In study teams, students are empowered to see themselves as mathematical thinkers. They recognize their own strengths and those of their peers as they investigate, build a personal understanding of mathematical concepts, and apply their learning to challenging problems.
Several methods of investigation and justification weave through this course. Classwork is intentionally written to be challenging, and thus assumes that students will have peer and teacher support. Lessons are not designed to have students working alone. Lessons often require students to solve problems in multiple ways so that they see the benefit of other strategies and ways of making sense of the problems. Students are encouraged to formulate mathematical questions, structure investigations, and justify their findings.
Each of these processes is more fully realized as students converse about the problems and their approaches to solving them. Students’ discovery of different ways to approach a problem and justify a solution, for example, has a more lasting impact when it emerges as they examine each other’s work than it does when students are simply told about them.
This is not to say that direct instruction has no place in this course. Rather, the role typically assumed by teachers must be modified when using study teams. The teacher becomes less of a “sage on the stage” and more of a “guide on the side,” allowing students to explore problems and construct their own initial understanding. To do this, students need to explain their ideas and listen to each other. Sometimes their solutions will not work, but our goal is to have students find this out for themselves as they investigate further and discuss their work with their peers. At the same time, teacher-led discussions are still essential to bring students’ ideas into the class conversation to summarize results of study team activities and to tie together big ideas after the students have had a chance to work on the pieces. These guided discussions should be conducted in an open, accepting way with the purpose of helping students make connections to understand where and how the pieces of information fit together. In short, most discussions and lectures with the entire class are based on what the teacher observes while the students work in their study teams.