22 June 2014

Argument Writing in Math - the Oldest "Fad" in Instruction

Either you are a long-time teaching vet and you've said this or you've heard one say something like it - "Common core is just a next the fad. We've seen things like this come and go just like NCLB did."

It's true that a lot of the content and practice standards we see in the common core may only be shuffled content from the SHOW-ME standards and course-level objectives we already had in Missouri. To think that the rest is only based on the latest fads and research, however, is to have misread the document and dishonor the history of mathematics. 

Look at this from the standards for mathematical practice (my favorite part of common core).

If you're not careful, getting your kids to construct arguments can feel like another add-on to curriculum that rarely gets anything taken away. There are probably going to be enough shifts within the content standards that actually do represent changes to your classroom (for example, descriptive statistics in algebra) for you to get bent out of shape about the things that should be there anyway. 

If constructing arguments in our math classes is the reaction to a call for "rigor and relevance" and just another fad, then I want to remind you that it's perhaps the oldest "fad" in instruction.

If you're familiar with our old friend Euclid, then you know that the whole purpose of his work was to build arguments proving the geometric ideas of his contemporaries. It's commonly agreed that Euclid did not make up the ideas from Elements, but that instead, he was the first to curate and examine what was already being discussed. 

Aren't our students working in a similar environment? There's little to be "discovered" in planar geometry at this point, but we can still do well engaging students in the same work of critiques and proof gathering as Euclid and great mathematicians have practiced for millennia. 

Is the idea of argument and proof new to the current generation (post NCLB) of math students? Perhaps. Should we go back to teaching two column proofs the way we did it fifteen to twenty years ago? I don't happen to think so. I mean, there's a reason that Geometry instruction became more formulaic in this century - two column proofs are hard, and the rigidity of their structure turns off kids who are already struggling to find relevance in their work. I prefer flowchart or paragraph proofs because flowcharts have more cross-curricular appeal (logic and systems planning for coders), and paragraph proofs are more familiar (and therefore approachable) to the non-fiction writing our students already do in their other classes. Which students should do this? Everyone. Keeping proofs only in honors classes or with the "good" kids is prejudiced and demeaning to "regular" students. Will it take more work getting "regular" students to think critically? Probably. I think the way you package argument writing and proof to your students has a huge determining factor in their attitude toward it and belief that they can do it. 

Present it as a trial or a chance to argue with you (or each other). Kids love debates.

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Thanks for sharing!