Chapter 12: Problem Solving What is a Problem? Problem: there is an ...
Chapter 12: Problem Solving What is a Problem? Problem: there is an obstacle between a present state and a goal and is not immediately obvious how to get around the obstacle 1. Well-defined problems: usually have a correct answer and certain procedures, when applied correctly, will lead to a solution 2. Ill-defined problems: occur frequently in everyday life, don’t necessarily have one “correct” answer and the path to their solution is often unclear The Gestalt Approach: Problem Solving as Representation and Restructuring •
Gestalt psychologists were interested in perception, learning, problem solving, attitudes, beliefs o How people represent a problem in their mind o How solving a problem involves a reorganization or restructuring of this representation
Representing a problem in the Mind • • •
Success in solving a problem is influenced by how it is represented in the person’s mind Solutions can be obtained by first perceiving the object and then representing it in a different way Restructuring: process of changing the problem’s representation
Restructuring and Insight • • •
Insight: the sudden realization of a problem’s solution o Involves suddenly discovering a crucial element that leads to the solution Some people often experience problem solving as an “Aha!” experience Participants working on an insight problem should not be very good at predicting how near they are to a solution as opposed to non-insight problems o Non-insight problems = algebra problems
Obstacles to Problem Solving •
• • •
Fixation: people’s tendency to focus on a specific characteristic of the problem that keeps them from arriving at a solution o Problem = focusing on familiar uses of an object o Functional fixedness: restricting the use of an object to its familiar functions Duncker’s candle problem: participants with materials and an empty box = twice as likely to solve the problem than participants with materials in the box Two-string problem: tying two strings on a ceiling that are far away from each other o Had to use pliers as weight to act as a pendulum Mental set: a preconceived notion about how to approach a problem – determined by a person’s experience or what has worked in the past o Can arise out of the situation created as a person solves a problem
•
Water-jug problem: participants are given three jugs of different capacities – required to use these jugs to measure out a specific quantity of water o Those solving problems 7 and 8 had no mental set, where they solved it in shorter solutions than the mental set group o Mental set group learned the formula when solving problems 1-6; tried to use this formula for problems 7 and 8
Modern Research on Problem solving: The Information-Processing Approach Newell and Simon’s Approach Term Initial State Goal State Intermediate State Operators Problem space Means-end analysis Subgoals
Description Conditions at the beginning of a problem Solution to the problem Conditions after each step is made toward solving a problem Actions that take the problem from one state to another – operators are usually governed by rules All possible states that could occur when solving a problem Way of solving a problem in which the goal is to reduce the difference between the initial and goal states Small goals that help create intermediate states that are closer to the goal – may appear to increase distance to goal state but in the long run can result in the shortest path to the goal
Tower of Hanoi Problem: three discs stacked on the left peg, and the goal state as these discs stacked on the right peg • Illustrates means-end analysis The Importance of how a problem is Stated Think-aloud protocol: participants are asked to say out loud what they are thinking while doing a problem • Reveals a shift in how the person perceives elements of a problem Analogy: process of noticing connections between similar problems and applying the solution for one problem to other problems Using Analogies to Solve Problems Analogical problem solving: using the solution to a similar problem to guide solution of a new problem (Ex: Russian marriage problem in solving the mutilated checkerboard problem) Analogical Transfer Analogical transfer: the transfer from one problem to another • Participants trying to solve a target problem are presented with a source problem or source story that shares some similarities with the target problem • Illustrates a way to solve the target problem • Good analogical transfer does not always occur
Analogical Problem Solving & the Duncker Radiation Problem • • • • • •
Fortress story is analogous to the Duncker radiation problem o Divide multiple low-intensity rays to meet at the tumour There are factors that help facilitate the noticing and mapping steps Surface features: specific elements that make up the problem o Problem = people focus on these – hard to notice analogous features between source stories and target problems Structural features: underlying principles that governs the solution o Ex: weak laser beams and rays in radiation and light bulb problem Analogical transfer is better when the structural features of the source and target problems are more similar There is a process of analogical problem solving that involves the following three steps
