Lecture 12_Problem solving.pdf

PSYC 5140 Cognitive Psychology Lecture 11: Problem-Solving & Creativity 2023 Instructor: Urs Maurer What Is a Problem? explicit • Problem: awa re = – An obstacle between a present state and a goal difficulty of tasks – Not immediately obvious how to get around the obstacle – Solution not i...

PSYC 5140 Cognitive Psychology Lecture 11: Problem-Solving & Creativity 2023 Instructor: Urs Maurer What Is a Problem? explicit • Problem: awa re = – An obstacle between a present state and a goal difficulty of tasks – Not immediately obvious how to get around the obstacle – Solution not immediately obvious ? Present state Goal state = problem ⑪ Gestalt Approach • Gestalt psychologists were interested not only in perception but also in learning, problem solving, and even attitudes and beliefs (Koffka, 1935) – They took a perceptual approach to dealing with all the above • Problem solving for Gestalt psychologists was about: – Representing a problem in the mind – Restructuring: reorganization or restructuring the problem’s representation • Köhler’s “circle” problem • If the length of the circle’s radius is r, what is the length of line x? • Different people might represent this problem differently • People’s representations is likely to be different from the picture on this slide Insight in Problem-Solving • Often solutions are obtained by first perceiving the object and then representing it in a different way ➔ restructuring of the problem’s representation • Gestalt psychologists related restructuring with insight – Sudden realization of a problem’s solution – Discovering a crucial element – They thought solutions come to people all of a sudden – “Aha” experience • Other researchers don’t necessarily agree with this – A lot of our problem solving does not require “Aha” experiences sudden Insight in Problem-Solving • Metcalfe and Wiebe (1987): designed an experiment to distinguish between insight and noninsight problems – Insight: triangle problem, chain problem – Noninsight: algebra – Hypothesis: • In insight problems: S should not be very good at predicting how near they wormer you get closer to it are to a solution - • In non-insight problems: involves more methodical process ➔ S should know how close they are to the solution – Warmth judgments every 15 seconds: “hot” ratings indicated that they are getting close to the problem Insight in Problem-Solving sudden impression is how >This it works I Show how you can move three of the blue dots to get the triangle to point to the bottom of the page possible to do it -> O 0 - / methodical rational 0 Join the pieces in to a single closed loop of chain. To open a link costs 2 cents and to close a link costs 3 cents. You only have 15 cents Insight in Problem-Solving • Metcalfe and Wiebe (1987) – Insight problems solved suddenly only apply to certain problems – Noninsight problems solved gradually type of Gradual increase Big jump from 3 to 7 Obstacles to Problem-Solving the obstacles What Why is there problem • Gestalt psychologists claimed that one of the major obstacles to problem solving is fixation ? are ? – Tendency to focus on a specific characteristic of the problem that keeps people from arriving at a solution I • Functional fixedness: restricting use of an object to its familiar functions - Candle problem: You are in a room with a #** *A vertical corkboard mounted on the wall. You are given the material on the right. Mount a candle on the corkboard so it will burn without dripping wax on the floor Seeing matchboxes as containers inhibited using them as supports • S who were given empty matchboxes instead, were twice as likely to solve the problem Obstacles to Problem-Solving • Gestalt psychologists claimed that one of the major obstacles to problem solving is fixation – Tendency to focus on a specific characteristic of the problem that keeps people from arriving at a solution • Functional fixedness: restricting use of an object to its familiar functions Two-string problem: Tie together the two strings # Function of pliers gets in the way of seeing them as a weight. Obstacles to Problem-Solving • Two string problem: once a hint was provided by “accidentally” setting the string in motion, most of the S were able to solve it – In Gestalt terms: the solution occurred when S restructures their representation obstacles • ↳ Mental set – A preconceived notion about how to approach a problem – Based on a person’s past experiences with the problem (or similar problems) – Water-jug problem: figure out how to obtain a required volume of water, given three empty jars for measure Obstacles to Problem-Solving Each problem specifies the capacities of jugs A, B, and C and a final desired quantity. The task is to figure out how to use the jugs with these capacities to measure out the desired quantity. Given mental set inhibited participants from using simpler solution Answer - ② Information-Processing Approach • Newell and Simon (1956): Logic theorist • Described problem solving as a process that involves search – Instead of just considering the initial structure and then the new structure achieved when the problem is solved goal stage • ➔ Newell and Simon described problem solving as a search that occurs between the posing of the problem and its solution – “searching for a way to reach a goal” – “getting around road-blocks” • Problem space – Initial state: conditions at the beginning of the problem – Intermediate state(s) – Goal state: solution of the problem *** back 2 forth Information-Processing Approach • Operators: rules specify which moves are allowed and which are not – Take the state of the problem from one state to another • Tower of Hanoi • Disks are used one at a time • A disk can be moved only when there are no discs on top of it • A larger disk cannot be placed on top of a smaller disk Information-Processing Approach Legend: monks in monastery near Hanoi are working on this problem, but with 64 discs (and world will end when problem is solved). With 64 discs, it will take a trillion years to solve it, even if each move was made in a second, and it was correct. Information-Processing Approach • According to Newell and Simon, we have to search the problem space to find a solution • Means-end analysis: reduce differences between initial and goal states – Subgoals: create intermediate states closer to goal • For Tower of Hanoi, applying means-end analysis reduces the size of the difference between initial and goal states Information-Processing Approach • According to Newell and Simon, we have to search the problem state to find a solution • Means-end analysis: reduce differences between initial and goal states – Subgoals: create intermediate states closer to goal • For Tower of Hanoi, applying means-end analysis reduces the size of the difference between initial and goal states The Importance of How a Problem Is Stated • One of the main contributions of Newell and Simon’s approach: provided a way to specify the possible pathways from the initial to goal states - • There is more to problem solving than specifying the problem space • How a problem is stated can affect its difficulty • Mutilated-checkerboard problem The Importance of How a Problem Is Stated Checkerboard: 64 squares, can be completely covered by placing 32 dominos on the board so that each domino covers 2 squares Mutilated checkerboard problem: If we eliminate 2 corners, can we now cover the remaining squares with 31 dominos? The Importance of How a Problem Is Stated • Mutilated-checkerboard problem – Key to solving it: understanding that 1. Each domino covers two squares 2. These squares must be of different colors – Conditions differed in how much information provided about the squares 1. Blank board 2. Colored board 3. Words black and pink on the board 4. Words bread and butter on the board - belong together , emphasis they are paired – Easier to solve when information is provided that points toward the correct representation of the problem • “Bread and butter” condition emphasized the difference between the squares • S solved this condition twice as fast as the blank condition . The Importance of How a Problem Is Stated • Think-aloud protocol – Say aloud what one is thinking when solving a problem • Instructed not to describe what you are doing, but verbalize new thoughts • Goal: what information S is attending to while solving the problem – Shift in how one perceives elements of a problem • S get the problem after realizing that the word “bread” and “butter” are important • Similar to the idea of reconstruction (Gestalt psychology) ③ Using Analogies to Solve a Problem • Using a solution to a similar problem guides solution to new problem – In a small Russian village, there were 32 bachelors and 32 unmarried women. Through tireless efforts, the village matchmaker succeeded in arranging 32 highly satisfactory marriages. The village was proud and happy. Then one drunken night, two bachelors, in a test of strength, stuffed each other with pierogies and died. Can the matchmaker, through some quick arrangements, come up with 31 heterosexual marriages among the 62 survivors? of co2 not . Using Analogies to Solve a Problem Using Analogies to Solve a Problem • Analogical problem solving: Using a solution to a similar problem guides solution to new problem – Russian marriage problem (source problem) → mutilatedcheckerboard problem (target problem) same solution problem to . – Analogical transfer: The transfer from one problem to another • Source problem to target problem – Target problem: the problem that S is trying to solve – Source problem: another problem that shares some similarities with the target problem • Learning about the Russian marriage problem enhances the ability to solve the mutilated-checkerboard problem Using Analogies to Solve a Problem • Duncker’s radiation problem (1945): – Try solving the following problem: – Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach. It is impossible to operate on the patient, but unless the tumor is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumor. If the rays I reach it all at once at a sufficiently high intensity, the tumor will be destroyed. Unfortunately, at this intensity the healthy tissue the rays pass through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but they will not affect the tumor, either. What type of procedure might be used to destroy the tumor with the rays and at the same time avoid destroying the healthy tissue? • Only 10% of S arrive at the correct solution use not be several rays all in rays center to I treat of the tumor tumor Using Analogies to Solve a Problem • A small country was ruled from a strong fortress by a dictator. The fortress was situated in the middle of the country, surrounded by farms and villages. Many roads led to the fortress through the countryside. A rebel general vowed to capture the fortress. The general knew that an attack by his entire army would capture the fortress. He gathered his army at the