Problem Solving

What is Problem Solving?

1. a situation where the method of solution is not obvious.
2. the process of applying previously acquired knowledge, skills and understanding to new unfamiliar situations.
3. the process used to find an answers to a statement or a question.

Why Problem Solving?

1. it is an appropriate vehicle for current emphasis on processes in mathematics teaching, ea. classification, organisation of data, analysis, generalisation, representation of data, hypothesis testing, etc.
2. it is an appropriate ways to introduce and develop concepts and relationships ie. by investigation
3. it enables children to apply mathematics to practical situations and as a result shows that mathematics is useful. Subject integration can be incorporated with application.
4. when problem solving, we incorporate a wide range of mathematical content.
5. it is suitable for:

• cooperative group learning
• catering for talented children

6. it should be motivating and interesting for all the children.

Why A Special Emphasis on PS?

1. in the classroom can lessen the gap between real world problem and the classroom world and this set a more +ve mood in the classroom.
2. PS shows an intraction between mathematical idea.
3. PS is an integral part of larger area of critical thinking, which is universally accepted goal for all education.
4. PS permits student to learn and practice heuristic thinking.

Routine Problem

1. those that merely involved an arithmetic operation with characteristics

• present a question to be answer
• gives the facts or number to use
• can solved by direct application of previously learned algorithms and the basic task is to identify the operation appropriate for solving the problem.

Non-routine problem

It is occurs when an individual is confronted with an usual problem situation, and it not aware of a standard procedure for solving it. the individual has to create a procedure. to do so, he/she must become familiar with the problem situation, collect appropriate information, identify an efficient strategy, and use the strategy to solve the problem.

Example:

I counted 7 cycle riders and 19 wheels go past my windows. How many were two wheelers and how many were three wheelers?

Polya Model

4 steps:

1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Look back

Understand the problem
1. Ask question
2. Explain the problem in your own words
3. Relate to similar problem
4. Highlight important parts
5. Act out or model the problem
6. Draw a diagram

Devise a plan
1. consider various strategies
2. compare to similar problems
3. fine the connection between the data and the unknown
4. consider auxiliary problem if an immediate connection can be found

Carry out the plan
1. make adjustment as you go noted the effect on your original plan
2. use the strategy you selected and work the problem
3. check each step of the plan as you proceed
4. Ensure that the steps are correct.

Looking back
1. check that all important information has been utilised
2. check computation
3. consider the reasonableness of the solution
4. look for alternative solution
5. re-read the question and ask yourself whether you have really answer the question


PS Strategies

1. Trial and error
2. construct a model
3. Use a diagram
4. simplify the problem
5. look for a pattern
6. act out the problem
7. investigate all possibilities
8. construct a table
9. identify a subgoal
10. work backward
11. use a formula
12. use logical reasoning ( non-routine)

--> http://www.mathstories.com/strategies.htm

Guess and Test

3 ways to guess:

• -random
• -systematic
• -inferens

example 1 :

place the numbers from 1 to 6 in the diagram below in a way that the total of each line is 12

example 2 :

Find A and B if
AB x BA = 114+3040 =3154

Construct a model

This strategy need to build a real model. from a model student can solve the question more easy without thinking to calculate

example :

How many ways can you arrange 5 squares which it side must touch to make one box without cover when you fold it.