I’m still clearing some links out of the filter, trying to get fresh for the new school year. Some great classroom action from the last school year.

Amy Zimmer shows us how to take a repetitive exercise worksheet and wring some more cognitive demand out of it:

My students were looking for and making use of structure, my students were constructing viable arguments and critiquing the reasoning of others, my students were looking for and expression regularity in repeated reasoning! I know just how geeky this sounds, but man, it was beautiful!

More adventures from Prof. Triangle Man in measurement in the elementary grades:

Groups of three are each given a dowel (or, in this year’s case, a paper strip). The dowels vary in length. The lengths are chosen to provide a useful combination of compatibility and incompatibility. One may be 9 inches long, while another is 15 inches long. But-and this is important-these lengths are never spoken of! You will never refer to these dowels using standardized lengths.

Bowman Dickson helps me see the benefit of starting at a low rung on the ladder of abstraction, even in highly abstract contexts like calculus:

So general pedagogical moral of the story? Letting students conceptualize something on their own before bringing in mathematical language and notation makes it more likely that the notation will aid in their understanding rather than provide another hurdle in learning.

Evan Weinberg used cell phones and TVs to drive calculations of similar figures.