head of one of the roads, ready to launch a full-scale direct attack. However, the general then learned that the dictator had planted mines on each of the roads. The mines were set so that small bodies of men could pass over them safely, since the dictator needed to move his troops and workers to and from the fortress. However, any large force would detonate the mines. Not only would this blow up the road, but it would also destroy many neighboring villages. It therefore seemed impossible to capture the fortress. Using Analogies to Solve a Problem share similar solution Using Analogies to Solve a Problem • After reading the fortress story, 30% of S arrive at the correct solution • Gick and Holyoak (1980,1983) I – Noticing an analogous relationship • Crucial, and the most difficult step 2 – Mapping correspondence between source and target • Elements of the source need to be mapped to element of the target 3 – Applying mapping • to generate parallel solutions in target • 70% of S where not able to see the correspondences – When S were told to think about the story they had read, success rate got to 75% radiosurgery Using Analogies to Solve a Problem • There are factors that facilitate the noticing and mapping steps • One reason noticing is difficult is that people often focus on surface surface of problem features – Fortress and tumor is different difficult to relationship • Can making surface features similar facilitate noticing analogous relationships? so identify the Using Analogies to Solve a Problem • • In a physics lab at a major university, a very expensive lightbulb, which would emit precisely controlled quantities of light, was being used in some experiments. One morning Ruth, the research assistant, came into the lab and found that lightbulb no longer worked. She noticed that the filament inside the bulb had broken into two parts. The surrounding glass bulb was completely sealed, so there was no way to open it. Ruth knew that the lightbulb could be repaired if a brief, high intensity laser beam could be used to fuse the two parts of the filament into one. However, a high-intensity laser beam would also break the fragile glass surrounding the filament. At lower intensities the laser would not break the glass, but neither would it fuse the filament. What type of procedure might be used to fuse the filament with the laser and at the same time avoid breaking the glass? Af D ↳ laser - from different center of angle bulb to fix filament Using Analogies to Solve a Problem • Duncker’s Radiation Problem used as the source – 81% of S that knew about the radiation problem solved the lightbulb problem – 10% of S in the control group were able to solve the problem 2 didn't • Surface similarity helped in solving the problem see the radiation problem Using Analogies to Solve a Problem • Lightbulb problem – High surface similarities aid analogical problem solving • Surface features: Specific elements of a given problem – What about structural features? • Underlying principle (similar) that governs the solution – Radiation: strong ray destroys tissue – Lightbulb: strong laser breaks lightbulb • Made two versions, keeping the surface features the same and varying the structural features -> -> Similar surface problem vary target problem Using Analogies to Solve a Problem • Source problem 1: Fragile-Glass version (source and target have similar structural features) • Problem: A high-intensity laser beam would break the fragile glass surrounding the filament. At lower intensities the laser would not break the glass, but neither would it fuse the filament. • Ruth’s Solution: Ruth placed several lasers in a circle around the lightbulb and administered low-intensity laser beams from several directions at once. The beams all converged on the filament, where their combined effect was enough to fuse it. Because each spot on the surrounding glass received only a low-intensity beam from each laser, the glass was left intact. high quite • 69% of S who read this solution were able to solve the radiation problem Using Analogies to Solve a Problem • Source problem2: Insufficient-Intensity version (source and target have different structural features) • Problem: The laser generated only low-intensity beams that were not strong enough to fuse the filament. A much more intense laser beam was needed. • Ruth’s Solution: Ruth placed several lasers in a circle around the lightbulb and administered low-intensity laser beams from several directions at once. The beam all converged on the filament, where their combined effect was enough to fuse it. • 33% of S who read this solution were able to solve the radiation problem solution are similar Using Analogies to Solve a Problem • Making structural features more obvious aids analogical problemsolving • Structural features: The underlying principle(s) that govern the solution to a problem • Analogical encoding: the process by which two problems are compared and similarities between them are determined – Effective way to get participants to pay attention to structural features that aide problem-solving – Having people compare source stories may be an effective way to force S focus on structural features Using Analogies to Solve a Problem • Analogical paradox Limitation x-ve – It can be difficult to apply analogies in the laboratory, but people routinely use analogies in real-world settings vive – Scientists use about 3 to 15 analogies in a 1-hour lab meeting • In vivo problem-solving research – People are