Ch.12 Problems & Goals: Using Info to Arrive at Solutions

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Components to a Problem

Initial State (Situation at beginning of problem)

Current State (after initial state but before goal state)

Operations (a set of rules (or constraints) that must be followed, and usually, a set of obstacles that must be overcome.

Goal State (Solution to the problem)

Types of Problems

Well-defined problems

clear and structured

initial state, goal state, and constraints all understood

once you reach a solution, it’s easily assessed

Ex. Solving an anagram (unscrambling letters to form a word) is an extremely well-defined problem.

VS.

Ill-defined problems -- fuzzy and abstract

Final project - not quite sure where to start, where i need to get to, or what the constraints are. The topic is up to me, the length is up to me, and I'm not 100% sure what the professor wants.

In addition, once you have come up with a solution, you're really not sure if it's a good one. You may think it is good but you aren't the one grading it.

Needless to say, ill-defined problems tend to present more of a challenge to the solver than well-defined ones.

Routine problems -- can be solved by applying well-practiced procedures

A senior psychology major writing a research paper.

VS.

Nonroutine problems -- require application of unfamiliar procedures in order to reach a solution

A beginning student writing a research paper for the first time.

The Varied Nature of Problems. (p. 496)

Mayer (1992) provides some order to the diversity by distinguishing between five sorts of problems.

5 Sorts of Problems

1. Transformation -- give goal state, and solver must find moves to get from initial-goal state (e.g., Tower of Hanoi)

2. Arrangement -- all elements given to solve problem, but person must figure out how to arrange elements (e.g., anagrams -- keroj, solution - joker)

3. Induction -- given series of instances and must figure out rule that relates the instances (.e.g., extrapolation -- A B M C D M ___ )

4. Deduction -- premises or conditions are given, and solver must determine whether a conclusion fits these premises

5. Divergent -- require solver to generate as many solutions as possible to a given problem (e.g., think of as many uses for a brick as you can)