Cuoco, Goldenberg, and Mark’s Habits of Mind.Common Core has their Standards of Mathematical Practice.But there are many alternative or additional things we could have included. We agreed to use the ones James had already been using. Of course, if you’re a math teacher, you know there are a lot of lists of mathematical habits of mind. One-sheet-mathematical-habits-of-mind Download If you want these posters, the PDF file is here. The key words are: Experimenter, Guesser, Conjecturer, Visualizer, Describer, Pattern Hunter, Tinkerer, Inventor I know, I know, the lighting is terrible. ![]() ![]() Photo of the posters hung up in one of my rooms: Most importantly, here is a link to James’ original blogpost with his habits of mind and rubric. Hopefully I’ll blog about it! But for now, I wanted to share with you posters I made using James’ Mathematical Habits of Mind. Right now I have an inchoate idea of how this is going to unfold. So when James shared this idea with me, I got excited. And interestingly, last year, I toyed with the idea of formally getting kids to be metacognitive about problem solving strategies - but decided to focus on something else instead. And he’s new to my school this year, and so when talking about the course, he shared with me how he formally incorporated Mathematical Habits of Mind in his teaching in previous years. Another teacher, my friend James, is also teaching the same course. One of the classes I’m teaching this year is Advanced Precalculus. And my classes are going to be with all my kids together in a single room, which is such an awesome thing compared to last year. At the time, I just didn’t have it in me to blog about the experience.īut now we’re about to start a new school year. As you can imagine, the pandemic took a toll on teachers, and at least for me and my teacher friends, we were working insane amounts of time, and it was so hard. (Even though I wasn’t able to fully exploit this structure in my thinking.) ![]() And the neat geometric structure that arises out of the setup. But what I thought was lovely is how many different places my brain when went trying to think through this problem. And I have no way to even start thinking about (d). And then I think I solve (c) for n=3 and n=4 (and got an answer for n=5, but haven’t proved it is optimal). I think I was able to successfully solve (a) and (b). This is from the 2019 entrance questions for a summer program. The problem that I got nerdsniped by and ended up spending hours working on over Thanksgiving break was as follows: And they shared this old entrance exam for this summer camp they were thinking of possibly applying for, and wanted some guidance. The second problem came from a student who emailed me about wanting to become a better problem solver. And I thoroughly enjoyed being wrong and telling the kids that this problem messed with my head, and they helped me see the light! And then I shared their thinking with James, who didn’t have the same answer, and he too was convinced. But the students who didn’t convinced me with their logic. I shared it with my class, and lo and behold, a couple students got what I got, and a couple students didn’t. It was marvelous! Finally, I felt like I understood things and felt confident. I kept switching back and forth between a couple different answers. ![]() So I made a simpler case, and then I thought I understood it. Then I tried but didn’t understand his logic. I thought I solved it successfully and was feeling really confident. If I were to have a computer program randomly create new groups: (a) what is the total number of different configurations/outcomes we could have? (b) what is the probability that your entire group was the exact same if you were in a 4-person group? So here’s the two-part problem I posed to my kids: First Problem: We have a class of 14 students, with two groups of 3 and two groups of 4. We had been finishing up our unit on combinatorics and also creating new groups, and he devised a great question. The first one came from my Precalculus co-teacher James. Here are two problems that have gotten me to think a lot.
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