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Problem Solving presented by Donna McLeish to Deming Elementary School Teachers January 19, 2005 Problem solving is MUCH MORE than solving word problems. Problem solving is a process of building a mathematical model of a situation and then reasoning with the model to draw conclusions about the situation. Problem solving is NOT a new idea or process… 1977 – National Council of Supervisors of Mathematics issued a position paper on basic skills. The first basic skill listed was problem solving: “Learning to solve problems is the principal reason for studying mathematics.” NCSM defined problem solving as “the process of applying previously acquired knowledge to new and unfamiliar situations.” 1980 – George Polya, in his classic How to Solve It, wrote “Solving a problem is finding the unknown means to a distinctly conceived end.” 1998 – The Principles and Standards for School Mathematics published by the National Council of Teachers of Mathematics states “Problem solving means engaging in a task for which the solution method is not known in advance.” Everyday Mathematics defines problem solving as the process of modeling everyday situations using tools from mathematics. Problem solving involves some or all of the following steps: 1. Identifying precisely what the problem is 2. Analyzing what is known and seeking further data as necessary 3. Playing with the data to try to discover patterns and meaning 4. Identifying mathematical techniques that can help in finding a solution 5. Looking back and asking “Does the solution make sense?” Everyday Mathematics K-3 focuses on four problem-solving representations 1. Concrete 2. Verbal 3. Pictorial 4. Symbolic Representations are closely related to solution strategies. Often, translating a problem into another representation is the key to solving it. As you discuss problem and solutions, compare various representations and ask children to translate from one to another. By encouraging multiple representations and translations among representations, you can help children develop into more powerful problem solvers.
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