Here’s an excerpt from my latest at Edutopia (including a diss on Robert Marzano and the like). It’s about engaging math teachers:
Keep This Rule of Thumb: Complete, Consistent, Correct
By “complete, consistent, correct,” I mean we should allow multiple pathways to a correct answer that a) allow for full understanding of a given procedure, b) can be used time and again without fail, and c) actually have a sound basis in math. While it sounds constricting, it removes some of the limitations we’ve set for ourselves when looking at student work.
For instance, when finding 25% of 80, the most basic thing we can do is turn the percent into a decimal (0.25) and multiply that decimal by 80. The result is 20. Yet when I presented this problem to a seventh grade class just learning this, one of the students astutely observed that 10% of 80 is 8, and 25% is just 10% + 10% + 5%. They doubled 8 (16), then took half of 8 (4), and added the results (16 + 4 = 20).
Some teachers might mark that incorrect because it doesn’t follow the exact procedure they asked for, but we really should accept such a response fully, not just because of the answer, but because the procedure the student used works time and again.
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Mr. Vilson, who wants Friday to be over already, and it’s only Thursday …