What Should Math Class Be Achieving?

It was illuminating to read about the highly politicized history of the math curriculum. I was surprised by a few points in the reading. First, I was struck by the timeline of Dewey's inquiry-based approach to teaching math (pre-1940s) described on page 396. If I heard about this approach out of context and was asked to guess from when it originated, I would have assumed it to be a quite modern idea. This made me feel sad for myself and other students who might have thrived in classrooms with this approach but didn't get a chance to due to the changing perspectives that favoured more traditional methods.

I found the shift to the Bourbaki group's "New Math" very interesting. It was truly ironic that a movement to create more skilled mathematicians seemed to completely backfire--alienating people further away from math rather than drawing skilled mathematicians in. How many brilliant mathematicians missed out on the opportunity to explore math further because the rigidness of the subject shut them out. I wonder if we still feel the impact of this today in the attitude many people have that mathematics isn't for them?

Jumping forward to the 90s, I was also struck by the desire to cling to traditionalist methods after the US didn't rank as high as they'd like in international mathematics standings, despite evidence that deeper understanding led to higher scores for the top-rated countries (described on page 400). This phenomenon or gut reaction to "dig your heels in" even when faced with evidence contrary to your actions is interesting to me, especially when it's done at the government level. How can we be more adaptable and open to change? In particular when faced with evidence that the change would be beneficial, and in particular on a governmental level (which can often feel quite out of reach as an individual).

Finally, as a whole the reading reminded me of a time in my masters degree when I heard a CBC radio show discussing narrative assessment. I'm paraphrasing, but one of the interviewees essentially said "Narrative assessment might be possible in 'soft' subjects but could never be used in a subject like math". I was a bit outrage by this use of math in their example. What did this person know about teaching math? What did they know about math at all? In my experience as a student and as a TA, narrative assessment was where the most influential learning happened. When we shifted the focus from the grade, we could instead discuss the actual content.

Sometimes things don't work out the way you planned

(Here's a parked car I saw squashed by a tree on a not even windy day, no one was injured)