The Curriculum and Evaluation Standards for Mathematics (1989) highlights the importance of problem solving and reasoning. The Standards considers mathematical reasoning to be fundamental to knowing and doing mathematics. The ultimate goal is for students to gain the ability to explore, to conjecture, to reason logically, and to use a variety of mathematical methods effectively to solve problems.
The important components of problem solving, problem posing, and mathematical thinking include problem models, strategic processes, metaprocesses, and affective models. Skilled problem solvers develop comprehensive mental models that focus on the principles of the domain, which in this unit is trigonometry, rather than the superficial characteristics of the problem.
By completing this unit, students will modify or extend their existing models by connecting new knowledge to their current knowledge structure, and then constructing new relationships among those structures. They will be given the opportunity to construct mathematical ideas and to reason mathematically in solving novel problems that are set within meaningful context.
A good way to use inquiry and discovery in a trigonometry unit is to use them throughout the unit. Inquiry and discovery can introduce the unit and form the focus of individual or group projects to extend or synthesize ideas. Student focused activities, where students work individually or collaboratively, can be used to review skills and concepts previously learned. The interweaving of these kinds of activities can show many situations where the mathematics is useful.
At the beginning of the problem solving process, drawing a diagram or making a physical model will provide useful direction toward the solution of the problem at hand. The problem solver should form a meaningful problem-situation from the beginning, know when to apply the heuristic, and monitor it's application, and then reflect on the results of their action.
Return to EMAT 6700