Skills to solve mathematics problem

Abdul Malek Osman

WHY?

• A pupil MUST be able to use his or her mathematical knowledge and skills– to solve the problems of everyday life &

school work– as a basis for further mathematical

understanding

• Learning standard steps will help students solve mathematical problems better

WHAT?

• What is a Problem?

• Schoenfeld (1989) defines a mathematical problem as a task– in which the student is interested and

engaged and for which he/she wishes to obtain a resolution

– for which the student does not have a readily accessible mathematical means by which to achieve that resolution

WHAT?

• Most of the textbooks “problems” are in fact just exercises.

• Polya (1969) defines the types of problems as routine and non-routine.– Routine problems – apply a specific rules or

procedures to solve them (eg. drill or practice). Does not demand invention or originality

– Non-routine problems – demands invention and originality for solution

HOW?• Polya’s “How to Solve It”

FIRSTYou have to understand the

problem.

SECONDFind the connection between the data and the unknown.

You may be obliged to consider auxiliary problems if

an immediate connection cannot be found. You should obtain eventually a plan of the

solution.

THIRDCarry out your plan.

FOURTHExamine the solution obtained.

i. Look for a pattern - Heuristicii. Use deduction (or induction) -TSiii. Work backwards - Heuristiciv. Guess & check - Heuristicv. Write an equation - Heuristicvi. Draw a picture/graph/table - Heuristicvii. Use a model - Heuristic

Step 1: Understand the problem

• Identify what type of problem is given– Routine?– Non-routine?

Routine problems

• Example: (Fractions, J01/I/D)• Giving your answer as simply as possible,

evaluate

2

1

7

3

Non-Routine problems

Example• I am a number. I am greater than the product of

4 and eight. I am less than the difference between 550 and 515. I am an even number. What number am I?

Example• A rectangular box has dimension 24cm by 9cm

by 7cm. A ball has a radius of 3cm.• Find the number of balls that can be placed in

the box.

Step 2: Find connection. What is the PLAN?

i. Look for a pattern - Heuristic

ii. Use deduction (or induction) -TS

iii. Work backwards - Heuristic

iv. Guess & check - Heuristic

v. Write an equation - Heuristic

vi. Draw a picture/graph/table - Heuristic

vii. Use a model - Heuristic

Step 3: Carry out the PLAN?Template to solve mathematics problems (adapted from Pat Mower & G. Polya) PROBLEM: (State the problem)

UNDERSTAND: (Rewrite the problem in your own word)

DEVISE A PLAN: (Choose the problem solving strategies listed below

Look for a pattern Write an equation

Use deduction (or induction) Draw a picture/graph/table

Work backwards Use a model

Guess & check

CARRY OUT THE PLAN: (Use the strategy to solve the problem)

LOOK BACK: (Create a similar problem)

Step 4: EXAMINE the solution.