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1. Polya's Models<br />Polya’s Problem Solving Model<br />This problem solving model is made by a Hungarian who immigrated to the United States in 1940. His name was George Polya (1887 – 1985). According to Polya (1957), a good problem solving includes 4 phases or steps. First phase is understanding the problem. Without understanding the meaning, students will not be able to find a correct solution. Once students understand the problem, they devise a plan. After devising the plan they carry out the devised plan. Polya suggested that in the end they must look back at the solution to verify its correctness.<br />First step: Understand the Problem<br />This seems so obvious that it is often not even mentioned, yet students are often stymied in their efforts to solve problems simply because they do not understand it fully, or even in part. Polya taught us to ask students questions such as:<br />Do you understand all the words used in the problem?<br />What are you asked to find or show?<br />Can you restate the problem in your own words?<br />Can you think of a picture or a diagram that might help you understand the problem?<br />Is there enough information to enable you to find a solution?<br />Second step: Devise a plan<br />Polya suggests that it were many reasonable ways to solve problems. The skill at choosing an appropriate strategy is best learned by solving many problems. We will find choosing a strategy increasingly easy. A partial list of strategies is included:<br />Guess and check<br />Make and orderly list<br />Eliminate possibilities<br />Use symmetry<br />Consider special cases<br />Use direct reasoning<br />Solve an equation<br />Look for a pattern<br />Draw a picture<br />Solve a simpler problem<br />Use a model<br />Work backward<br />Use a formula<br />Be ingenious<br />There are a few questions that guides us in the process of devising a plan to solve the problem:<br />· What is the relationship between the data and the unknown?<br />· Is this problem similar to another problem that you have solved?<br />· What strategies can you see?<br />Third step: Carry out the plan<br />This step is usually easier than devising the plan. In general, all you need is care and patience, given that you have the necessary skills. Persistent with the plan that you have chosen. If it continues not to work discard it and choose another. This is how mathematics is done, even by professionals.<br />· Use the strategy you have selected and solve the problem.<br />· Check each step of the plan as you proceed.<br />· Ensure that the steps are correct.<br />Forth step: Look back<br />Polya mentions that much can be gained by taking the time to think and look back at what you have done, what worked and what did not. Doing this enables us to predict what strategy to use in solving future problems. This step is always overlooked in problem solving. As a teacher, we should remind our students to always check their answers. Some guidelines are as following:<br />· Reread the questions.<br />· Did the question asked answered?<br />· If it is answered, is it correct?<br />· Does the solution seem reasonable?<br />We need to teach our students how to solve mathematical problems. Learning to use Polya’s Model is a first step towards becoming a good problem solver. In Step 2 of Polya’s Model, we need to know various strategies to enable us to solve problems.<br />