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Problem Solving Is that a problem

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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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