Mathematical problem solving is the process by which an individual uses previously acquired knowledge, skills, and understanding to satisfy the demands of an unfamiliar situation. The essence of the process is the ability to use information and facts to arrive at a solution. There are two characteristics of problem solving that must be remembered when solving problems using mathematical processes.
1. The mathematical process does not always give you the answer—just more information so that you can make a more informed decision. Good decision-making requires good information.
2. Whenever perfection is not possible or expected, levels or intervals of acceptability must be established. When perfection is not possible someone must determine the amount of error that is acceptable. The acceptable level of error may be determined by standards, manufacturers' recommendations, comparison to another situations or machines or personal experience.
Both of these characteristics will be utilized and explained in more detail in later chapters by using examples.
Problems can be solved in different ways. One of the objectives of this chapter is to increase the reader's knowledge of problem-solving methods. Seven different approaches to solving mathematical problems will be discussed: diagrams and sketches, patterns, equations and formulas, units cancellation, intuitive reasoning, spreadsheets, and flow charts.
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