Rethinking Grade School Algebra

There’s a question I like to ask random people: where is the flaw in the argument that because ? I very rarely get a satisfactory response. Usually the answer is that “you’re not allowed to multiply both sides by zero.” But we can come up with a slightly subtler argument: because . Some just don’t answer, other will insist that its not allowed… To me it suggests something is deeply wrong with how most people understand algebra.

They don’t know mathematics, they know voodoo-mathematics, a series of mysterious steps that result in their test being returned with a checkmark beside the question.

Now it may seem that I’m being a pedant. After all, they know it isn’t true; what does it matter if they can’t tell me why? But even if we set aside the fact that it simply feels wrong to not understand why the math works, it has practical implications because there are cases where the mistake won’t be as overt as above. And then these people won’t see the mistake.

So I’d like to use this essay to go over grade school algebra from a different perspective.