Thinking & Problem Solving Thinking: process used to transform or manipulate information Problem solving: manipulation of data with a specific goal in mind, using a specific solution Remember that understanding and creating not same thing, may use different mechanisms http://www.starlight-tower.com/images/starlight_tower/The_Thinker_Rodin-2.jpg

Studying Problem Solving Types of problems Well-defined problems Ill-defined problems Well-d : clear goal, small set of info to start with, and sometimes rules Real-life examples: How to get car to mechanic after an accident How to earn enough money for down-payment on house Ill-d : opposite; no goals, no starting info, no steps to take that are clearly spelled out Complete a perfect paper Or clean the house (could be well defined if limits set) or learn to crochet Research uses only well-defined b/c easy to present to subject, take little time, easy to change, easy to score, We will be talking mostly well-defined problems

Studying Problem Solving Methods Logic puzzles Introspection Researchers often use puzzles to study problem solving Why use puzzles? What do they have to do with everyday thinking? Everyday thinking very fast and automatic We all have different backgrounds, so it’s hard to find an example of everyday thinking (test) that would be equally challenging for everyone introspection – detailed observation of steps taken as a problem is worked through

Classic Problems and Solutions Generate-and-test technique Generate-and-test technique Think of a number of ideas about how to solve problem (generating) Test each one to see if it works (testing) (whether it works often depends on rules of the solving process or requirements about goal) example: you are very sick and need to get to the hospital Call an ambulance, call police, call a friend, drive yourself, take a bus, take a taxi One problem with this technique less effective if it has too many possible solutions; time-consuming, requires a system to keep track of what has been tried, frustrating Ex. moon puzzle But is useful if there are not a lot of solutions

Classic Problems and Solutions Means-ends analysis You start with a current state of something, have in mind the wanted end state (goal) List possibilities like before, but instead of simply trying them randomly, selection directed by how the solution changes difference b/t start and goal Poor  I want to have an opulent lifestyle Med school, getting into med school, finding a job… Some things may require you to break solution into smaller problems (subgoal) Directs search for a solution more, but might cause you to overlook a solution, Get so caught up in a subgoal, take longer to get to goal than another way ? Current State Goal http://tell.fll.purdue.edu/JapanProj/FLClipart/Adjectives/poor.gif

Classic Problems and Solutions Working backwards Example of working backwards Start from goal and work backwards Can have subgoals Similar problem with my filing cabinet Usually solver does not make a move and then wait to see what happens Instead moves are planned ahead of time (solitaire) Works best when there is only one, unique solution to a problem

Classic Problems and Solutions Backtracking Think of tree with lots of different choices and subchoices or a maze I go down one path, see where it leads me (picking most logical one if you can) If it doesn’t work out, go back up to the point where I could have made another choice and chose something else It’s like saying to yourself, I don’t know if this is true, but let’s just suppose that is Process of elimination

Classic Problems and Solutions Backtracking Five women, with different dogs, diff occupations, and diff # of children Cathy and irish Teacher no children Owner of lab is surgen Linda not sheepdog Sonya lawyer Sheepdog not 3 kids Retriever 4 kids Judy 1 kid Executive retriever First rec could be debbie or linda

Classic Problems and Solutions Solving by analogy Not simple blind trial and error People have to have deeper understanding to solve problem, have to see a pattern/principle/schema Solve a new problem by finding similar problem and making comparison Tumor problem General story of fortress Two groups read both, but only one told that there was a clue in first story, 75% solved it Group w/o hint only 10%

nine-dot problem six-matches problems Blocks to Problem Solving Mental set Times when you can’t find a solution Reasons for it Mental set – tendency to adopt a framework/idea, instead of other possible ones And when you do, don’t think about other one to solve problems, make assumptions Only takes a few trials for this effect to set in nine-dot problem six-matches problems

Blocks to Problem Solving Mental set Solutions to problems Error/assumption: going outside “box” Error: putting them in 2D Figure 10-6 (p. 370) Answers to the nine-dot and the six-matches problems.

Blocks to Problem Solving Mental set Functional fixedness String problem. Two strings, goal to tie together, but not long enough to grab both at same time On table is screwdriver, pieces of cotton, book of matches, Solution: use screwdriver as weight

The mutilated checkerboard problem. Blocks to Problem Solving Incomplete or incorrect representation Initally misunderstand a problem, or focus on wrong info Q: can you fit 31 dominoes (fill 2 squares) onto broad (2 cut away)? 64 squares on normal board, this one has 62 A: no, (b/c squares are same color, can’t be near each other The mutilated checkerboard problem.

A tic-tac-toe board representation of the numbers game. Blocks to Problem Solving Incomplete or incorrect representation List of Numbers 1-9, goal to pick three numbers add to 15 Each player crosses off one number at a time to pick it Now if you had originally seen tictactoe grid it would be easy Representations were a list of numbers or a board A tic-tac-toe board representation of the numbers game.

Problem Solving Techniques for solving problems Lack of problem-specific expertise Chess game, one player playing 4 opponents, all at same time, but his playing ability does not change, weird b/c he’s not allowed any extra time Player could recognize pattern more quickly than other players Not that he was better at planning, He had more knowledge than others

Problem Solving Techniques for solving problems Lack of problem-specific expertise Experts vs. novices Have more knowledge in that area Deeper level representation Check for errors more often Experts, takes about 10 yrs Know – expert Rep - spend more time understanding problem than novices errors

Figure 10-10 A generic problem space. The Problem Space Hypothesis Figure 10-10 A generic problem space. Every possible state for a situation shown = Circles/nodes Goal of being rich Lines = what has to be done to go from one state to another

The Problem Space Hypothesis Path Not all states will lead to the desired goal Path – a progression that will lead from start to goal “good” problem solving finds fastest path

The Problem Space Hypothesis Figure 10-12 (p. 377) A part of the problem space for the Towers of Hanoi problem, showing the solution.

Expert Systems Why bother studying this? Extreme example Depression = if we understand how people create solutions goal: pay bills, start: broke, solutions: sleep or find a job One practical application We could make machines/systems that replace human experts Which would be helpful if Too few experts Avoid bias/overload

Creativity Unconscious processing/ incubation Everyday cognitions We have been talking about solving problems using step by step methods But we also sometimes seem to just get a solution out of the blue, aha, eureka Called insight (Gestalt could be talked about here) Two ways to think about where it comes from (special process in its own – people can have more or less creativity, like intelligence or Uses other processes) Uncon: special process sleep on it; Still working on problem even if doing something else Everyday: For example, many artists do drafts, noticing new mistakes and correcting them

Critical Thinking Critical thinking: looking at solutions and evaluating them` `to` do a “good” job critically thinking, ````Perkins suggests that person should question solutions