Problem Solving

Problem solving

• process of determines the steps needed to reach a goal

  • “I want to go to the store but Tom took my car. How can I get there?”

  • “I really want Amy to notice me; how can I get her attention?”

Problem solving as search

• the set of all states that can be reached in solving the problem

• the problem space for most real-life problems is extensive

  • e.g., the problem space in a game of chess has approx 700 mil m=paths within just a few turns

• problem-solving heuristics can help to narrow the search

Hill-climbing strategy

• at each step in solving a problem, choose the option that moves you in the direction of your goal

• limited use: many problems require briefly moving away from the goal

  • “This must be the wrong strategy; I’m going the wrong way.”

means-end analysis

• “What means do I have to make my current state more like my goal state?”

  • this strategy helps you break a problem into small subproblems

problem solving via analogy

• uninstructed use of analogies is rare

  • requires focusing on the problem’s underlying structure

  • mapping problems onto structurally related cases can be difficult

• problem solving improved by encouraging people to focus on structure

  • “Relational mindset” during initial learning

    • so that, from the start, participants thought about the cases in terms of their underlying structure

      • E.g., “This is an example of a trade-off” or (for da different case) “This is an example of a postive feedback loop.”

  • no benefits if “relational mindset” is induced later

Expert problem solvers

• experts are more likely than novices to use analogies

  • novices tend to think about problems in terms of their superficial structures

  • experts think about problems in 

Setting subgoals

• problems can be broken up into subproblems

  • experts are more likely to do this than novices

• experts also

  • know more about their domains of expertise

  • have already-assembled routines

  • organize their knowledge effectively 

    • cross-referenced

ill-defined and well-defined problems

• ill-defined problem: the goal state and the available operators for reaching the goal are not clearly specified

  • “having a good time while on vacation”

  • “Saving more money for college”

• such problems are best solved by

  • creating well-defined subgoals

  • adding extra constraints or assumptions

SMART Goals

• a goal-setting method that helps ensure objectives are attainable within a specific time frame. 

  • Specific - objective should be clear and state what will be done and who will do it

  • Measurable - objective should include how progress ill be measured 

  • Achievable - goal should be something that can be accomplished

  • Relevant - goal should be aligned with overall objectives and there should be a good reason for setting it

  • Time-bound - goal should have a realistic deadline

Functional Fixedness

• rigid in thinking about an object’s function

Problem-solving set

• collection of beliefs and assumptions a person makes about a problem

  • narrow your options for approaching the problem

    • reduces distraction from futile strategies

    • usually eases the search for a solution

    • but can sometime blind you to important options or solutions

Case Studies of Creativity

• hihgly creative people have shared “prerequisites” for creativity:

  • great knowledge and skill in the domain

  • certain personality traits

    • Ex: willingness to take risks, to ignore criticism

  • motivated by the pleasure of the work, not external rewards

  • “In the right place at the right time”

The Moment of Illumination

• Wallas (1926) argued that creative thought proceeds in four stages:

  • preparation - information gathering

  • incubation - conscious break

  • illumination - insight emerges; “Aha!” moment

  • verification - confirmation that the new idea leads to a solution

incubation

• we often have exp of a solution popping into our heads after a problem has been set aside

• studies of the incubation effect have been somewhat mixed

• “mind wandering”

  • spreading activation could be the process involved

    • related ideas may come to mind through memory connections

  • alternatively, early efforts may lead to fatigue and frustration, but these feelings will dissipate with a break

insight illumination

• many creative discoveries do not include these steps or happen in a back-and-forth sequence

• the “Aha!” moment only signals a new approach, not that the approach will lead to the solution

The nature of creativity

• convergent thinking: ability to spot ways in which seemingly distinct ideas might be interconnected

  • remote associates test

    • sets usually of three words

      • vary in terms of semantic distances

• forward flow: how much one’s current thinking breaks away from past thoughts

• divergent thinking, convergent thinking, and forward flow all seem distinct from one another

  • there may be different ways to be creative

  • creativity may depend on a combination of factors