observed to determine how they solve problems in the real world • Advantage: naturalistic setting • Disadvantages: time-consuming, cannot isolate and control variables Using Analogies to Solve a Problem • Series of studies manipulated surface features and structural features – Structural features are important for success of transfer • Having subjects pay more attention to structural features increases transfer – Participants pay attention to surface features • Similarity of surface features increases transfer * mechanism must be similar How Experts Solve Problems • What is an expert? – “A person who, by devoting a large amount of time to learning about a field and practicing and applying that learning, have become acknowledged as being extremely knowledgeable or skilled in that field.” • Chess expert: someone who has spent 10,000 to 20,000 hours studying and playing chess • Experts solve problems in their field faster and with a higher success rate than beginners • But why are they better? How Experts Solve Problems • Experts possess more knowledge about their fields • Chase & Simon (1973): compared how well a chess master and a beginner (fewer than 100 hours) were able to reproduce the positions of pieces on a chessboard after looking at an arrangement for 5 seconds • Two conditions: – – Pieces arranged in actual game positions Pieces arranged randomly • Experts did much better than non-experts in the first condition – – – They had stored these actual position in their LTM The positions were accessed in chunks These chunks were not available in the random condition How Experts Solve Problems • Knowledge is organized so it can be accessed when needed to work on a problem • Chi et al. (1982): presented 24 physics problems to a group of experts (physics professors) and a group of novices (students with one semester of physics) – They were asked to sort the problems into groups based on their similarities – Novices: sorted based on surface features (what the object looked like) – Experts: sorted based on structural features (the underlying principles involved) How Experts Solve Problems different principles How Experts Solve Problems • Experts spend more time analyzing problem – Slower start, but this strategy usually pays off • Experts are no better than novices when given problems outside of their field • Being an expert is not always an advantage • Experts less likely to be open to new ways of looking at problems – Being an expert may be a disadvantage when confronting a problem that requires flexible thinking • Problems whose solution may involve rejecting the usual procedures in favor of other procedures that are less frequently used Practical Creativity • Analogical problem solving – Innovations often involve applications of analogous solutions from other problems • Some examples y apply – Velcro: Burrs (the things on the right) covered pants and dogs of inventor (of Velcro) after a F T nature hike – Odon’s device: • Inspired by a Youtube video about how to remove a cork in a bottle https://www.youtube.com/watch?v=NLMH0NrdfNE • Used to save a baby stuck in the birth canal • Endorsed by WHO as an alternative to Cesarean sections e Creative Problem-Solving • Creativity – Innovative thinking – Novel ideas – New connections between existing ideas – Divergent thinking: open-ended; large number of potential “solutions” Creative Problem-Solving • Problem solving as a process: most creative problem solving includes far more than just getting an idea – It involves a lengthy period of trial-and-error – Stages: • Problem generation: Problem finding, fact finding • Problem formulation: Problem definition, idea finding • Problem solving: Evaluation, planning • Solution implementation: selling idea, taking action • Generating ideas is only one part of the creative process – Without ideas, the process stops • Too much knowledge can sometimes hinder creative problem solving – Often problems require thinking flexibility and rejecting accepted procedures Example: Brainstorming Practice • Half of class in Brainstorming groups: – 3-4 people in each group – Follow 4 brain storming rules • Half of class working individually • Tasks: – Write down all ideas for 5 minutes – Rate how much you liked this task (1: lowest, 5: highest) – Guess whether groups or individuals are more productive Rules for Brainstorming Does Brainstorming in groups lead to more creative solutions? • Study by Taylor et al. (1958): – 12 groups with 4 people each – 48 individuals (later randomly assigned to 12 groups) – Solve same 3 problems (tourists, thumbs, teachers) • Results: – Real groups lower than nominal groups in number of ideas, number of unique ideas, quality of ideas write ideas separately -> then combine • Conclusion: generate more ideas – Group participation when using brainstorming inhibits creative thinking (unique ideas) Does Brainstorming in groups lead to more creative solutions? • Reasons for poorer performance in groups: – Some people may dominate discussion in groups – Group members may still be afraid of being judged and inhibit certain ideas – Group members may pay attention to the other members instead of focusing on own ideas • Conclusion: – Group brainstorming not effective for generating ideas – Individual brainstorming can be effective tre : Too many ideas/off topic . Some Questions to Consider • What makes a problem hard? • How can analogies be used to help solve problems? • How do experts in a field solve problems differently than nonexperts?