skills to solve mathematics problem abdul malek osman
TRANSCRIPT
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.