Chapter 10 Thinking, Problem Solving, and Reasoning
Thinking has been defined in many ways by different people:
1. Going beyond the information given (Bruner, 1957).
2. Complex and high-level skill that fills up gaps in the evidence (Bartlett, 1958).
3. Process of searching through a problem space (Newell & Simon, 1972).
4. What we do when we are in doubt about how to act, what to believe, or what to
desire (Baron, 1994).
There are two types of thinking: focused and unfocused thinking:
1. Focused Thinking begins with a clear starting point and has a specific goal.
2. Unfocused thinking has the character of daydreaming, or unintentionally calling
to mind a number of different and loosely related ideas.
Creative thinking has been described as including aspects of unfocused thinking.
Formal reasoning encompasses the cognitive processes we use when we draw inferences
from information given to us.
Introspection the detailed, concurrent, and non-judgemental observation of the contents
of your consciousness as you work on a problem.
The key to proper use of this technique is to avoid doing more than is asked for: dont
explain or justify what youre thinking about just report it.
The type of problems that occur can be classified as either well-defined or ill-defined:
1. Well-defined problems have a clear goal, (you know when you reach the
solution), present a small set of information to start from, and often (but not always)
present a set of rules or guidelines to abide by while you are working toward a
2. Ill-defined problems dont have their goals, starting information, or steps clearly
Psychologists have focused on well-defined problems for several reasons: They are easy to
present, they dont take months to solve, they are easy to score, and they are easy to
1 In a study by Schraw and Dunkle, they demonstrated that performance on well-defined
problems was not correlated with performance on ill-defined problems.
Classic Problems and General Methods of Solution
We use domain-specific problem solving approaches they work for only a limited class of
Generate and Test Technique
Generate and test technique as the name suggests, this technique consists of generating
possible solutions to a problem/question and then testing them.
This technique loses its effectiveness very rapidly when there are many possibilities and
when there is no particular guidance for the generation process and when you cant keep
track of the possibilities tested.
It is useful when there arent a lot of possibilities to keep track of.
The means-ends technique involves comparing the goal with the starting point, thinking of
possible ways of overcoming the difference and choosing the best one. Sub-goals can also
Newell and Simon gave several problems to participants and the GPS (General Problem
Solver). They compared the thinking of both and found that human participants
generated verbal protocols; GPS produced a printout of its goals, its sub-goals, and the
operations it applied as it worked.
They found many similarities in performance between the Yale participants and the GPS.
The means ends analysis, the general heuristic, or shortcut strategy, used by GPS, is a more
focused method of solution than generate and test: it guides the problem solver more in
choosing what step to take next. Means ends analysis also forces the problem solver to
analyze aspects of the problem before starting to work on it and generate a plan to solve it,
and often this require establishing sub-goals.
Means ends analysis 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.
Means ends analysis makes it more difficult to see that the most efficient path toward a
goal isnt always the most direct one.
Problem space (Newell & Simon, 1972)
2 Initial state: conditions at beginning of problem
Goals state: condition at the end of problem
Intermediate states: the various conditions that exist along pathways between the
initial and the goal state
Operators: permissible moves
Reduce the difference between initial state and goal state.
Involves generating a goal and then sub-goals
Any sequence of moves beginning at the initial state and ending at the final goal state
constitutes a solution path.
Working backward the user analyzes the goal to determine the last step needed to achieve
it, then the next-to-last step, and so on. Working backward like means-ends analysis, often
involves establishing sub-goals.
This technique is especially evident in trying to solve the Towers of Hanoi, in trying to
move three disks each varying in size from the first peg to the third peg without placing a
larger disk on a smaller disk.
Working backward is most effective when the backward path is unique, which makes the
process more efficient than working forward. It shares with means-ends analysis the
technique of reducing differences between the current state and the goal state.
But sub-goals are created working backwards from the goal state.
Example: I didnt do great on the last test. How can I get an A on the next test?
Before I do better I need to have a better understanding of the material; to
understand the material better, I need to be studying better; to improve how I study I
need to do X.
Problem solving often involves making working assumptions.
In order to correct mistakes in problem solving, need to:
1. Remember your assumptions
2. Assess which assumptions failed