Problem Solving - Cognitive Psychology Lect. Notes PDF

Problem Solving In today’s lectures, we will discuss:  What is Problem solving?  Approaches to problem solving:  Problem s...

Problem Solving In today’s lectures, we will discuss:  What is Problem solving?  Approaches to problem solving:  Problem solving involving restructuring  Problem solving involving search  Problem solving using analogies  Experts and non-experts approach to problem solving KMF 1023  Creative cognition COGNITIVE PSYCHOLOGY  Metacognition in Problem Solving Lecturer: Norehan Zulkiply FSKPM, Universiti Malaysia Sarawak  The brain and problem solving What is a problem?  Problem  Involves some difficulty and has a solution that is What is Problem Solving? not immediately obvious  We solve problems everyday  A problem happens when there is an obstacle between a present state and a goal and it is not immediately obvious how to get around the obstacle (Lovett, 2002) What is a problem? Problem Solving  Another definition……  The situation people face when they want something but do not know right away what to do to get it (Newell and Simon, 1972) 1  Three Approaches in Problem solving involving Problem Solving Restructuring Problem solving involving restructuring Problem Solving as Restructuring  Proposed by Gestalt Psychologists  Example:  Problem solving for them was about:  The Circle Problem  1. How people represented a problem in their  Circle with radius r. mind,  How long is x?  2. How solving a problem involves a reorganisation or restructuring of this r representation Problem Solving as Re-representation Insight in Problem Solving  Solution: x = r  Problem Solving :  Problem  Insight : sudden realisation of a problem’s perception solution (‘Aha!’ experience)  Representing the problem in a different way Restructuring  Solution to circle problem requires (perceptual) insight 2 Insight in Problem Solving Insight in Problem Solving  Another example of  Insight problem insight problem:  Solution to the triangle problem: (a) Triangle problem: Move 3 pins so that the triangle faces downwards.  arrows indicate movement;  colored circles indicate new positions Insight in Problem Solving Obstacles to Problem Solving  Are insight problems qualitatively different from  Experience can help or hinder problem other problems? solving…  Non-insight problems : involve participants to work a)Functional Fixedness on a more methodical process, in which they have some b)Mental Set knowledge that they are getting closer to the situation Functional fixedness : familiarity with an  Examples of non-insight problems: object’s function can inhibit other possible uses  Solve for x: (1/5) x + 10 = 25  Factor 16y2 – 40yz + 25z2  Toothbrush? Hanger? Belt? (algebra problems) Obstacles to Problem Solving Solution to the Candle Problem Functional Fixedness  Necessary ‘insight’:  The match box must be seen as a support, rather than Duncker (1945)’s candle problem a container.  Two groups of participants:  Results:  group 1 was presented with all the items in a small  Group 1 found the problem more difficult that did the cardboard box Group 2.  Group 2 was presented with the same materials but outside the box. 3  Results of the Candle Problem  Adamson’s (1952) replication- Functional Fixedness obtained the same results as Duncker’s.  Maier’s (1931) two-string problem:  Presentation mode  Using only a chair and matters: empty boxes pliers tie together the two less likely to be viewed ends of these strings only as containers.  Solution: the pliers can be used as a weights to create  Functional fixedness : a pendulum to swing the familiarity with an strings object’s function can inhibit other possible uses Maier’s (1931) two-string problem. As hard as Sebastian tries, he can’t grab the second string. How can he tie the two strings together? Mental set Mental Set Luchin’s (1942):  Mental Set Mental set and Water- jug problems  a person’s tendency to respond in a certain manner based on past experiences Each problem specifies the capacities of jugs A, B, and C, and a final desired quantity.  Functional Fixedness creates mental set by The task is to use the jugs to measure out the final causing the person to focus on a particular quantity. function of an object. The solution to problem 1 is  E.g., “a box can only function as a container” shown. All of the other (Mental set) problems can be solved using the same pattern of pouring, but there are more efficient B – A – 2C = desired quantity solutions to problems 7 and 8. Mental Set Mental Set  Comparing solutions of participants with vs.  