So, this week my students continued their work with congruent triangles. The thought-process behind this part of the unit has been intentionally moving up from physical/concrete reasoning to more and more abstract and rigorous reasoning. Going step by step along the way.
We started last week by creating and measuring physical triangles in order to establish sufficient criteria for showing two triangles to be congruent. Then, this week we used diagrams of triangles with sides and angles marked to determine whether or not the two were congruent. After we got good at that we moved on to writing proofs that two triangles were congruent. Finally, we added on to that the next day by using CPCTC to prove various things were congruent. By the time we got to CPCTC students were like:
And I was like:
Yep. That’s it.
And they continued to be awesome.
I don’t know what it is that I’m doing right–whether it’s my trust in students’ writing and critiquing skills, or my amazingly coherent lesson planning which allows students to build skills incrementally, or if it’s the insightful feedback I give on student work, or if I just got lucky (again)–but I feel like when I teach proofs, students do well (a feeling that some of my colleagues do not share).
I feel particularly successful this year. And I do think it has to do with the first item on my (somewhat tongue-in-cheek) list up there. The students read and commented on A LOT of proofs over the course of this unit. They saw good stuff; they saw mediocre stuff; they saw some pretty crappy stuff too. And seeing work that is effective, alongside work that isn’t, is one of the best ways that I know to become a better writer.
Turns out it works with mathematical writing too.
Also, this week I got a great email from the mom of one of my students, letting me know that her child was really excited about what we’re doing in class and was eager to tell Mom all about it–something that this child apparently doesn’t do very often.
Talk about making my