in the algebraic water.
Improve learning – lay off the tricks.
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- Understanding Math – Let Kids Fake It
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- The Learning Cycle
- GeoGebra – Who’s It Really For?
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