A simple solution to Luchin’s (1942) problem 7: without mental set for Problem 7 All of the participants who began the Luchin’s water- jug problem with problem 7 used the shorter solution for problem 7 (right bar) But less than a quarter who had established a mental set by beginning with problem 1 used the shorter solution to solve problem 7 (left bar) A + C = desired quantity 4  Summary: Gestalt Approach to P.S. Problem Solving involving Search Modern Approaches: Problem solving involving Search Modern Approaches: Problem (The information processing approach) solving involving Search  Newell and Simon  Initial state – condition at the beginning of the problem (1956, 1972):  Goal state – condition at the end of the problem  Intermediate states – conditions that exist along the  A problem space consists way between the initial and goal states of:  Operators- permissible moves between states to 1. Initial state achieve the goal 2. Goal state 3. Intermediate states  Problem solving = searching the problem space 4. Operators Modern Approaches: Problem solving involving Search The Tower of Hanoi (ToH)  Example of problem :  Rules (or operators)  The Tower of Hanoi (ToH) problem  Starting with the three rings of different sizes on 1.you can only move one ring at a time, peg A your task is to move all of the rings to peg C 2.you may not place any large ring on top of a smaller ring, and, Initial state Goal state ?? 3.rings may only be placed on pegs and not on, for example, the table or the floor 5 The Tower of Hanoi (ToH) Solving the ToH  Use means –end – analysis strategy  Aim is to reduce the difference between the initial and goal states by creating subgoals – goals that create intermediate states that are closer to the goal Initial steps in solving the (a) Initial and goal states for the Tower of Hanoi problem. Tower of Hanoi problem, (b) Operators that govern the Tower of Hanoi problem. showing how the problem can be broken down into subgoals. Means-ends Analysis approach in Problem Solving Means-ends analysis  Goal: to reduce the difference between the initial  Another Example: writing a compare-and- and goal states, by creating subgoals contrast essay. 1. Identify the goal state (the position you want to  Steps: defend)  1. Set up a (global) goal or (local) subgoal 2. Break down the paper into smaller problems (e.g.:  2. Judge difference between current and goal/subgoal state introduction, comparison of evidence, conclusion)  3. Look for an operator that will reduce or eliminate 3. Proceed through the paper one section at a time. the difference  4. Apply the operator  5. Apply steps 2 to 4 repeatedly until goal has been achieved Problem Solving using  Means-ends analysis is successful for many problems but not suited for problems that are difficult Analogies to specify a clear goal state or specific operators  Also not suited for insight problems  Many problems are ill-defined (e.g., vague initial or final states, flexible operators…)  Eg. Whom should I marry? Should I go to graduate school? Which university should I attend? 6  A classic experiment on analogical Problem Solving using Analogies problem solving  Analogies :  Occur when they are parallels between two different  Duncker’s (1945) Radiation Problem: situations. (structural similarity between situations or events) “A man has an inoperable stomach tumor. A technique which can help him is to use laser  Eg:‘floats like a butterfly, stings like a bee’ (Muhammed Ali) rays which can destroy organic tissue at sufficient intensity.  Analogical problem solving = a solution to one problem is presented that is analogous (similar) to the solution of another problem that we are trying to How can he get rid of the tumor using these solve. rays and at the same time avoid destroying the healthy tissue which surrounds it?” Duncker’s (1945) Radiation Problem Duncker’s (1945) Radiation Problem Consider the story of “The General” who wanted to overthrow a strong dictator who ruled a country Solution to the radiation problem: Bombarding the tumor, shown in the center, with a number of low-intensity rays from different directions destroys the tumor without damaging the tissue it passes through. How the general solved the problem of how to capture the fortress. The Process of Analogical Duncker’s (1945) Radiation Problem P.S. Note: Solution to radiation problem is actually used in modern radiosurgery Gick & Holyoak (1980): 1. Noticing parallels – Most difficult step! 2. Mapping corresponding elements 3. Applying the mapping to generate a solution According to Gick and Holyoak (c) Radiosurgery, a modern medical technique for irradiating brain (1980), the process of tumors with a number of beams of gamma rays, uses the same analogical problem solving principle.. involves these three steps. 