Reflection: Problem Solving If done correctly, problem solving should engage people in the task of finding a solution and the method to finding the solution should be unknown to the problem solvers. Problem solving in mathematics causes people, no matter what their age, to draw upon prior knowledge to find a solution. In the process of solving the problem, often times people are deepening their mathematical knowledge as well as gaining a new awareness of mathematical concepts. Perhaps the most wonderful thing about problem solving is that it is often a puzzle/challenge in which many people become immediately engrossed in finding the solution. As a mathematics teacher, problem solving offers a way to engage students from all grades in various mathematical topics (e.g. probability, geometry, calculus). Besides meeting the standards for mathematics, problem solving is essential to teach students because it helps build new mathematical knowledge, makes previous mathematical knowledge more concrete, and allows a variety of problem solving strategies to be applied and adapted. The following problem I would use to enhance my students' understanding of 2-D & 3-D shapes as well as basic geometry concepts and formulas.
Favorite Problem A cylinder 120 cm high has a circumference of 16 cm. A string makes exactly 4 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?