in.fbsbx.com Mathematics in the Modern World Hand Outs Done Problem-solving and Reasoning Problem-solving has been an integral part of the mathematics curriculum that must be taught alongside the various mathematical concepts and skills necessary for success in school and in real life. Most occupations require good problem-solving skills. This section aims to help you become a better problem solver and to show that problem-solving can be an enjoyable experience. In cognitive psychology, problem-solving refers to the mental process people go through to discover, analyze, and solve problems. George Polya (1877-1985) defines it as an act to find a way out of difficulty, find a way around an obstacle, find a way where none is known, and attain a desired end that is not immediately attainable by direct means. Problem-solving involves all of the steps in the problem process, including the discovery of the problem, the decision to tackle the issue, understanding the problem, researching the available options and taking actions to achieve your goals. Common Problem Solving Strategies/Heuristics Heuristics are procedures or strategies that do not guarantee a solution to a problem but provide a more highly probable method for discovering the solution to a problem. There are many reasonable ways to solve problems. You will find choosing a strategy increasingly easy. Here is a partial list of problem-solving strategies: 1. Working backwards - This strategy is used to solve problems is used to solve problems that include a number of linked factors or events, where some of the information has not been provided, usually at the beginning of the problem. This entails starting with the end results and reversing the steps you need to get those results to figure out the answer to the problem. 2. Guess and Check - Often referred to as "Trial and Error", it is important to recognize that an error really isn't a mistake at all, it helps to guide the problem solver to the next attempt at the answer. The following are the essential features of the guess and check strategy: a. Make an "educated" guess at the solution. b. Check the guess against the conditions of the problem. c. Use the information obtained in checking to make a better guess. d. Continue this procedure until the correct answer is obtained