7  Experts and Non-experts Expert vs. Novice Problem Solvers approach to problem  Experts := ~ 10 years of domain experience. solving  Examples: Chess, Physics, Music, Computer Gaming…  Fact: Experts exhibit better (faster & more accurate) problem solving. Expert vs. Novice Problem Solvers Expert vs. Novice Problem Solvers Experts have … more knowledge Experts … Spend more time analyzing, rather than solving differently organized knowledge a problem Chi et al. (1982): Experts spend more time at the beginning of In Categorizing problems, problem solving process to identify and represent Experts the problem compared with novices, so spend  Represent problems at a deeper level considerably less time choosing appropriate  Focus more of their solution strategy once the problem had clarified attention on the underlying structure of the problem RATHER THAN on superficial surface features The kinds of physics problems that were grouped together by novices (left) and experts (right) (Chi et al, 1981). Some more…. Expert vs. Novice Problem Solvers  Faster than novices  at processing meaningful information – search and represent problem efficiently (e.g. expert mathematician) But: Expertise is domain specific  at performing skills of their domain, and quickly solve problems with little error due to  They have many skills in a domain practiced to the point of Experts are no better than novices outside their field automatization of expertise  Many problem for them are no longer problems that require  Expertise is domain specific -- experts are no better able to searching for a solution – rather a solution has been stored solve problems in unfamiliar domain than novices  E.g. Compare Political scientist vs. expert chemist -  Monitor their performance better solving a problem about political science. The result is  Experts are aware of how they are doing as they work on a sophisticated analysis vs. simplistic solution tasks in their domain of competence  Such domain-specific expertise does not transfer far,  More likely to generate alternative hypotheses before solving however a problem and are quicker to reject inappropriate solutions during problem solving  Judge the difficulty of problems more accurately than Caveat: Expertise can result in functional fixedness novices and ask more appropriate questions at all stages of (blindness to creative alternatives) the problem-solving process 8  Process information in large units  Organize information more efficient than novices – chunking Creative cognition information into larger recognizable units that a novice might use.  E.g. chess expert view complex chess configurations for as little as five seconds yet remember them in remarkable detail; novices remembered very little of what they saw.  Hold more information in STM and LTM  The biology capacity underlying STM is no greater for experts than novices -- the difference is that, experts have many skills and strategies automatized.Being automatic allows experts to use their STM and LTM in a more efficient way, compared with novices Creative & Divergent Thinking Creative Cognition  Convergent vs. divergent thinking  So far we have seen P.S. by restructuring, Convergent thinking searching, and by analogy   Thinking that works towards finding a solution to a specific problem that usually has a correct answer.  Problem converges onto the correct answer  What about creativity?  Divergent thinking ( Creative Cognition)  Creative Problem Solving  Thinking that is open-ended  There are a many potential solutions and no correct answer ….having the ability to think and (although some might work better than others)  Can lead to the creation of many ideas create something new (characterized by originality and expressiveness)  Tests of Creativity Task: Think of multiple uses for familiar objects. Metacognition in Problem Solving  Metacognition  the knowledge that people Problem Solving and have about their own thought processes the Brain (thinking about thinking)  In P.S., one can use metacognition:  To identify the “actual problem” that needs to be solved  To identify when you do not understand a problem  To recognize which parts of the problem were difficult  To monitor your own performance (e.g., progress in P.S.) 9 Problem Solving & the Brain Problem Solving & the Brain  Yes, the brain is involved….  Many brain areas involved in P.S. (due to different types of task), but one particularly crucial area in P.S. is Prefrontal Cortex  Prefrontal Cortex (PFC):  Important for planning (multistep tasks), and executing strategies, reasoning and making connections among different parts of a problem or a story. Areas of the brain that are activated by playing chess – evidence from PET Summary Summary  What is a problem?  Four key differences between experts and  Three approaches to problem solving novice in problem solving:  Experts possess more knowledge about their  Restructuring (Gestalt) fields  Search (Newell & Simon)  Experts’ knowledge is organised differently from  Analogy (Gick & Holyoak) novices’  Experts spend more time analysing problems  Experts are no better than novices when given problems outside of their field 10