2. INTRODUCTION
“The ability to solve problem is the heart of
mathematics… mathematics teaching at all
levels should include opportunities for problem
solving, including the application of
mathematics to everyday situations”
Cockcroft Report, 1982
3. INTRODUCTION
“Problem solving should be the central focus of
the mathematics curriculum. As such it is
primary goal of all mathematics instruction and
an integral part of all mathematical activity.
Problem Solving is not a distinct topic but a
process that should permeates the entire
program and provide a context in which
concept and skill can be learned”
NTCM, 1989
4. INTRODUCTION
Build new mathematical knowledge through
problem solving;
Solve problems that arise in mathematics
and in other contexts;
Apply and adapt a variety of appropriate
strategies to solve problems;
Monitor and reflect on the process of
mathematical problem solving
NTCM, 2000
5. WHAT IS A PROBLEM?
A problem is a task for which:
The person confronting it wants or needs to
find a solution,
The person has no readily available
procedure for finding the solution,
The person must make an attempt to find a
solution.
(Charles & Lester, 1984)
6. A PROBLEM OR AN EXERCISE?
As most textbook “problems” are practice
tasks, which can be solved by direct
application of a procedure illustrate in the
chapter to which they are appended, they are
mere exercises.
7. A PROBLEM OR AN EXERCISE?
Solve the following pair of simultaneous
equations using the method of elimination:
x + y = 12
3x – 2y = 16
8. A PROBLEM OR AN EXERCISE?
Cows, Chickens and Snakes
On a farm there are cows, chickens and
snakes. Altogether they have 10 heads and 24
legs. How may cows, how many chickens and
how many snakes are there? Explain how you
worked it out?
9. WHAT IS PROBLEM SOLVING?
Problem solving is a complex process which
requires an individual to coordinate previous
experiences, knowledge, understanding and
intuition, in order to satisfy the demands of a
novel situation.
In simple terms it is the mental journey one
takes to arrive at a solution starting with the
given of a situation.
10. PROBLEM SOLVING STAGES
Read the problem
Understand the problem
Think of a way to solve the problem
Translate the problem into a mathematical model/sentence
Do the mathematical computations, etc.
Arrive at a solution
Check solution for accuracy/reasonableness, etc.
11. COMMON DIFFICULTIES
Inability to read the problem
Misinterpretation of the conditions of the
problem
Lack of strategy knowledge
Inappropriate strategy used
Inability to translate the problem
Incorrect formulation
Computational errors
Imperfect mathematical knowledge
13. UNDERSTAND THE PROBLEM
Look for information given
Visualize the information
Organize the information
Make a table
Connect the information
14. DEVISE A PLAN
To make representation
Draw a diagram
Make a systematic list
Use equations
To make calculated guess
Guess and check
Look for a pattern
Make suppositions
15. DEVISE A PLAN
To go through the process
Act it out
Work backwards
Before after
To change the problem
Restate the problem
Simplify the problem
Solve part of the problem
16. CARRYING OUT THE PLAN
Use mathematical knowledge
Use mathematical skills
Use logical thinking
17. LOOK BACK (REFLECTING)
Check the solution – is it reasonable?
Improve on the method used
Seek alternative solutions
Extend method to other problems
18. PROBLEM TO SOLVE
On a farm there are cows and chickens.
Altogether they have 41 heads and 100 legs.
How many chickens are there?
21. PROBLEM TO SOLVE
Ramli has 15 pebbles and he wishes to place
them in 3 piles with an odd number of pebbles
in each piles. How many ways can he do it?
27. PROBLEM TO SOLVE
Planet Marston has only two types of
creatures, triads with 3 legs and pentads with 5
legs. Their legs glow in the dark. While on
Marston, one nights Balpz counted 34 legs.
How many triads and pentads were there on
Marston?
As most textbook “problems” are practice task, which can be solved by the direct application of a procedure illustrated in the chapter to which they are appended, they are mere exercices.
