Transcript analytical tools for ps m2

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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)
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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?
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
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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?
try to simplify the problem ?
 act it out?
 draw a diagram?
 make a table?
 guess & check?
 look for a pattern?
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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.
Read the following problem and try
to help Ramon and Kyle.
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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?
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Guess, check and
improve
 Make a random guess Check the answers
 Guess systematically Guess the answers according
to certain sequence.
How many squares are there in
a 6x6 grid?
Can you …?
simplify the problem?
 list out your solutions?
 make a table?
 look for a pattern?
 make an inductive generalization?
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Simplify a problem
 Some
complicated
problems can be solved
by trying simpler
problems or use the
similarities found to
simplify the problem.
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 Tom
I am Dick
The one in
the middle
is Harry
 Intuitive
reasoning
 Inductive
reasoning
 Deductive
reasoning
PS Strategies…
Guess and Check
Simplify a problem
Draw a diagram
Make a table
Act out a situation
Look for a pattern
Work backwards
Experimenting
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.”
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