1. Noticing: that there is an analogous relationship between the source story and target problem o The most difficult of the three steps to achieve o Stories most similar to target problems = most effective 2. Mapping: the correspondence between the source story and target problem o Must map corresponding parts of the story onto the test problem by connecting similar elements 3. Applying: the mapping to generate a parallel solution to the target problem Analogical Encoding Analogical encoding: comparing two cases that illustrate a principle – when learners compare cases, they become more likely to see the underlying structure •
•
Participants tended to use negotiating strategy that was emphasized in sample cases they had read previously o Contingency strategy used in sample and new task o Trade-off solutions used in sample and new task People compare source stories – pay attention to structural features that enhance their ability to solve other problems
Analogy in the Real World Analogical paradox: participants in psychological experiments tend to focus on surface features in analogy problems, whereas people in the real world frequently use deeper, more structural features In vivo problem-solving research: observing people to determine how they solve problems in real-world situations • Analogies play an important role both in scientific problems and in designing new products How Experts Solve Problems
Experts: extremely knowledgeable or skilled in a particular field having devoted a large amount of time to learning and practicing. Differences between how Experts and Novices solve problems •
Solve faster with a higher success rate than do novices
1. Experts possess more knowledge about their fields • Chess masters: able to recognize specific arrangements of pieces • Knowledge is organized so it can be accessed when needed to work on a problem 2. Experts’ knowledge is organized differently from novices’ • Novices categorize problems based on their surface features (what the objects look like) • Experts categorize problems based on their deep structure (underlying principles) 3. Experts spend more time analyzing problems • Get off on a slow start – understand problem first rather than immediately trying to solve it Expertise is only an Advantage in the Expert’s Speciality • •
Differences hold only when problems are within an expert’s field Disadvantage = knowing about the established facts and theories in a field may make experts less open to new ways of looking at problems
Creative Problem Solving Divergent thinking: thinking that is open-ended, involving a large number of potential “solutions” and no “correct” answer – associated with ill-defined problems Convergent thinking: thinking that works toward finding a solution to a specific problem that usually has a correct answer – associated with well-defined problems Design fixation: fixation inhibiting problem solving where a sample design is presented containing forbidden features Creative cognition: training people to think creatively via creating inventions out of abstract objects
Gestalt psychologists were interested in perception, learning, problem solving, attitudes, beliefs o How people represent a problem in their mind o How solving a problem involves a reorganization or restructuring of this representation
Representing a problem in the Mind • • •
Success in solving a problem is influenced by how it is represented in the person’s mind Solutions can be obtained by first perceiving the object and then representing it in a different way Restructuring: process of changing the problem’s representation
Restructuring and Insight • • •
Insight: the sudden realization of a problem’s solution o Involves suddenly discovering a crucial element that leads to the solution Some people often experience problem solving as an “Aha!” experience Participants working on an insight problem should not be very good at predicting how near they are to a solution as opposed to non-insight problems o Non-insight problems = algebra problems
Obstacles to Problem Solving •
• • •
Fixation: people’s tendency to focus on a specific characteristic of the problem that keeps them from arriving at a solution o Problem = focusing on familiar uses of an object o Functional fixedness: restricting the use of an object to its familiar functions Duncker’s candle problem: participants with materials and an empty box = twice as likely to solve the problem than participants with materials in the box Two-string problem: tying two strings on a ceiling that are far away from each other o Had to use pliers as weight to act as a pendulum Mental set: a preconceived notion about how to approach a problem – determined by a person’s experience or what has worked in the past o Can arise out of the situation created as a person solves a problem
•
Water-jug problem: participants are given three jugs of different capacities – required to use these jugs to measure out a specific quantity of water o Those solving problems 7 and 8 had no mental set, where they solved it in shorter solutions than the mental set group o Mental set group learned the formula when solving problems 1-6; tried to use this formula for problems 7 and 8
Modern Research on Problem solving: The Information-Processing Approach Newell and Simon’s Approach Term Initial State Goal State Intermediate State Operators Problem space Means-end analysis Subgoals
