See Part 1 of my notes from Phoenix: A Brief History of Math Education (NCTM President Matt Larson’s presentation.)

Here is Part 2.

#### Growth Mindset: telling is not teaching

In his short session, Dylan Kane pointed out that talking about growth mindset may be helpful to students “in the middle”. But there are students in our classes who have a long history of failure in math, some of whom have expended considerable effort over many years. To tell them that if they work hard their brain will grow can be counterproductive, as they have not seen evidence of that in previous math classes, and they may have grown cynical about this. To instill a growth mindset in those students is a difficult, but important challenge. Read Dylan’s summary of his talk, and how he takes on this challenge, on his blog. (In fact, you should check out his blog routinely: he frequently questions edu-fads and assorted silver bullets by trying things, paying close attention to his students, and learning from his experience. As he puts it, “teaching is messy.”)

I completely agree with Dylan: merely talking about growth mindset, and putting up slogans on bulletin boards like many schools do, does not accomplish a lot. Our actions day-to-day are what can make a difference: how we handle mistakes, how we support struggling learners, how we encourage risk-taking, and so on. I would add that there are *structural* actions we can take that carry a strong growth mindset message, such as extending exposure, and giving points for test corrections. I discussed this very topic in a post about math education research.

#### Exploding Dots

James Tanton is a great speaker, with excellent insights into both math and pedagogy. His *exploding dots* presentation was really fun. I won’t summarize it here, other than to say he took the idea of *chip trading*, which was a common way to introduce place value in various bases when I taught elementary school in the 1970’s, and turned it into a wonderful environment for mathematical exploration. In this microworld, students can do arithmetic right to left, or left to right, or in some other order. (Though I still need to check whether right to left would work in the case of division.) He also took the model further, as a way to do polynomial division and find some Taylor series. In other words, this one idea works from grade 1 to grade 12. I suspect James speaks at a lot of conferences, so if you can catch his talk, do. Or just go to his Web site.

#### Structured Rehearsals

David Wees, Sara Toguchi, and Liz Ramirez presented a fantastic way to get teachers to discuss teaching. It is a role-play of sorts, which they call a *structured rehearsal. *One participant plays the teacher, another facilitates the role-play, and the rest play the students. Periodically, when there’s a teaching decision to make, the facilitator calls “time out” and the “students” become teachers again and discuss what the “teacher” could do at this juncture. The facilitator runs that discussion. When she calls “time in”, the role-play resumes. This is a very efficient way to get teachers to learn from each other, far more so than visiting each other’s classes (which of course is a good thing to do — just not as efficient.) David, Sara, and Liz work for New Visions for Public Schools in New York. Check out their curriculum ideas for high school, and their *instructional routines.*

#### Equivalent Expressions

That was the title of my grades 6-8 workshop, in which I presented the Lab Gear as an entry point into equivalent expressions: the distributive law, factoring, combining like terms. It went reasonably well, in spite of some logistical complications. It was fun to see people I knew from Twitter Math Camp at one of the tables.

So that was Phoenix for me! I’ll be attending the California Math Council meeting in Asilomar, in about a month. I hope to see some of you there. Watch this blog for more info!* *

–Henri