1. Skills to solve mathematics problem Abdul Malek Osman

2. 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

3. 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

4. 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

5. HOW? Polya’s “How to Solve It” FIRST You have to understand the problem. SECOND Find 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. THIRD Carry out your plan. FOURTH Examine the solution obtained. 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

6. Step 1: Understand the problem Identify what type of problem is given –Routine? –Non-routine?

7. Routine problems Example: (Fractions, J01/I/D) Giving your answer as simply as possible, evaluate

8. 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.

9. 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

10. Step 3: Carry out the PLAN?

11. Step 4: EXAMINE the solution.