Ch. 11: Decision Making
Garber and Goldin-Meadow
- 24 college students (12 males, 12 females) 4-disk version Tower of Hanoi - 25 children, 8 to 10 years old (11 boys, 13 girls) 3-disk version Tower of Hanoi - Practice with (n-1)-disk version - Solve 3 or 4-disk version three times - At the end of each trial, explain solution steps without moving disks - Quiet room, sessions videotaped - Coded gesture-speech mismatches e.g., "Blue disk to peg 2" when gesture indicated blue disk to peg 3 - Identified choice point vs. non-choice point moves results: - Both adults and children produced mismatches at choice point moves - No age effects - Mismatch can be used as an index of cognitive uncertainty, choice points in other paradigms - May be used to understand individual problem-solvers
insight and verbalization Sigler and Stern (1998)
- 2nd graders solving arithmetic problems e.g, 18 + 24 - 24 = ? Computational method 12 s Insight method 2.7 s - 90% discovered the insight - Could not verbalize solution on initial trials - By five trials later, 80% could verbalize Initially unconscious then conscious solution
Adaptive control of thought (ACT)?
- Anderson (1983; 1990; 1998) - Declarative, production and working memory - ACT*, ACT-R
what are some Problem solving in natural real world domains?
- Chess, reading, physics - Complex computerized systems (many variables)
explain candle problem
- Dunker (1945) study □ Mount a candle using only a box of push pins and matches - Problem solve: empty the box, thumbtack it to the wall, then mount the candle in it
what are difficulties of problem-solving?
- Dunker and Luchins (gestalt psychologist) researched humans and found 2 major contributions: (1) a set of negative effects related to rigidity or difficulty in problem solving (2) creativity during problem solving
What are computer simulation?
- General problem solver (GPS) - adaptive control of thought (ACT)
Search for relations between problems
- In searching for relations among problems, you actively consider how the current problem may resemble one you've already solved or know about Ex. The four - and more disk Tower of Hanoi problems: are situations in which you search for an analogy - Bowden found that people often found and used info form related problems, but only if sufficient time was allowed for them to do so
Neuroimaging that supports insight
- Kounios study - they used electroencephalographic and functional magnetic resonance imaging recording (FMRI) - they found increased cortical activity centered o the frontal lobes (particularly the anterior cingulate cortex) when people produced insight solutions as compared to normal problem solving - His theory is that part of the frontal lobe suppresses the irrelevant info that tends to dominate a person's thinking up to that point - When these dominant thoughts become suppressed, this allows more weakly activated ideas, like those remote associations drawn by the right hemisphere, to come to the fore, possibly providing the solution to a problem - Basically when dead-end thoughts are moved aside, alternative solutions can then present themselves
explain water jug problem
- Luchins (1942) study □ He demonstrates a negative set involving sequencing the problems so that people developed a particular set or approach for measuring out the quantities together □ You are given 3 jugs, each of a different capacity, and are to measure out a quantity of water using just the 3 jugs □ Jug A = 5 cups, Jug B= 40 cups, and Jug C= 18 cups - If you need to measure out 28 cups of water then you can use jug A twice and just C once □ The second problem, A=21 cups, B=127 cups, and C=3 cups and you need to fill 100 cups - Fill B(127), subtract jug C from it twice (-3,-3), then subtract jug A(-21) = 100 - People are less likely to show mental set effects if they are given actual water jugs as compared to just paper and pencil problems
explain two string problem. what was the functional fixedness?
- Maier (1931) study □ Two strings are suspended from the ceiling, and the goal is to tie them together □ Problem is that the strings are too far apart for a person to hold one, reach the other, then tie them together □ There were other available objects, including a chair, some paper, and a pair of pliers □ Standing on the chair doesn't get the person close enough to the two strings □ Results: 39% of the people came up with the correct solution during a 10-minute period □ Solution involves tying the pliers to one sting, swing it like a pendulum, then catch it while holding the other string □ This functional fixedness in the situation was failing to think of pliers in any but their customary function □ People were fixed on the normal use for pliers and failed to appreciate how they could be used as a weight for a pendulum
what's problem structure?
- People must find a parallel structure between the source and target problems to map elements from the source to elements in the target - Figuring out theses correspondences or mappings is important because it corresponds to working out the relationships of the analogy Ex. Of mapping: attack --> radiation; central fortress --> tumor; attacking troops --> rays; small groups of men --> weaker rays
what's Subgoal Decomposition?
