Problem Solving: Guiding the Experience

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Problem Solving Guiding the Experience

• Professional Development Workshop
• KATM 2003 Annual Conference
• October 24, 2003
• David S. Allen, Ed.D.
• and
• Melisa Hancock
• Teacher in Residence, KSU

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Sample Problems
Acrobats, Grandmas, and Ivan Round 1 On one side
are four acrobats, each of equal strength. On the
other side are five neighborhood grandmas, each
of equal strength. The result is dead even. Round
2 On one side is Ivan, a dog. Ivan is pitted
against two of the grandmas and one acrobat.
Again its a draw. Round 3 Ivan and three
grandmas are on one side, and the four acrobats
are on the other. Who will win the third round?
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There is no royal road to critical thinking.
Theres not even a paupers paved path to easy
problem solving. Teaching todays children to
become the thinking, caring leaders who will be
able to solve the worlds increasingly complex
and quantitative problems requires a total
commitment, not just a Friday afternoon
contribution. (Willoughby, 1990)
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Problem Solving Defined!

• Problem Solving means engaging in a task for
  which the solution method is not known in
  advance.
• NCTM, 2000
• A problem is a situation in which a person
  is seeking some goal and for which a suitable
  course of action is not immediately apparent.
• (Marilyn Burns, 2001)
• Problem Solving is more than obtaining
  answers. It is a tool, a means of thinking, and a
  philosophy. It is a predisposition to learn from
  every available opportunity the most that can be
  gleaned from that experience.
• (NCTM, 2000)

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Math Standards (2001)

• Content Standards
• Number and Operations
• Algebra
• Geometry
• Measurement
• Data Analysis and Probability

• Process Standards
• Problem Solving
• Reasoning and Proof
• Communication
• Connections
• Representation

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Three Problem Solving Approaches

• Teaching for problem solving.
• Teaching about problem solving.
• Teaching via problem solving.

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Teaching for Problem Solving

• Uses real-life problems as a setting in which
  students can apply and practice recently taught
  concepts and skills.
• Janalea has 2 dogs. Landree has 5 dogs. How many
  more dogs does Landree have than Janalea?
• Traditional problem-solving experiences familiar
  to most adults.

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Teaching About Problem Solving

• Refers to instruction that focuses on strategies
  for solving problems
• Polya, 1954
• Four Step Method
• Heuristics
• Process vs. Procedure
• Critical Thinking
• Examples

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Pedagogical Approach to Problem Solving

• Four Step
• Process
• Read and understand the problem
• Devise a plan
• 3. Carry out the plan
• 4. Check your answer

• Blooms
• Taxonomy
• Knowledge
• Comprehension
• Application
• Analysis
• Synthesis
• Evaluation

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Recommendations for Teaching About Problem Solving

• Heuristics
• Strategies taught in isolation are not meaningful
  to students.
• Allow students to identify or create meaningful
  solution strategies.
• Post strategies and refer to them often.
• Demonstrate the need to draw upon a wide variety
  of solutions strategies.
• THERE IS MORE THAN ONE WAY TO SKIN A CAT!

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Problem Solving Pitfalls

• Rules often provide the thinking for the
  children.
• If 1 man can jump a stream that is 3 meters wide,
  how wide a stream can 5 men jump?

• 2. Key Words often encourage students to avoid
  thinking about the problem.
• Mary walked 11 meters north. She then turned and
  walked 7 meters west. Did she turn right or left?

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Problem Solving Pitfalls

• 3. Unrealistic Problems
• Marys mother needs three hours to do the
  laundry. If Mary helps her, they can do the
  laundry in only two hours. How long would it take
  Mary to do the laundry by herself?

• 4. Non-pertinent Clues
• If there are two numbers that are bigSubtract
• If there was one large and one smallDivide
• If it does not come out evenMultiply

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Sample problems (About)
Jennifer wants to buy 12 new baseball
cards. The Collector Store sells two cards for 25
cents. The Cards and Book Store has three cards
for 33 cents. Where should Jennifer buy the
cards? Why?

• The center region on a dart board is worth
  100 points the next ring is worth 50 points the
  next, 25 points and the outermost, 10 points.
  Betty throws six darts and earns a score of 150.
  Where might her darts have landed?

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Sample problems (About)
Rebecca has a pocketful of change. She
would like to buy a soda, which costs 0.55. How
could she pay for the soda so that she would
eliminate the most change from her pocket?

• I counted 22 legs in my house. All the legs
  were on cats, people, and spiders. How many of
  each creature--cats, people, and spiders--might
  be in the house? See how many different ways you
  can answer this riddle. How many can you find?

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Teaching via Problem Solving

• Uses a problem as a means of learning new ideas
  and for connecting new and already existing
  constructs.
• Sample problems teaching via problem solving.

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Sample Problems (Via)
If you spill 6 counters and record how many
red sides and yellow sides come up each time, do
you think youll get one result more often than
the others? If so, what will it be? Why do you
think that? Try it, spilling the counters at
least 25 times. Record your prediction and your
actual results. Extension Try the
experiment with other numbers of
counters. Theoretical Probability vs.
Experiments
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Problem Solving Guiding the Experience
Professional Development Workshop KATM 2003
Annual Conference October 24, 2003 David S.
Allen, Ed.D. and Melisa Hancock Teacher in
Residence, KSU