Thinking and Problem Solving: A New Look at Mathematics

Course Description

Students should have experience with geometry and algebra in order to get the most from this class. Students interested in developing new skills, perspectives, ways to think about problems should strongly consider this course, as well as students who feel limited or frustrated with traditional approaches. This course specializes in building students' confidence in mathematical abilities and reorienting perceptions about math.

This course is designed to introduce students to an inductive approach to mathematics, doing math as it is done by mathematicians. Instead of starting with a formula and applying it, for example, students start with a real world problem and work together to discover the formula that best solves the problem. Students work in groups to test creative solutions to these problems, and analyze the diversity of approaches taken by each group.

There is an emphasis on valuing the process of eliminating incorrect solutions as well as locating effective ones, trying different approaches and recording the utility of each approach. Working in pattern identification, students gain a deeper understanding of why a particular formula solves a problem or describes a pattern; why it is that this formula must give the answer, given its form and the logic of the problem. Students take a new approach to proofs, and continue on to study useful applied areas such as elementary probability theory and finance.

The combination of subjects and methods in this course allows students to see math in a way traditional high schools are unable to teach it, approaching these problems as open-ended opportunities for creativity and intellectual excitement, with emphasis and pressure taken off of the final result alone.

Instructor(s)