The document discusses problem solving and Polya's model of problem solving. It defines problem solving as applying previously acquired knowledge to new situations. Polya's model includes 4 steps: 1) understand the problem, 2) devise a plan, 3) carry out the plan, 4) look back to confirm the results and assess the solution process. The document provides more details on each step of Polya's model, such as asking questions to fully understand the problem and considering different strategies to devise a plan.

1. Introduction of problem solving
Meaning of problem solving
Problem solving means different things to different people; the majority of people
believe that it is solving word problems, and this includes non routine problems
and real problems.
Problem solving is the process of applying previously acquired knowledge, skills,
and understanding to new and unfamiliar situations.
Problem solving is the process used to find an answer to a statement or a
question (Hamada, R.Y. & Smith).
Problem solving should also incorporate communication and justification or
defense of the mathematical ideas that arise from the problem
Problem solving means engaging in a task for which the solution method is not
known in advance. In order to find a solution, students must draw on their
knowledge, and through this process, they will often develop new mathematical
understandings.

2. POLYA MODEL
Polya (1945 and 1962) was the first to describe a problem solving model based
on classroom experience
understand the problem
devise a plan
carry out plan
look back
Polya First Principle: Understand the Problem
This seems so obvious that it is often not even mentioned, yet students are often
stymied in their efforts to solve problems simply because they don't understand it
fully, or even in part. Polya taught teachers to ask students questions such as:
Do you understand all the words used in stating the problem?
What are you asked to find or show?
Can you restate the problem in your own words?
Can you think of a picture or a diagram that might help you understand the
problem?
Is there enough information to enable you to find a solution?

3. Polya Second Principle: Devise a plan
Polya mentions (1957) that it is many reasonable ways to solve problems. The
skill at choosing an appropriate strategy is best learned by solving many
problems. You will find choosing a strategy increasingly easy. A partial list of
strategies is included:
Guess and check Look for a pattern
Make and orderly list Draw a picture
Eliminate possibilities Solve a simpler problem
Use symmetry Use a model
Consider special Work backward
cases Use a formula
Use direct reasoning Be ingenious
Solve an equation
Polya third Principle: Carry out the plan
This step is usually easier than devising the plan. In general (1957), all you need
is care and patience, given that you have the necessary skills. Persistent with the
plan that you have chosen. If it continues not to work discard it and choose
another. Don’t be misled; this is how mathematics is done, even by
professionals.
Polya Fourth Principle: Look back
confirm results and arguments
assess effectiveness of solution
assess accuracy of results
assess usefulness of solution for solving other problem