Description Conditions at the beginning of a problem Solution to the problem Conditions after each step is made toward solving a problem Actions that take the problem from one state to another – operators are usually governed by rules All possible states that could occur when solving a problem Way of solving a problem in which the goal is to reduce the difference between the initial and goal states Small goals that help create intermediate states that are closer to the goal – may appear to increase distance to goal state but in the long run can result in the shortest path to the goal
Tower of Hanoi Problem: three discs stacked on the left peg, and the goal state as these discs stacked on the right peg • Illustrates means-end analysis The Importance of how a problem is Stated Think-aloud protocol: participants are asked to say out loud what they are thinking while doing a problem • Reveals a shift in how the person perceives elements of a problem Analogy: process of noticing connections between similar problems and applying the solution for one problem to other problems Using Analogies to Solve Problems Analogical problem solving: using the solution to a similar problem to guide solution of a new problem (Ex: Russian marriage problem in solving the mutilated checkerboard problem) Analogical Transfer Analogical transfer: the transfer from one problem to another • Participants trying to solve a target problem are presented with a source problem or source story that shares some similarities with the target problem • Illustrates a way to solve the target problem • Good analogical transfer does not always occur
Analogical Problem Solving & the Duncker Radiation Problem • • • • • •
Fortress story is analogous to the Duncker radiation problem o Divide multiple low-intensity rays to meet at the tumour There are factors that help facilitate the noticing and mapping steps Surface features: specific elements that make up the problem o Problem = people focus on these – hard to notice analogous features between source stories and target problems Structural features: underlying principles that governs the solution o Ex: weak laser beams and rays in radiation and light bulb problem Analogical transfer is better when the structural features of the source and target problems are more similar There is a process of analogical problem solving that involves the following three steps
1. Noticing: that there is an analogous relationship between the source story and target problem o The most difficult of the three steps to achieve o Stories most similar to target problems = most effective 2. Mapping: the correspondence between the source story and target problem o Must map corresponding parts of the story onto the test problem by connecting similar elements 3. Applying: the mapping to generate a parallel solution to the target problem Analogical Encoding Analogical encoding: comparing two cases that illustrate a principle – when learners compare cases, they become more likely to see the underlying structure •
•
Participants tended to use negotiating strategy that was emphasized in sample cases they had read previously o Contingency strategy used in sample and new task o Trade-off solutions used in sample and new task People compare source stories – pay attention to structural features that enhance their ability to solve other problems
Analogy in the Real World Analogical paradox: participants in psychological experiments tend to focus on surface features in analogy problems, whereas people in the real world frequently use deeper, more structural features In vivo problem-solving research: observing people to determine how they solve problems in real-world situations • Analogies play an important role both in scientific problems and in designing new products How Experts Solve Problems
Experts: extremely knowledgeable or skilled in a particular field having devoted a large amount of time to learning and practicing. Differences between how Experts and Novices solve problems •
Solve faster with a higher success rate than do novices
1. Experts possess more knowledge about their fields • Chess masters: able to recognize specific arrangements of pieces • Knowledge is organized so it can be accessed when needed to work on a problem 2. Experts’ knowledge is organized differently from novices’ • Novices categorize problems based on their surface features (what the objects look like) • Experts categorize problems based on their deep structure (underlying principles) 3. Experts spend more time analyzing problems • Get off on a slow start – understand problem first rather than immediately trying to solve it Expertise is only an Advantage in the Expert’s Speciality • •
Differences hold only when problems are within an expert’s field Disadvantage = knowing about the established facts and theories in a field may make experts less open to new ways of looking at problems
Creative Problem Solving Divergent thinking: thinking that is open-ended, involving a large number of potential “solutions” and no “correct” answer – associated with ill-defined problems Convergent thinking: thinking that works toward finding a solution to a specific problem that usually has a correct answer – associated with well-defined problems Design fixation: fixation inhibiting problem solving where a sample design is presented containing forbidden features Creative cognition: training people to think creatively via creating inventions out of abstract objects
