Every summer since 2001, EDC has conducted a three-week course for teachers as part of the Park City Mathematics Institute in Park City, Utah. Bowen Kerins helped develop the curriculum and looks forward to teaching the course—and learning from it—every year.
This year, we had about 60 middle and high school teachers attend the course, coming from Canada, Turkey, Spain, and all around the United States. Many of these teachers are national leaders—former or current directors of the National Council of Teachers of Mathematics and other major organizations. These are good teachers from around the world who want to get better and who want to network and learn.
For three weeks in July, we get to work in a really picturesque part of the country. Teachers who attend usually receive grants to cover their costs—some from the National Science Foundation, Teach for America, or various professional development groups.
Back in 2000, the director of the Park City Mathematics Institute discovered the programs EDC was doing with Boston University and asked us to design something for their teachers in Utah. Since then, it has really expanded. Now the EDC course is just one piece of the Park City Mathematics Institute, which is organized by the Institute for Advanced Study in Princeton, New Jersey.
The goal of our course is to build mathematical thinking skills and content knowledge for teachers to use when they return to the classroom. We are really building what we call mathematical habits of mind: the ability to generalize, problem solve, and think about what you’re doing and writing. Habits of mind are the mathematical big ideas—what you’re really learning when you’re learning math.
In the workshop, we expect teachers to be students. We give them problems and let them figure the problems out for themselves. A popular comment from teachers is, “I really see what it is like to be a math student again.” They seldom get to play this role, as they are always in the role of the math expert. At the end of three weeks, they see how much they have learned. The results are night and day when compared to a standard lecture format. Teachers retain this new knowledge so much better because of the collaborative experiences and discussions they have had. And, this is a style that they can use in their own classes. It translates so easily.
This sort of training can be a paradigm shift for any teacher, especially those whose experiences as teachers and students are more traditional. Some teachers enter the program skeptical of the approach. They get to see how well it works for them as a student, and often decide to transform the ways they work with their own students.
I can give you two problems we do as an example. For instance, a rectangular box has the same volume and surface area. What are some possible dimensions for the box? There are 9 or 10 possible answers.
Teachers work by themselves and in groups, trade ideas, share with the class. We stress connections among several problems that may look very different.
And here is the second problem: Three fractions add up to ½, and all three fractions have the numerator 1. What are the three fractions?
These two problems are actually closely tied together, and what we do is translate the solving and connecting experience to what teachers will do with their own students back in the classroom.
Through leading this workshop, I have seen a number of teachers change their thinking about math: While skills and concepts are important, there is a deeper level. Mathematical habits of mind are the reason why we learn and teach mathematics. It’s amazing to get the chance to have this kind of impact on teachers and on conversations about what mathematics really is.
Originally published on October 27, 2011