Algebra Epiphany

Two seemingly unconnected thoughts:

  1. I have observed many students – and adults – that don’t get algebra
  2. Sometimes a very small change in thinking can have an outsized impact

Here’s the epiphany:

x equals 1 times x

or put another way:

x = 1x

Really? That’s an epiphany?

Here’s why…

When people solve an algebraic equation, they put the x’s on one side. For example:

Starting with: 2x – 5 = x + 4

We end up with: 2x – x = 4 + 5

Since 2x – x = x and 4 + 5 = 9, x = 9.

Checking our work: 2(9) – 5 = 9 + 4; 18 -5 = 13; good.

And simple.

But some people have trouble with the 2x – x. A possible reason? There’s no 1 in front of the x.

2x – 1x is obviously 1x. But it’s not so obvious to algebra neophytes that 2x – x = x.

The reason might be that 2x – x breaks the pattern of having a number times x, while 2x – 1x keeps that pattern. And many successful people look for patterns to help solve problems.

A reasonable conclusion is that if smart people see and act on patterns better, smart people have an issue with not putting the 1 in front of a lone x.

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