DANCEST 805 Lecture Notes - Lecture 21: Pomona, California, Problem Solving, Solution Process
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Task – Nail it
Learning goals:
1. What are theories of problem solving?
2. What cultural differences are there?
3. How do we decide which strategy/theory to use?
4. What’s the connection between creativity & problem solving?
1. What are theories of problem solving?
Galotti – Chapter 11: Thinking & Problem Solving
• Thinking: going beyond the information given; a complex & high-level skill; fill[s] up gaps in the evidence; searching
through a problem space → what we do when we are in doubt about how to act, what to believe, or what to desire
o Focused thinking: begins with a clear starting point & has a specific goal
o Unfocused thinking: has the character of daydreaming, or unintentionally calling to mind a number of different &
loosely related ideas
• Introspection: detailed, concurrent, & non-judgmental observation of the contents of your consciousness as you
work a problem
o can at the very least provide the basis for hypotheses & tests using more objective measures
o important to avoid doing more than is asked for → just reporting, NO interpretation etc.
• Well-defined problems: have a clear goal (you know if you’ve reached the solution), present a small set of info to
start from, often (not always) present a set of rules or guidelines to abide by while you are working toward a solution
+ easy to present
+ don’t take weeks or months to solve
+ easy to score
+ easy to change
• Ill-defined problems: don’t have their goals, starting information, or steps clearly spelled out → connection to insight
problem
CLASSIC PROBLEMS AND GENERAL METHODS OF SOLUTION
• domain-specific problem-solving approaches: only work for a limited class of problems
• domain-independent techniques: stated at a general enough level that, can be used with a wide variety of problems,
not just with problems of a certain type or domain
Generate-&-Test Technique
• generating possible solutions (listing words that start with “c” & are eatable/drinkable) & then testing them
(checking whether the words meet the criteria)
− loses its effectiveness very rapidly when there are many possibilities & when there is no particular guidance for the
generation process
+ useful when there aren’t a lot of possibilities to keep track of
Means–Ends Analysis
• Means–Ends Analysis: comparing the goal (destination: Summit, New Jersey) with the starting point (Pomona,
California), thinking of possible ways of overcoming the difference (walking, bicycling, taxi, etc.), & choosing the best
one
• The selected option (taking a plane) may have certain prerequisite conditions (e.g. being at the airport, with a ticket)
If preconditions aren’t met, then a subgoal is created (e.g. “How can you get to the airport?”)
• Through the creation of subgoals, the task is broken down into manageable steps that allow a full solution to be
constructed
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more focused method of solution than generate-&-test → guides the problem solver more in choosing what step to
take next
forces problem solver to analyse aspects of the problem before starting & to generate a plan to solve it
Often requires establishing subgoals
➔ problem solver is acting less “blindly” & only after some thought
− is not always the optimal way to reach a solution, because sometimes the optimal way involves taking a temporary
step backward or further from the goal
can make it more difficult to see that the most efficient path toward a goal isn’t always the most direct one
• Newell & Simon (1972) studied means–ends analysis while solving certain arithmetic problems
o created GPS (General Problem Solver), a computer program which solves problems in crypt arithmetic & in logic
using means–ends analysis
o basic strategy of GPS:
▪ looks at the object it is given (e.g. cryptic arithmetic problem)
▪ compares it with the desired object
▪ detects any differences between the actual & the desired object
▪ considers the operations available to change objects
▪ operations used are chosen with the aim of reducing differences between actual & desired objects
▪ if none of the available operations applies to the actual object, GPS tries to modify the actual object so that
operations can apply
▪ keeps track of various kinds of differences between desired & actual objects, works on the most difficult
differences first → ranking the different operations such that certain ones are used first
o difference reduction
o works best with well-defined problems → problem: everyday problems are mostly ill-defined
o Newell & Simon gave several problems in logic & in crypt arithmetic to both human participants & GPS &
compared the “thinking” of both
▪ Human participants generated verbal protocols
▪ GPS produced a printout of its goals, its subgoals, & the operations it applied as it worked
➔ there were many similarities between the performance of GPS & humans
Working Backward
• analysing the goal to determine the last step needed to achieve it, then the next-to-last step, & so on.
• very important technique for solving many problems, e.g. Towers of Hanoi problem
• solution process usually does not start with the problem solver making a move & seeing what happens
usual pattern is to plan moves in advance, setting up many intermediate goals along the way
• shares with means–ends analysis the technique of reducing differences between the current state & the goal state
+ most effective when the backward path is unique, which makes the process more efficient than working forward
Backtracking
• keeping track of when & which assumptions were made in the problem-solving process, so you can back up to certain
points of choice & start over
since, in problem solving it’s often necessary to make certain provisional assumptions, which sometimes turn out
to be wrong & need to be “unmade”
• such problems can often be solved by setting up a chart
Reasoning by Analogy
• Analogy & problem differ in their surface features but share an underlying structure
• To use the analogy, participants must engage in the “principle-finding” analysis (Duncker): moving beyond the details
& focusing on the relevant structures of the problem → induction of an abstract schema (Gick & Holyoak)
• E.g. The tumour problem (Duncker): “by what procedure can one free a patient from an inoperable tumour by rays
(which destroy organic tissue at sufficient intensity) & at same time avoid destroying healthy tissue surrounding it?”
o Only 30% of participants spontaneously noticed the analogy
o 75% solved the problem if told that the analogous story would be useful in constructing the solution
o only about 10% solved the problem without the story
• providing multiple analogy examples (e.g. stories) helps participants to form an abstract schema, which they later
apply to new, analogous problems
• 3 steps in problem solving?
+ Participants who construct such a representation are more likely to benefit from work on analogous problems
➔ Instead of just trial & error the problem has to be deeply understood
Document Summary
Galotti chapter 11: thinking & problem solving loosely related ideas. + don"t take weeks or months to solve. Ill-defined problems: don"t have their goals, starting information, or steps clearly spelled out connection to insight problem. + useful when there aren"t a lot of possibilities to keep track of. Means ends analysis: means ends analysis: comparing the goal (destination: summit, new jersey) with the starting point (pomona, California), thinking of possible ways of overcoming the difference (walking, bicycling, taxi, etc. ), & choosing the best one: the selected option (taking a plane) may have certain prerequisite conditions (e. g. being at the airport, with a ticket) Problem solver is acting less blindly & only after some thought is not always the optimal way to reach a solution, because sometimes the optimal way involves taking a temporary step backward or further from the goal. There were many similarities between the performance of gps & humans.
