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Problem Solving

Dive deep into the art of problem solving, explore various solution strategies, and learn how to engage students in mathematical modeling. Discover the importance of multiple representations and translations to enhance problem-solving skills in children.

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Problem Solving

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  1. Problem Solving presented by Donna McLeish to Deming Elementary School Teachers January 26, 2005

  2. 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.

  3. 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.”

  4. 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.”

  5. Everyday Mathematics defines problem solving as the process of modeling everyday situations using tools from mathematics.

  6. Problems for which the solution method is known ahead of time may be useful exercises. But, these are not genuine “problems” as we refer to in problem solving. In Everyday Mathematics, problem solving is broadly conceived and permeates the entire curriculum.

  7. These broader definitions of problem solving are not restricted to arithmetic and certainly not to arithmetic “word problems.” Central to all of them is the idea that solution methods are not known in advance. A problem is NOT a problem if the problem solver knows exactly what to do right away.

  8. Problem solving involves some or all of the following steps: • Identifying precisely what the problem is • Analyzing what is known and seeking further data as necessary • Playing with the data to try to discover patterns and meaning • Identifying mathematical techniques that can help in finding a solution • Looking back and asking “Does the solution make sense?”

  9. Everyday Mathematics focuses on four problem-solving representations • Concrete • Verbal • Pictorial • Symbolic

  10. 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.

  11. The Importance of Problem SolvingPages 53-55 Everyday Mathematics Teacher’s Reference Manual Grades 4-6

  12. Essay 10 Problem Solvingpage 284 Everyday Mathematics Teacher’s Reference Manual Grades 4-6

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