Problem Solving

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Problem Solving

• Psyc 494
• Talia Ben-Zeev

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When is a behavior an instance of problem solving?

1. Goal directedness
2. Subgoal decomposition
3. Operator Selection
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Types of Problems

• Well defined
• Ill defined

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Ill defined problems

• How can we maximize our potential?
• How can we sustain a romantic relationship over
  the long term?

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Well defined problems
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Well defined problems

• Monster Change Problem
• 3 monsters small, medium, and large.
• Small monster -- holding a medium globe.
• Medium monster -- holding a large globe
• Large monster -- holding a small globe
• Goal expand/shrink globes to fit monster size
• 1. Only one globe can be changed at a time
• 2. If two monsters have equal size globes, only
  the larger monsters can be changed
• 3. A globe cannot be changed to a size of a
  larger monster

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Rational Errors A window into problem solving
A hard problem 23 - 7 ??
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More rational errors From counting to algebra

• Counting
• Twenty-five, Twenty-six, Twenty-seven,
  Twenty-eight, Twenty-nine, (pause), ...
  Twenty-ten!
• Fractions
• 1/2 1/3 2/5
• Arithmetic Word Problems
• There are 26 sheep and 10 goats on a ship. How
  old is the captain?
• There are 125 sheep and 5 dogs in a flock. How
  old is the shepherd?

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More rational errors From counting to algebra

• Radicals
• Word Problems
• The number of quarters a man has is seven times
  the number of dimes he has. The value of the
  dimes exceeds the value of the quarters by two
  dollars and fifty cents. How many has he of each
  coin?

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What is a rational error?

• A rational error results from a strategy
  that is
• rule-based
• internally consistent
• based on prior problem-solving experience

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What is the origin of rational errors?
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Addition in a new number system
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The NewRoman number system
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Two addition algorithms in NewRoman
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Results from the NewRoman study
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Results from the NewRoman study
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Conclusion and Educational Implications

• Teaching for thinking How can we promote it?