PROBLEM SOLVING
goal directed sequence of cognitive operations

CLASSIFYING PROBLEMS

    A.)    Arrangement

  • Arrangement problems present some objects and require the problem solver to arrange them in a way that satisfies some criterion; i.e., Duncker's 'candle' problem.
  • The problem requires the rearrangement of objects to form a new relation among them. Often much trial and error is The skills needed to solve such problems include
  • (1)    Fluency generating possibilities and rejecting poor ones.
  • (2)    Retrieval of previous solution patterns.
  • (3)    Knowledge of principles that constrain search.
  •     B.)    Inducing Structure

  • (1) The encoding process identifies attributes that could be important in establishing relations.
  • (2) The inference process establishes a valid relation between the 1st and 2nd items.
  • (3) The mappingprocess establishes relations between the 1st and 3rd items.
  • (4) Finally the application process attempts to establish a relation between the 3rd and 4th items that is analogous to the one between the 1st and 2nd items. Ex:  Washington : Lincoln :: 1 : ______ (5/10/20)
  •     C.)    Transformational Problems

    NEWELL & SIMON'S THEORY OBJECTIVES & METHOD

        A.)    Theoretical Assumptions

    Performance on a problem-solving task is influenced by capacity, storage time, and retrieval time of STM and LTM--limited STM capacity places a constraint how many sequential operations that can be carried out mentally. The time required to store new information in LTM can influence the efficiency of a human problem solver. (Shades of Kintsch & language comprehension!)

        B.)    The Problem Space

    (1)    the task instructions that give a description of the problem and which may contain helpful information.
    (2)    previous experience with the same task or a similar one
    (3)    previous experience with analogous tasks.
    (4)    plans stored in LTM that generalize over a range of tasks.
    (5)    information accumulated while solving a problem.

    COMPUTER-SIMULATION DEFINITION OF THINKING

        A.)    Means/Ends Analysis

        B.)    Memory and Problem Solving

    SOME GENERAL STRATEGIES

        A.    Heuristics: rules of thumb—

    These are shortcuts for problem solving (and for decision making). They allow us to reach a solution relatively quickly and effortlessly however do so at the expense of accuracy--they do not guarantee a correct solution. Example: 'i' before 'e' except after 'c', and in long 'a' as in 'neighbor' and 'weigh'

        B.    Algorithms:

    These are strict protocols, which, if followed exactly will always lead to a correct solution. The trade-off is that they are relatively more time and effort consuming. Example: look up each word in a dictionary.

        C.    Use of Subgoals:

    This refers to breaking up a problem into component parts. However, this is often difficult. See below.

        D.    Analogy

    This is applying previously successful solution strategies to a new problem. As research shows, below, most people are very poor at this, especially when the deep structure of a problem remains the same but the surface structure changes.

    MORE ON THE PROBLEM SPACE

    Solving a problem, can be seen as finding the correct path through a problem space. Several techniques accomplish this:

        A.)    Subgoals -

        B.)    Working backward -

        C.)    Related problem spaces -

    THE TOWER HANOI -

        A.)    Example of a Problem Space

        B.)    Strategies to Search the Problem Space