Problem Solving

==How do we solve problems?==

Three phases to solving the problem

  1. Represent the problem
  2. Generate possible solutions
  3. Evaluate the solutions
    • Happens when a mismatch between state and some goal state
      • What I have vs what I need or want
    • Information Processing Approach
      • Representational Change Theory
    • Focus on the mental representation of the problem space, and spreading activation in semantic memory

==The Problem Space==

Includes:

  • Initial state
  • Goal state

==Knowledge-rich vs Knowledge-lean and Expertise==

  • Experts apply heuristics with previously learned experiences from tasks
    • Chess masters who regularly study previous games – have more an extensive memory and better organized
  • Experts understand the relationship in their area of expertise
  • The greatest difference between both
    • Experts recognise the deep structure of problems and ignore the superficial structure
    • Novices look at superficial aspects of the problems

  Research by Schoenfield and Herman, 1982

  Mathematics professors and mathematics novices were presented with problems and asked to group them by similarity

  • Novices tended to group the problems by superficial details (surface structure)
  • Professors tended to group problems by the similarity of solution methods (deep structure)

==Four Common Heuristics==

  1. Hill Climbing method (difference reduction): constantly working forward toward goal
  • Trying to always move closer to the goal state – a simple measure
  • Based on a depth-first search & simple measure of distance – choose the shortest distance to the goal
  • Non-demanding, many people try out first

Problem: Possibilities of local maxima

  • Where we take one route and get stuck so must go backwards and re-route to reach the goal
  • Doesn’t represent much information about problem space as a hole
  1. Working backward: start at the goal state and work towards the initial state
  • Easier to imagine where you want to be than the steps in between
  • Help to re-represent problem space, but can be slow if lots of possibilities for getting stuck
  • Does not work well with lots of intervening steps
  1. Means-ends analysis (goal reduction: the creation of sub-goals (that are solvable)
  • Involves selecting methods known to be effective in the past AND;
  • Dividing the problem as a whole into several smaller sub-problems to then solve one at a time (goal reduction)
  1. Analogy heuristic: mapping the solutions from one problem onto another
  • Mapping solutions from one problem onto another
  • Works best for problem isomorphs – problems with the same structure (solution path) but different content (surface representations)