Breaking Through the Mathematics Education System Despite Itself
There is a psychological tactic employed by some classroom teachers following a strict curriculum: to bond with one’s students by casting the enforced textbook as a common enemy. “We’re in the system and this is the game we have to play,” is the sad and perhaps demoralizing approach to this. But if conducted with grace and care, elements of this psychological stance can be respectful, uplifting, and pedagogically good.
After all, any passage of text provides opportunities to question content, probe inconsistencies, explore missed opportunities, counter seemingly inflexible assertions and definitions with exceptions and alternative approaches, and so on. That is, all texts can serve as an invitation to examine the place and context of content. And in this content-rich, content-at-the-ready world, isn’t it all the more important that 21st-century education should help students learn to be the arbiters and assessors of their own knowledge?
This applies to mathematics education and its availability of content too. Once everyday number facts and facilities are at hand by middle school, the remaining six years of mathematics education could attend to the thinking and meta-thinking of mathematics, and the self-reliance of thought this induces. We could, with intention, help students learn how to learn, to personally assess what they know and how they know it, and to differentiate between familiarity and understanding: the familiarity that comes from repetition and rote doing versus the empowerment of knowledge.
So how does one foster student metacognition, self-confidence, and nuanced understanding when presented with a rigid, upper-school curriculum that is content focussed and content laden? The “system” need not be an enemy, per se, but can we identify opportunities within the system that extend beyond itself perhaps despite itself?
For starters, we might argue that the volume and nature of the mathematics content we are expected to cover in high school mathematics in and of itself holds a message. Factor trinomials, use 2x2 matrices to represent certain geometric transformations, analyse the ambiguous case of the Law of Sines, and so on and so on and so on. The count of disparate topics makes us realise that they can’t all be sacred topics that need to be taught. No topic is important because students will “need to know it later on.” (Or, if I am wrong about that, then the topic could wait until “later on”…