# Mathematics Where Students Learn by Doing

From the Winter 2011-12 *Caller*

### By Jim Wysocki

**In a progressive school, the methods by which courses are taught will often differ greatly from what we teachers experienced as students. **One such method is problem-based learning in mathematics, a popular example being the Harkness Method, which originated at Phillips Exeter Academy in New Hampshire. Catlin Gabel’s goal of producing young adults who are independent learners and resilient students can be seen in many aspects of this problem-based learning method. Asking questions, both by student and teacher, is a fundamental component of this method. In that vein, there are several questions to consider when introducing it. What is problem-based learning? How is it uniquely used at Catlin Gabel? How is it similar or dissimilar to the way other schools are approaching it? How can it help students become more successful mathematics students?

**“What do you mean, we have to do the problems before you teach us the material?”**asks a student at the beginning of a course taught in a problem-based format. This is then followed by, “Wait, we have to present the solutions? Aren’t you going to teach us?!” the next day. Students initially struggle with the method because they have come to expect certain practices in a math classroom. Although this is an overgeneralization, many students have come to expect, rightly or wrongly, that a math classroom is about taking notes, writing down procedures, and then practicing those procedures. Even when they have not been successful with such an approach, they cling to it because it is familiar.

**It is becoming more commonly accepted and realized that students need to have an opportunity to work through ideas with feedback from others in order to master concepts.**This does not merely need to be feedback from the teacher, although their role is critical to the success of the method, but from the students as well. In fact, as the year has progressed our students are beginning to recognize the value of their peers’ feedback, and their ability to provide it. As one student said, “I like how in class we share our work on the board, because I like to see how other people decide to do different problems. It gives me insight on other possible ways to do something, and I learn a lot.”

*Jim Wysocki,**chair of Catlin Gabel’s Upper School math department, has been at the school since 2010. He previously taught in California at Chadwick School and the Irvine Unified School District, and was a Math-Science Fellow with the Coalition of Essential Schools.*

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