Chapter 10 - Problem Solving Flashcards
What are 3 major aspects of problem-solving?
1) Purposeful/goal-directed -> meant to achieve some goal
2) Based on controlled processes rather than automatic ones
3) You cannot produce an immediate solution to the problem because you lack the relevant knowledge
What are some different types of problems?
1) well-defined vs ill-defined problems
- well-defined: all aspects of the problems are clearly specified (including initial state or situation, the range of possible moves or strategies, and the goal or solution). For such problems, you know when the goal is reached.
- ill-defined: not obvious when the goal has been reached, and not obvious what information is relevant.
2) knowledge-rich vs knowledge-lean problems
- knowledge-rich: very important in real-life: experts spend their lives dealing with such problems
- problems that can only be solved by those having much relevant specific knowledge.
- knowledge-lean: don’t require such knowledge as most of the info needed is contained in the initial problem statement
- Most research on problem-solving involves this, in part because this minimises individual differences.
How can you solve well-defined problems?
algorithms: a list of well-defines instructions for completing a task.
While past experience can facilitate problem-solving, what are some problems associated with using past experience to solve problems? (2)
1) Functional fixedness
2) Use of mental sets.
Functional fixedness can only be found when one has much prior experience. True or false?
False. Happens even when you have limited experience.
- Asked people to decide whether each of 9 objects could be used for a given function (eg can this be used as packing material for packing an egg in a box?)
- Then participants were asked if the same object can be used for another function (eg play catch over a distance of 15 feet). Some items can be used for both. However, deciding that one of these objects possess the 1st function significantly reduced the probability of detecting that it also possessed the 2nd function.
How else is functional fixedness hard to avoid?
Participants designed various objects (eg disposable, spill-proof coffee cup)
1 condition: Showed picture of an inadequate coffee cup with accompanying description explicitly stating various problems with it. Howeevr, participants’ designs consistently included elements of the example coffee cup identified as problematic. The ideas we encounter often constrain our subsequent thinking related to insight.
What is funcitonal fixedness?
When we sometimes fail to solve problems because we assume from past experience that any given object only has a limited number of functions.
How did Duncker study functional fixedness and what results did he obtain?
Study: Gave participants a candle, a matchbox containing matches, some tacks and several other objects. They are supposed to find a way to attach the candle to the wall so that it didn’t drip onto the table below. Most participants couldn’t solve it correctly, with most of them trying to nail the candle directly to the wall or to glue it to the wall by melting it. Only a few thought of the correct solution, which was to remove the matchsticks from the box, nail the box to the ball and place the candle on it.
Why couldn’t many people solve the problem in Duncker’s study?
Participants fixated on the box’s function as a container rather than it as a platform. This is supported by the finding that more correct solutions were produced when the matchbox was empty rather than full. When the container was empty, it appeared less like a container in that state.
How do you improve performance in Duncker’s study?
ie reduce functional fixedness
Use a condition: Underline candle, box of matches, box of tacks in the list.
- % of people who came up with solutions was more than double then % of people who came up with solutions when there was no underline.
- Underlining led participants to focus more directly on the key objects involved in problem solution.
This shows that problem-solving performance could be impaired by functional fixedness caused by accumulated past experience within the crucial object in the problem. We sometimes fail to solve problems because we assume from past experience that any given objects only has a limited number of solutions.
What are mental sets?
A readiness to act or think in a given way, often because this has shown to be successful in the past. It allows problems to be solved aster and with less processing demands.
Are people prone to sticking with mental sets? Provide evidence
hint: water jar luchins (cute right the name ok pls rmb)
Yes even though when the mental set doesn’t solve a problem.
Water jar problem by Luchins
1) Jar A: 28 qt, Jar B: 76 qt, Jar C: 3 qt. You are to get 25 qt of water.
- This is easy, most people can solve this. 95% of participants who had previously been given similar problems solved it.
- Participants in another condition were given complex problem to solve first, and were then asked to solve this water jar problem which is relatively simpler. So only 36% of participants in this condition could solve it
- This condition’s results shown that people often maintain a mental set even when it presents a problem from being solved.
What does Levine’s experiment illustrate about how mental sets can prevent us from thinking clearly?
(Adam Le-vine sounds like Adam Le-B: it’s the A B experiment! lame ways for u to rmb)
Participants were presented a series of card bearing either the letter A or B. with instrucutions to work out the hypothesis the experimenter had in mind. On each trial, the participant said “A” or “B” and the experimenter then indicated if this was correct.
- 1st few problems: got position sequence (eg 1st trial: left correct, 2nd trials: right correct)
- After several problems involving a position sequence, participants were given a very simple problem not involving a position sequence. “A always correct, B always wrong”. However, approximately 80% of uni students failed to solve this problem within 100 trials. They assumed that the answer must be some kind of position sequence like before, and this thus resulted in endless position sequences.
Which type of people are most susceptible to mental sets and why?
Experts, because their attentional processes are over-influenced by their mental sets, which are accumulated over the years.
Provide evidence about how experts are susceptible to mental sets.
