I put this up as the opener for algebra today:
A large chunk of students quickly jumped to “the previous number times two”.
That wasn’t my rule.
Then they shifted to +2, +4 +6…
That wasn’t my rule either.
Silence for about 2 minutes… Then a student asked “Is the next number 10?”
“That fits my rule” I replied.
This threw ’em all off… They dabbled around with different numbers for a bit, I had fun with it, especially when they pitched crazy numbers like 54, 81, and 1092, which fit my rule.
Eventually, they drifted into trying to find numbers that didn’t fit my rule… which is awesome problem solving.
This really is the heart of what I want to get at through all this factoring, solving, graphing and so on. To me math isn’t so much about memorizing or reproducing a certain skill, but more about taking what you know and tweaking it to solve some crazy problem you have never seen before.
That moment where you have abandoned all hope and try some crazy technique in a problem that you learned months or years ago, which ends up working is what I love about math. The struggle leading up to that moment; following hundreds of self-imposed rules and just sheer grit isn’t easy. It is even more difficult to learn and teaching it takes someone really special.
Everyday I try and very delicately move students towards that direction. With the hopes that maybe, at some point in their lives, in a situation that isn’t even close to math related, they will be able to use their critical thinking abilities, which took years to develop, to solve a difficult problem and experience that felling of having everything fall perfectly into place.
For me, that hope makes everyday worth it.
By the way… my rule was each number had to be larger than the previous. They went crazy over this, some nasty reverse psychology on my end: They automatically see something math related and dive into testing different equations and rules, when really the rule doesn’t require anything fancy. Credit.