"How fast would we have to drive to keep up to the sun?"

The other day I wrote a post on crowdsourcing a math test. I was extremely pleased with the results. The basic idea was that students worked in groups on a multiple choice test until everyone in the class had 100% on the test. It took 20 minutes for all of them to succeed. I thought at the time that it was a wonderful strategy for peer learning and maybe it was.

Sadly, I gave a short traditional computation-based test after three days. The result was that half the class failed. It appears that what was happening in the crowdsourcing test was that the students who understood it did most of the work and that very little teaching took place within the groups. I am not done with this strategy as I think it has great merit for collaborative learning and peer coaching.

Why is -3 X +2 such a hard idea to grasp for many students? Is it our failure to teach students to conceptualize math processes, skills and strategies? Is it that we don't try hard enough to make math real-life? Do we fail to allow students to be creative? Do we frame the problem for students and not allow them to frame it themselves? Is it because we emphasize computation in our classrooms at the expense of the other components of mathematics?

Perhaps a personal experience will help me to understand. At Christmas my family was driving to Calgary to see my dad and brother. My 13 year old son took a break from his playstation and asked,

"How fast would we have to be driving to keep up with the sun?" It just so happened that I knew a fact (if light could travel around the earth it would go seven times around the earth in one second) that enabled us to work out the answer to his question without a calculator. We may have made calculation errors, but the process was fun. His mother thought we were nuts.

I thought I'd make a list of the key factors enabling that great "math learning":

1. he asked the question, he was interested, it was relevant to him
2. he had success previously when he asked similar questions
3. interested parents and some skill (education) to talk to
4. he knew it would make me happy if he asked me the question
5. he is still curious
6. time was available to talk about it
7. he was not evaluated
8. the right answer wasn't that important
9. he wasn't worried about looking too interested in front of his peers

It is not that easy to do this in class every day. Commonly, the students you teach will not have parents who support deep thinking in math (they have bad experiences themselves). In order to have this type of situation in our classrooms more often, we will all need to do some deep thinking, sharing and collaboration.

I plan to keep up the battle with the help of my on-line math PLC (mostly twitter) and my school CIT (community of interest team).