Two seemingly unconnected thoughts:
- I have observed many students – and adults – that don’t get algebra
- 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?
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.
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.