Problem Solving (exam3)

Obstacle between a present state and a goal where it is not immediately obvious how to get around the obstacle

Problem

Obstacles to Problem Solving Tendency to focus on a specific characteristic that keeps one from reaching the solution

fixedness

Tendency to use an object in its most familiar or common use

functional fixedness

Subgoals -A goal that solves part of a problem - Can be an efficient means of reaching a solution 1. ex

subgoal 1: free up large disc 2: free up 3rd peg 3: move large disk over

A goal that solves part of the problem

subgoals

Prob with creativity 1. Don't know what ___ processes involved, what are you doing in the mind -Can't just be asked "what did you do in your mind" idk it just popped into my head -WELL WHY DID IT POP INTO YOUR HEAD?? HOW???

underlying

Expertise and analogical reasoning How are these problems related? (Silver, 1981) (1) A farmer is counting the hens and rabbits in his barnyard. He counts a total of 50 heads and 140 feet. How many hens and how many rabbits does he have? (2) Bill has a collection of 20 coins that consists entirely of dimes and quarters. If the collection is worth $4.10, how many of each kind of coin are in the collection? (3) A farmer is counting the hens and rabbits in his barnyard. He counts six coops with four hens each, two coops with three hens each, five cages with six rabbits each, and three cages with four rabbits each. How many hens and rabbits does the farmer have? 1. 2 are related on deep relationship: __ and __ 2. surface relationship: __ and __ 3. experts are better at focusing on similarity on ____ LEVEL (strategy you need to utilize to solve the prob) 4. they would say 1 and 2 are most similar whereas novices would say 1 and 3 are most similar

1. 1 and 2 2. 1 and 3 3. deep

*Enhancing Creativity* Visual imagery (Finke, 1990) -Subjects were given a set of basic parts (think geons) -Instructed to close their eyes and imagine combining them to make *a practical object or device* Judgments based on practicality and originality Conditions: -Subjects selected parts but were assigned a category -Subjects given parts but could choose category -Subjects told what parts and what category *Which would result in the most creative output?* 1. which group did best? = constraints help creativity 2. what group did they find after that was actually the most successful in creative thinking (4th condition)?

1. 3rd group: given both parts and category 2. Subjects given parts but didn't find out the category until after they had assembled their objects (preinventive forms)

Strategies for Problem Solving 1. Heuristics: A strategy that is often helpful in solving a problem - Can fail Examples: Working backwards, means-end analysis, subgoals, etc. 1. __ : A procedure of steps that will solve a problem if followed correctly 2. IF you follow __, you will get to solution Example: Rules for multiplication 3. Prob: you may not know the ____...so you can't use them to get solution 4. ___ EASIEST BEC GETTING CLOSE TO A SOLUTION IS OFTEN GOOD ENOUGH IN THE REAL WORLD

1. alogrithm 2. correctly 3. rules 4. heuristics

3 Types of well defined problems 1. Some objects are presented and the problem solver must rearrange them in a way that satisfies come criterion a) ex. 2. A problem that requires finding a pattern among a fixed set of relations a) they are presented in arranged fashion already and you have to figure out the rule associated with the relationship 3. A problem that requires *changing the initial state* through a sequence of operations until it matches the goal state a) you have an initial and goal state and a set of rules for how to transform items to get from A to B (ex. math problems)

1. arrangement a) rubics cube 2. inducing structure 3. transformation

Goal: Place the candles at eye level on a door. Presented as either *empty box* 1. (more likely to see ohhh okay, the ___ can be used) or 2. *boxes with matches* (less likely to see box as a tool and instead __ on using the matches) 3. ex of?