- Subgoal: an intermediate goal along the route to eventual solution of the problem - subgoals represent the decomposition, or breaking apart, of the overall goal into separate components - Subgoals themselves must be further decomposed into smaller subgoals - Thus a problem involves breaking the overall goal into subgoals, then pursuing the subgoals, and their subgoals, one after another until the final solutionis achieved - This yields a hierarchical or nested structure to the problem-solving attempt
what are the jug problem results?
- Subjects who solved problems 1 through 7 in succession used a lengthier method to solve problems 6 through 10 than those who only saw problems 6 through 10 - Longer method: 80% vs. 1% - 1 through 7 subjects had developed a "set" or approach
what's Tower of Hanoi?
- The goal of the problem is to move all 3 disks from peg 1 to peg 3 so that C is on the bottom, B is in the middle, and A is on top - You may not place a larger disk on top of a smaller one - goal: to move the ABC stack of disks from peg 1 to peg 3 - Step 1 : Applying the means-end analysis, your step sets up this goal - Step 2: there is a difference between your current state and the goal, simply the difference between the starting and ending configurations - Step 3: look for a method or operator that reduces this difference and then apply it □ Your major subgoal is "clear off disk C," this entails getting B off C, which entails another subgoal, getting A off B - Step 4: involves a simple operator that satisfies the most immediate subgoal, "move A to 3," which permits satisfying the next subgoal, "getting B off C."
what the purpose of the analogy?
- The person's goals, and the goal stated in the problem, are important - This is deeper than merely the general purpose of trying to solve the problem - Processing goals and tactics, in this case direct comparison of 2 stories, can influence whether people actually use analogies or not ex. Goals don't match in the parade or radiation stories
what's problem similarity?
- There must be some degree of similarity between the already-understood situation, the source domain, and the current problem, the target domain Ex. In the parade story, the fortress and troops are similar to the tumor and the rays in the radiation story
Gick and Holyoak study about analogy and findings
- They asked to read and solve the 2nd story the radiation problem. - Reducing the intensity of the rays was more productive - there were similarities between the problems, suggesting that the parade story can e used it develop an analogy for the radiation problem Found - 8% solved radiation story, control group - 76% of these participants used the attack analogy in solving the radiation problem - 92% of those who got a hint that used the analogy found it "very helpful" - no hint only 20%
who is Wolfagang Kohler?
- a German psychologist, went to the Spanish island of Tenerfie to study "the psychology of anthropoid apes" - Was trapped there during WWI - He experimented with visual discrimination among several animal species - Applied Gestalt principles to animal perception - He concluded that animals don't perceive individual elements in a stimulus, but that they perceive relations among stimuli - Kohler also observed that the perception of relations is a mark of intelligence, and he called the sudden perception of useful or proper relations insight" - He continued to examine "insight learning" - He presented problems to chimpanzees and searched for evidence of genuine problem solving in their behavior
what's production systems?
- a condition-action pair of an if- then pair - Important characteristic of GPS - First model proposed in psychology - In the GPS application to the Tower of Hanoi, three sample productions might be: 1. If the destination peg is clear and the largest disk is free, then move the largest disk to the destination peg 2. if the largest disk is not free, then set up a subgoal to free it 3. If a subgoal to free the largest disk is set up and a smaller disk is on it, then more the smaller disk to the stack peg
what's insight?
- a deep, useful understanding of the nature of something, especially a difficult problem - eureka "aha!" reaction - Sometimes, the necessary insight for solving a problem comes from an analogy ○ Ex. Historical example; story of Archimedes. The Greek scientist who had to determine whether the king's crown was solid gold or whether some silver had been mixed with the gold. He knew the weights of both gold and silver per unit of volume but couldn't imagine how to measure the volume of the crown. He stepped into his bath one day and noticed how the water level rose as he sank into the water. The volume of the crown could be determined by immersing it in water and measuring how much water it displaced. "Eureka! I have found it"
what's an analogy?
- a relationship between two similar situations, problems, or concepts - an already-solved problem is similar to a current one, so the old solution can be adapted to a new situation useful for solving problems Ex. "merchant: sell:: customer: ____" you figure out the structure for the first pair of terms and then project or map that structure onto the 2nd par of the analogy (buy) ○ Researchers argue that analogies provide excellent, widely applicable methods for solving problems ○ Analogical problem solving is better when people receive the info by hearing about it rather than reading it
what's functional Fixedness?
- a tendency to use objects and concepts in the problem environment in only their customary and usual way - Idea is that we generally think only of the customary uses for objects, whereas successful problem soling may involve finding novel uses - Simply from the standpoint of routine retrieval from your semantic memory, then, we can understand why people experience functional fixedness
what is Gestalt?
