Thinking About Mathematics
A major premise of the Interactive Mathematics Program is that most students are capable of thinking about mathematics and understanding complex concepts. This is a change from the philosophy of many traditional programs in which students do mostly rote work. The role of the program teacher also differs from that of a traditional mathematics teacher. In IMP, the emphasis is on guiding students and helping them make connections between key mathematical ideas and concepts, while minimizing time spent lecturing to the class. While students have both the teacher and their peers as resources, each is expected to think and to create in mathematics class.
The Interactive Mathematics Program is a problem-based curriculum. For example, each unit, such as Meadows or Malls?, begins with a motivating problem, too difficult for almost any of the students to solve at first. Students examine this initial situation and then look at similar, perhaps simpler, situations in shorter problems. At every step along the way, students must pose questions, look for patterns, and make connections between the current problem and the mathematics they have learned in previous units. By solving a variety of problems, students deepen their understanding, and they begin to abstract the concepts and refine the techniques needed to apply to the complex original problem.
In order for a problem to build mathematical power in the student, the student needs the opportunity to do genuine thinking about it. In IMP, this means giving students a chance to explore, conjecture, experiment, and reflect on their results. If students fail initially, they return to the problem for more exploration, new conjectures, and more experimentation. The real thinking in problem solving takes place in examining an unfamiliar situation and finding the underlying mathematical ideas. This will occur only if problems are presented without a fixed procedure or solutio
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