I had my first away game this morning at CMC-South in Palm Springs, meaning I gave my first presentation outside the comfort of the bay area and more importantly outside the comfort of lots of familiar faces (thanks Dan for providing one familiar face). It was also nice to meet @johnberray offline and I very much appreciated his enthusiasm.
I'm making the slides available, including the notes to myself which might make some of them more meaningful if you weren't there (on the other hand, I wrote these notes for myself so they might just make things more confusing).
Overall, I'm pretty happy with how the presentation went. Maybe would have wanted a little more energy, but it was 8:30 in the morning. Maybe would have wanted to be a little more coherent and structured at times, but that's something I always have to work on and is inherently difficult when you let (expect?) participants to actually participate (I wouldn't want it any other way). The best (ie funniest) feedback I got was someone who rated the workshop a 5 out of 6, noting that we're never finished...a recurring theme from the presentation. Also got some helpful feedback from a few people who were expecting to learn about the Common Core Standards of Mathematical Practice specifically. While there is abundant overlap between my mathematical habits of mind and the Common Core Standards, I didn't address this directly. Maybe next time...
I posed some open ended questions at the end of the session that I think are worth reposting and expanding on here.
- The practice standards are broad and are not delineated by grade. How do we make specific changes to how we teach? What are appropriate ways to address each practice standard at each grade? What habits should we expect students to have when they enter my class in grade x?
- Resources for teaching habits of mind are few and far between. Where are new resources going to come from?
- The practice standards are easier to implement with good problems. Good problems are hard to find/create. What's the best structure/community for doing this?
- No one talked about habits of mind when I was a student. How can I be supported to teach in a way that is so different from my own experience?
- Are the standards for mathematical practice actually valued? The amount of text devoted to the content standards versus the amount of text devoted to the process standards seems to imply that this value is cursory. Furthermore, are habits of mind valued beyond their ability to help students access content? Are they valued as mathematics in and of themselves?
- Developing habits of mind in a deep way is not an easy task. How do we convince ourselves and our students that this time and effort is worthwhile?
- How do we redefine success from getting the right answer quickly and often to the messier definition of success that includes making progress, having an insight, solving a simpler problem, creating your own problem, helping someone else, etc?
- Will habits of mind be taught in most classrooms if they’re not explicitly assessed? How do we assess these things?
And two questions that I'm thinking about based on specific feedback/questions from participants.
- If so much time and energy is expended on mathematical thinking, will content skills be lost in the crowd? In other words, is the counting diagonal problem a problem about factoring?
- How do we create an atmosphere in our classroom where students don't think twice about asking about something they don't understand (such as the vocabulary "relatively prime"), where failure is encouraged, and where students want to be challenged?