- a whole pattern, a form, or a configuration - German word that translates poorly into English = "whole," "shape," or "field" fail to capture what the term means - Boring (1920s-50s) remarked that Gestalt psychology "suffered from its name" - The term Gestalt is used rather than an inadequate translation - It shows that humans tend to perceive and deal with integrated, cohesive wholes through early 70s - Simple novel tasks: - Clearly defined solutions, relatively short time frame, problem solving steps could be traced ex. Duncker's X-ray problem ex. Tower of Hanoi
what's Sequence of Operations?
- an activity must have a sequence of operations or steps to be problem solving - This excludes retrieval from memory like 2 x 3 = 6 Ex. Discerning problem or solving the locked-car problem definitely involves a sequence of mental operations
what's well-defined problem?
- an explicit and complete specification of the initial and goal states (recreational problems)
what are means-end analysis?
- no other heuristic comes close to means-end analysis - the problem is solved by repeatedly determining the difference between the current state and the goal or subgoal state, then finding and applying an operator that reduces this difference - Nearly always implies the use of subgoals because achieving the goal state usually involves the intermediate steps of achieving several subgoals along the way - An intuitive level, means-end analysis and subgoals are familiar and represent "normal" problem solving Ex. Write a term paper: select a topic, find relevant material, read and understand the material, etc.
what's negative set?
- or simply set effects; a bias or tendency to solve problems in a particular way, using a single specific approach, even when a different approach might be more productive - If people develop a routine way of solving problems then they are more likely to experience Einstullung - Evidence that experts at a task are more prone to this than others because they are more likely to have developed a set of routine for solving certain kinds of problems - Rough translation to German word Einstellung ("approach" or "orientation)
what is multi-constraint theory?
- predicts how people use analogies in problem solving and what factors govern the analogies people construct - By Holyok and Thargard - It says that people are constrained by 3 factors when they try to use or develop analogies: problem similarity, problem structure, and the purpose of the analogy
What is problem solving?
- requires us to examine a lengthy sample of behavior, often up to 20 or 30 minutes of activity - Is part of thinking - Occurs if an organism or artificial intelligence system does not know how to proceed from a given state to a desired goal state.
what's Cognitive Operations?
- solving problem involves the application of various cognitive operations - Various operators can be applied to different problems, where each operator is a distinct cognitive act, a permissible step or move in the problem space - Cognitive operations have a behavioral counterpart, some physical act that completes the mental operation, like writing down a number during long Ex. Retrieving an answer would be an operator in Long division, as would be subtracting or multiplying 2 numbers at some other stage in problem solution
what's ill-defined problems?
- states, operators, or both may be only vaguely speed Ex. Problems with real-world character often are distressingly vague in their specification of the goal ("write a term paper that will earn you an A," "write a computer program that does X in as economical and elegant a fashion as possible,")
what is problem space?
- the initial, intermediate, and goals states of the problem - It includes the problem solver's knowledge at each of these steps - Both knowledge that is currently being applied and knowledge that could be retrieved from memory and applied - Inclued any external devices, objects, or resources that are available - A difficult arithmetic problem that must be completed mentally has a different problem space than the same problem as completed with pencil and paper example: - VaLehn (1989) describes one man's error in the "three - The man focused only on the arithmetic of the problem ad said essentially "400 pounds of people, 200 pound per trip, it'll take two trips of the boat." - When he was reminded that the boat couldn't row itself back to the original side, he adopted a different problem space
what is goal directness?
- the overall activity we're examining is directed toward achieving some goal - This excludes day dreaming Ex. If you've locked your keys in your car, both physical and mental activity are going on. The locked car, makes this an instance of true problem solving
what is an operator?
- the set of legal moves that can be done during problem solution - Legal= permissible in the rules of the problem Ex. "three men and a rowboat," an illegal operator is having the men swim across the river or loading the boat with too heavy a load - For transformation problems, applying an operator transforms the problem into a new or revise state from which further work can be done - A legal operator moves you from one node to next along some connecting pathway in the search space Ex. In solving algebraic equations, one transformation operator is "move the unknowns to the left" --> 2X + 7 = 14 X + 10 - Applying the operator would move the single X to the left of the equal sign by subtracting X from both sides of the equation - Constraints within the problem prevent us from applying certain operators Ex. Destruction of healthy tissue was such a constraint in radiation problem - It prevented the simple solution of applying the ray directly, where direct application would be simple operator Ex. Algebra, you can't subtract X from one side of the equation without subtracting it from the other side
what is verbal protocol?
