Analytical tools or Strategies to solve problems Satu daripada 3 aspek penting diberi penekanan dalam kurikulum (semakan) agar murid dapat melatih minda mereka supaya berfikir secara bersistem dan membuat keputusan yang bijak.

What is problem solving ? Solving problem is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice…if you wish to learn swimming you have to go into the water, and if you wish to become a problem solver you have to solve problems. (Polya 1962, p.v)

How to go about solving problems ?

Do you. . .? recognize a problem if you see one? understand the problem statement? have the heuristics to solve the problem? have the repertoire of strategies to help you solve problems? have the right attitude towards problem solving?

Some Problem solving strategies Suggested strategies for primary schools are: Guess and Check Simplify a problem Draw a diagram Make a table Act out a situation Look for a pattern Work backwards Experimenting

Activity 1.1: Handshakes There are 12 people in a small tutorial group. At the start of the semester they shake hands to introduce themselves. How many handshakes altogether? What if there were 50 people in a lecture theatre?

How would you solve this problem ?

What strategy did you use ?

Did you . . .? try to simplify the problem ? act it out? draw a diagram? make a table? guess & check? look for a pattern? Which strategy is most effective?

Simplify & Act out a situation Students dramatise or simulate a problem situation. This will help them understand the problem and devise a plan.

Let us try more problems ...

Read the following problem and try to help Ramon and Kyle. They are weighing in their sheep at the county fair. Ramon notices that his sheep weighs 15 pounds more than Kyle’s. Together the two sheep weigh 205 pounds. How much does Kyle’s sheep weigh?

How did you solve it? How did you start? What strategy did you use? Were you successful doing it alone? Does talking with a friend help? What was your thinking process? Did you use Polya’s or Krulik & Rudnick’s heuristic model?

Strategy used ? Trial & Error ? Quess & Check ?

Guess, check and improve  Make a random guess - Check the answers Guess systematically - Guess the answers according to certain sequence.

Other strategies used ?

Using algebraic equation ?

Which strategy is more elegant ?

N e x t . . .

Example: How many squares are there in a 6x6 grid?

How would you go about solving this problem ?

Can you …? simplify the problem? list out your solutions? make a table? look for a pattern? make an inductive generalization?

Simplify a problem Some complicated problems can be solved by trying simpler problems or use the similarities found to simplify the problem.

The Three Golfers

Tom, Dick and Harry ... Three golfers named Tom, Dick and Harry are walking to the clubhouse. Tom, the best golfer of the three, always tells the truth. Dick sometimes tells the truth, while Harry, the worst golfer, never does. (a) Can you figure out who is who ? (b) Explain how you know. (Hint: First figure out which one is Tom.)

The one in the middle is Harry The one in the middle is Tom I am Dick

What strategy did you use ?

Deductive Reasoning ?

3 types of reasoning Intuitive reasoning Inductive reasoning Deductive reasoning

Let us review what we have done . . .

Analytical Tools for PS PS Strategies… Simplify a problem Guess and Check Draw a diagram Make a table Act out a situation Look for a pattern Work backwards Experimenting Deductive Reasoning Using Algebra

A strategy can be mastered by practice … “If you give a man a loaf of bread, you feed him for a day; but if you teach the man to bake, you feed him for a lifetime.” “If you give a boy a fish, he will have fish for a meal; but if you teach him how to fish, he will have fish for a lifetime.”

tools for problem solving You have been given . . . tools for problem solving Now . . . Use it for your everyday life !