PS+Learning+Math

=Learning Mathematics Through Problem Solving (due July 15, 2009)= ** ARCHIVE - What does it mean to learn mathematics through problem solving? a. Explain one idea in one paragraph. Include a math example to support your idea. b. Put your name at the end of your paragraph. **

Everyone's learning is unique. Thus, it is important that all opportunity is given for students to learn and understand according to their needs. According to George, " Learning and teaching mathematics through problem solving means that we give our students an opportunity to struggle/play with a problem, giving them an assurance that it is okay to make a mistake and having them understand that there are many different ways to find an answer to the problem.". Learning through problem solving gives each student a chance to comprehend mathematics and to utilize their prior knowledge. As Jerry states, "Through problem solving, students (and teachers), often reason their way to a new understanding. Often, this conjecture is a generalization of mathematical knowledge gained through solving a problem that can be used in other similar problems. One math example is from our class when we considered how many possibilities there are when two dice are rolled. We calculated that there were 36 possibilities (6 squared). We then made a conjecture that the number of possibilities is (number of choices) squared. We tested our conjecture considering a spinner that had 4 equal sections and discovered that there were, in fact, 16 possibilities (4 squared); we tested it again considering a problem involving a suit from a deck of cards and discovered that, in fact, there were 169 possibilities (13 squared). By extending our understanding from one specific example, we were able to develop new mathematical knowledge that can be applied to many situations." It is important to see that mathematics should be learned through problem solving. Not only does it allow students to develop their own learning, it also allows them to relate mathematics to their everyday life. (Penny Senior)