- the transcription and analysis of people's verbalizations as they solve the problem - A major type of data - It influenced many opinions abut problem solving - Danalysis of s's verbalization to solve problem
what are goals?
- the ultimate destination or solution to the problem - desired end-point of the problem-solving activity - Problem solving consists of goal-directed activity, moving from some initial configuration or state through a series of intermediate steps until finally the overall goal has been reached-- and adequate or correct solution - well defined problem - ill-defined problem
what are Characteristics of Problem Solving?
1. Goal Directedness 2. Sequence of Operations 3. Cognitive Operations 4. Subgoal Decomposition (a subgoal is an intermediate goal along the route to eventual solution of the problem).
how can you improve problem solving skills
1. Increase your domain knowledge 2. Automate some components of the problem-solving solution 3. Follow a systematic plan 4. Draw inferences 5. Develop subgoals 6. Work backward search for contradictions 7. Search for relations between problems 8. Find a different problem representation 9. Stay calm 10. It all else fails, try practice
what did Metcalf and Wiebe find in how people love problems compared that with how they solved algebra problems?
1. People were rather accurate in predicting whether they'd be successful in solving routine problems but not in predicting success with insight problems 2. Solutions to the insight problems seemed to come suddenly, almost without warning
summarize means-end analysis in 5 steps
1. Set up a goal or subgoal 2. Look for a difference between the current state and the goal or subgoal state 3. Look for an operator that will reduce or eliminate this difference. One such operator is the setting of a new subgoal 4. Apply the operator 5. Apply steps 2 - 4 repeatedly until all subgoals and the final goal are achieved
what are 3 characteristics that define what qualifies as problem solving? or problem solving vocabulary
1. problem space 2. operators 3. the goal
Do gesture-speech mismatches have cognitive significance?
Evidence from learning paradigms - Children with more mismatches more likely to learn Evidence from problem-solving - Adults use strategies compatible with both spoken and gestured information - When these are mismatched, S's are using two different strategies to solve the problem
what is the history of Gestalt?
before 70s - Lab tests don't generalize to more complex, real-life problems
what's the difference between problem solving and memory/ attention (cognitive domains)
memory/attention (cognitive domains): - Short span of time - Rt - Accuracy - More precise problem solving: - Lengthy behavior - Verbal protocol - Less precise
who is Sulan?
□ Chimpanzee Sultan was able to use a long pole to reach through the bars of his cage and get a bunch of bananas □ Kohler made the situations more difficult by giving Sultan □ Kohler went inside the cage and demonstrated putting one end of the pole to the other □ Kohler found this to be an apt demonstration of insight, a sudden solution to a problem by means of an insightful discovery □ Another situation, Sultan discovered how to stand on a box to reach a banana that was otherwise too high to reach □ All these perceptions of relations and the importance of insight in problem solving
neurocognition in insight study and findings
○ Bowden and Beeman (1998) found a significant role for right hemisphere processing in solving insight problems - "what one word can form a compound word or phrase with each of the following? Pie luck belly? (POT) - Stimuli presented to either the LVF/RH or RVF/LH - Named POT faster when presented to LVF/RH—right hemisphere advantage for insight
Develop subgoals
○ Breaking a large problem into separate subgoals ○ Heart of the means-end approach ○ Sometimes in the real-world problem solving, there is only a vaguely specified goal and even more vaguely subgoals Ex. Subgoal: "find enough articles on a particular topic to write a term paper that will earn an A"? ○ Simon's satisficing heuristic is important: satisficing a heuristic in which we find a solution to a goal or subgoal that is satisfactory although not necessarily the best possible one ○ Ex. A term paper problem included, an initial satisfactory solution to subgoals may give you additional insight for further refinement of your solution. When you begin to write your rough draft, you realize there are gaps in your info. What seems originally to be satisfactory solution to the subgoal of finding references turns out to be insufficient, so you can recycle back to that subgoal to improve your solution. You might only discover their deficiency by going ahead and working on that next subgoal, the rough draft
Increase your domain knowledge
○ Domain knowledge: what one knows about the topic ○ A person who has only limited knowledge or familiarity with a topic is less able to solve problems efficiently in that domain ○ Extensive domain knowledge leads to expertise ○ Much work comes from Simon's work with chess ○ Chess masters need only a glimpse of the arrangement of chess pieces to remember the arrangement, far beyond what novices or players of moderate skill can do ○ Advantage is only when the pieces are in legal locations ○ When the locations of the pieces are random, then there is no advantage for the skilled players ○ This advantage of expertise in remembering legal board positions is attributed to experts; more skilled perceptual encoding of the board, literally more efficient eye movements and fixations while looking at the board
