This year in geometry, I am striving for a more constructivist approach. Many concepts (like perpendicular or supplementary) are familiar. The challenging part is to write the definitions in polished, conditional form and then integrate them into two column proofs. Approaching new material this way is more engaging and promotes retention.
Rather than announcing the definitions from on high, I have been having students discuss the terms and attempt the if-then form in small groups. Sometimes instead of discussion, they investigate the concept using geogebra or math open ref. Then we collect the attempts and discuss as a class. Once we agree on the ideal wording, they add it to their flash card deck with an accompanying diagram. Most lessons close with students using the new theorems along with ones they already know to write a two column proof with their partner.
Starting class with more generative activities, making time for retrieval practice (with their flash cards) and free recall sessions, all support my goal of teaching in a way that uses and models strategies based in cognitive science. Last year when I read Make it Stick, my approach to teaching study skills and to structuring class changed. Moreover, it was a hot topic in one of my grad school classes. My Instructional Leadership professor, Kevin, used the term "effective effort" to describe the retention promoting strategies argued for in Make it Stick. It isn't enough to preach Dweck's "effort is the path to mastery" if it is not accompanied by what type of effort makes for more effective learning.
Once again, I am thankful for the Mtbos. While I was away in grad school, discussing Make it Stick in class, a handful of math teachers (Julie, Meg, Lisa) made resources for teaching the strategies to students. I happily used their resources.
My geometry classes started by watching this video on study strategies followed by a jigsaw reading/discussion of this and this. I had wished that I would have found time at the beginning of the year to have this discussion. However, I think that waiting until they had been in class a month was good because we were able to discuss how what we do in class and fits in with cognitive based learning strategies.
|We add to our Effective Effort Wall as we discover strategies that work.|
Standards based grading in geometry is coming along and supports the idea of effective effort well. I give them frequent skill checks that both provide a chance for me to give them feedback and for them to calibrate what they know and don't know.
So far I am not giving them retakes for each skill check, just including skills that students haven't yet mastered on subsequent skill checks. I provide time for corrections but not yet for reflection! I need to make that praise polish form to pass out from time to time to collect their reflective thoughts... Or maybe it should be a gdoc journal? Or maybe it could be on their blogs? I am still thinking.