Example is related to the game happy birthday guy likes to play.
presented expert chess players with a chess problem and told them to find the shortest way to win.
- can be solved in 5 moves, but actually the shortest in 3 moves, provided you use a less familiar move!
- only 50% of the international Masters and 0% of the Candidate Masters found the short solution.
a similar study was done to clarify why expert chess players often failed to find the shorter solution.
- after these players have found the familiar solution, they reporterd they were looking for a better one.
- however, their eye movements revealed that they were still looking at features of the chessboard position related to the familiar solution.
Direction of attention remained partly under the control of the processes responsible for the initial solution.
What’s the difference between solving problems using analysis and using insight?
Analytic: There is a gradual increase in warmth before the solution is reached.
Insight: For some problems, there is barely any increase in warmth until right before a solution is reached. You suddenly know how to do a question. Answer comes up unexpectedly, like it hits you in the face and you go “h0LeY sHiT”. Eureka effect.
Provide a well-known example of an insight problem.
Hint: the game is something like what the previous example mentioned.
Mutilated checkboard.
- remove 2 corner squares of a checkboard, top right and bottom left.
- asked participants if dominos can fit the entire checkerboard.
- nearly everyone given this problem starts by mentally covering squares with dominoes (i did too! how encouraging.). very few can solve this problem.
- how to solve: realise that each domino covers one black and one white square, and the pieces u took out were both white.
- so you cannot fit the whole board with dominoes.
What does the mutilated checkerboard problem imply about how we think about problems involving INSIGHT?
How we think about a problem (the problem representation) is often of great importance in problem-solving. However, what happens with many problems is that we initially construct one or more problem representations. Eventually, we form the correct problem representation, which involves a sudden restructuring of the problem.
List 4 other differences between insight and non-insight related problems.
(note rmb there are actually 5 if you include their definitions!)
1) There is a progressive increase in “warmth” for non-insight problems, which is expected since they involve a sequence of processes. However, for insight problems, the warmth rating remained at the same low level until suddenly increasing dramatically just before the solution is reached.
2) Activation of anterior superior temporal gyrus only occurs when solutions involved insights
3) Insight is more associated with the right hemisphere than the left because integration of weakly active and distant associations occur mostly in the right hemisphere. These processing activities are very relevant for producing insight. In contrast, strong activation of closely connected associations occur mostly in the left hemisphere.
4) Working memory also seems to be more implicated in analytic rather than insight problems.
How did Bowden study how the right hemisphere plays an important role in insight?
Used remote associate problems.
Eg: Fence Card Master
You are to think of a word that can form a compound with these.
Ans: Fencepost, postcard, MasterCard.
Participants were then to indicate if their answers involved insight.
How did Bowden study how activation of anterior superior temporal gyrus occurred only when solutions involved insights?
Record ERPs.
- Found that there was a burst of high-frequency brain activity 1/3 of a second before the participants indicated that they have achieved an insightful solution
Brain activity was centered on the right anterior superior temporal gyrus. This area is vital to insight because it is involved in processing general semantic (meaning) relationships.
Working memory also seems to be more implicated in analytic rather than insight problems.
^ how was this studied?
Considered the effects of counting auditory stimuli, which involves working memory (phonological loop?), on various problems.
- Counting task impaired performance on analytic problems but not on insight ones.
- Fleck also found out that individual differences in working memory did predict performance in analytic problems but not insight ones.
What theory can explain the factors that facilitate insight? What does it propose?
Representational Change Theory
- A problem is represented in a certain way; this serves as a probe for information from LTM
- Retrieval process spreads activation across items in LTM (memory search)
- Block occurs if the way a problem is represented does NOT lead to successful memory search.
- Hence the SOLUTION is to represent the problem differently, which will extend the memory search.
What can be done to change the representation of your problem, and hence solve insight problems? (3)
1) Elaboration - adding new information
2) Constraint relaxation - rules are reinterpreted
3) Re-encoding - removing functional fixedness
Insight occurs when a block is broken.
What are 2 studies that were done to talk about the importance of constraint relaxation?
1) Bulbrook’s BEADS problem
2) Knoblich’s ROMAN NUMERALS problem
What did Bulbrook do in his study that talked about constraint relaxation? (How insight can involve relaxing
Presented participants with a string of beads. Most of the string consisted of 2 small white beads alternating with one larger yellow bead, except in the middle where there were 5 white beads together.
Task: To produce a regular patten without unstringing or restringing the beads.
To solve the problem, you have to use a pair of pliers provided to break some of the beads. However, even though pliers were readily available, 43% of the participants failed to solve the problem. Could not see that they can actually break the beads. There was no rule that said they cannot break the beads if you think about it.
What did Knoblich do in his roman numerals study?
Presented math problems involving Roman numerals. Each problem presented was incorrect, and the task was to move one stick to turn it into a true statement.
Our experience with equations often involve changing numerical values, but not changing operators. Insight of problems of this type would requires us to relax the normal constraints of artihmetic.
What happens when successive problems require the same or different kind of insight?
Same kind involved (eg constraint relaxation): facilitation
Different: Interference and slowing of solution times.