If all else fails, try practice
○ Ebbignahaus recommend that practicing within a particular knowledge domain stragnthens that knowledge, pushes the problem-solving components closer to an automatic basis, and gives you a deeper understand of the domain ○ Ericsson and Charness's rebiew people routinely believe that stunning talent and amazing accomplishments result from inherited, genetic, or "interior" explanations, when the explanation usually is dedicated, regular, long term practice ○ Ericsson, Krampe, and Tesch-Romer found that people who had higher levels of expertise also were the ones who engaged in more practice O Unclear if there's innate characteristic like motivation, interest, or talent that could also be driving those people to practice more
Find a different problem representation
○ How you choose to represent and think about the problem you're working on ○ When you get stuck on a problem, it's useful to goa back to the beginning and reformulate or reconceptualize it ○ Simon makes a compelling point that one representation of a problem may highlight a particular feature of a problem while masking or obscuring a different, possibly important feature Ahlum-heath and DiVesta say verbalizing your think also helps in the initial stage of problem solving ○ Learning a set of motor response, even a complex sequence, relies on implicit memory ○ So working the Tower of Hanoi manually by moving real disks or coins around should enable you to learn how to the problem from implicit and explicit basis
Follow a systematic plan
○ Important in multistep problems - People often make errors when planning how long a task will take, but can plan their time better if they break the task down into the problem subgoals, estimate the time needed for each of those, and then add those times together
Automate some components of the problem-solving solution
○ Kotovsky, Hayes, and Simon tested adults on various forms of the Tower of Hanoi problem and also on problem isopmorphs, problems with the same form but different details ○ Results: a heavy working memory load was a serious impediment to successful problem solving. If the person had to hold 3 or 4 nested subgoals in working memory all at once, performance deteriorated ○ A solution to this memory load problem was to automate the rules that govern moves, just as you were supposed to master and automate the 7 step sequence in the Tower Hanoi ○ This frees working memory to be used for higher level subgoals
What's General problem solver (GPS)
○ Newell, Shaw, and Simon created this computer simulation ○ it was for a general-purpose, problem-solving program, not limited to just one kind of problem but widely applicable to a large class of problems in which means-end analysis was appropriate ○ They drew an analogy between the way computer programs solve problems and the way humans do: human mental processes are of a symbolic nature, so the computer's manipulation of symbols is a fruitful analogy to those processes - GPS had what amounted to a planning mechanism that abstracted the essential feature of situations and goals then devised a plan that would produce a problem-solving sequence of moves - it's limited because it doesn't characterize human problem solving
neurocongition in analogy study and findings
○ Wharton et al (2000) identified brain regions that are associated with the mapping process in analogical reasoning - Study: people saw a source picture of geometric shapes, followed by a target picture. - They had to judge whether the target picture was an analog pattern (whether it had the same system of relations as the source picture) - Control condition: they judged whether the target was literally the same as the source - Literal condition: Preserved both the spatial relations in the source and the object relations - Analogy condition: preserved spatial relations - Response to time analogy was 1,400 to 1,500 ms range and approx. 900 to 1,000 in the literal condition - Results: PET scan images showed significant activation in the medial frontal cortex, left prefrontal cortex, and left inferior parietal cortex
Draw inferences
○ Wicklegren advice to draw inferences from the givens, the terms, and the expressions in a problem before working on the problem itself ○ It can help you abandon a misleading representation of the problem and fid one that's more suitable to solving the problem ○ Beware of unwarrentated inferences, the kinds of restrictions we place on ourselves that may lead to dead ends Ex. Nine-dot problem: an unwarranted inference is that you must stay within the boundaries
Work backward search for contradictions
○ Working backward is another heuristic, in which a well-specified goal may permit a tragic of the solution pathway in reverse order, thus working aback to givens Ex. Many math and algebra proofs can also be worked backward or in a combination of forward and backward methods ○ In problems that ask "is it possible to?" or "is there a way that?" you should search for contradiction I the givens or goal state ○ Wicklegran uses "is there an integer x that satisfies the equation x^2 + 1+0? - Simple operation subtracting 1 form both sides, yilds x^2 = -1, which contradicts the known property that any squared number is positive ○ This heuristic can also be helpful in multiple choice exams -Maybe some of the alternative contradict some idea or fact of the question or some fact you learned in the course