1. box 2. fixate 3. fixedness

Transformation problems Modifying an initial state through a sequence of operations until the goal state is achieved Example: Five missionaries and five cannibals who have to cross a river find a boat. The boat is small and can hold no more than three people. If the cannibals on either bank of the river or in the boat are outnumbered at any time by missionaries, they will be corrupted. Find the simplest schedule of crossings that will allow everyone to cross safely. At least one person must be in the boat at each crossing. 1. ___ in how to manipulate to get where you wanna go 2. Use rules/operations 3. Primarily focusing on __ __ANALYSIS: what mechanism will get me closest to where I want to go 4. Trial and error with focus on connecting __ state with __ state

1. constrained 3. means end 4. goal; current

Well-defined 1. Have a ___ answer 2. Certain ___ will lead to a solution Ill-defined -No one "correct answer" -Path to the solution is unclear 3. ex

1. correct 2. procedures 3. baby picture "What do you want to be when grow up"? Can get to teacher in multiple routes

How Experts Solve Problems Experts: Individuals who are extremely knowledgeable or skilled in a particular field 1. __-__ knowledge - Knowledge about a particular subject 2. Solve problems ___ and at a higher rate of __ than beginners What might account for these differences?

1. domain-specific 2. faster; success

Impeding Creativity (impairing) *The effect of examples* Task: design new creatures to inhabit a planet; some shown examples 1. Compared to controls, ___ group less creative test 2: now given explicit instructions: "We showed you these examples in order to help you think about creating your own original creatures and to get your creative juices flowing. However, we do not want you to copy any aspect of the examples." Results 2. Effective ____ ONLY (didn't copy example) but led to inadvertent *plagiarism* when participants completed task a __ __ 3. o So the instructions can lead to "inadvertent plagiarism" bec not intending/realizing your copying when presented with __

1. example 2. immediately; day later 3. delay

Expertise and reasoning "If a letter is sealed, then it has a 50-lira stamp on it." (BRITISH POSTAL) 17 out of 24 correct; 0 of 24 in original abstract problem Why the improvement? -Better reasoning or Recall from memory? SO they gave it to american participants 2. U.S. subjects did poorly on both tasks - no ____ with British postal system 3. So these situations are best when you have prior ____ bec draw from ____ 4. So experts are better bec they can remember "I used the strategy last time nad it worked"

1. experience 3. experience; memory

Fixedness: Tendency to focus on a specific characteristic that keeps one from reaching the solution 1. keeps us thinking "__ the box" Moving sticks to get solution 2. People take longer to generate solution because they're looking at ___ and become fixed on how to do it 3. Very last one is most difficult bec did most manipulation outside of how we usually use ____—overcome fixedness(switch the sign from + to =) a) The hardest problem is the one that requires the change in ___ rather than changing the numeric values

1. inside 2. numerals 3. numbers a) sign

Transformation problems 1. Solutions require planning based on __ __analysis 2. Identifying what ____ exist between the current state and the goal state and selecting operations that will ___ these differences

1. means end 2. differences; reduce

Gestalt psychology 1. Representing the problem in mind a) utilize ___ conceptualization to solve 2. *Restructuring the problem* - changing its representation a) We rearrange the ideas in mind to lead to ___ (when you come upon the way to solve) b) Once you see you can construct the rectangle, you know r is the same length as x

1. mental 2. a) insight

Expertise and analogical reasoning - People often fail to spontaneously notice a useful analogy (remember the radiation and military problems?) 1. Expertise in particular subject matter increases ability to perceive how problems are ____, even when they have different content 2. Experts are better at understanding ____ STRUCTURE of a problem (what is the underlying method needed to solve) 3. Novices focus on the __ structure

1. related 2. deep 3. surface

Arrangement Problems 1. Objects must be arranged to ___ a specific criterion 2. Typically solved using __ and __ 3. Partial solutions are formed and evaluated Example: 4. ___ - form a word from a string of letters KEROJ RWAET

1. satisfy 2. trial and error 3. anagrams

Analogies: Solving a problem by using a solution to a related problem 1. *Success requires recognizing ___ and recalling the solution of the analogous problem* Radiation problem Group 1: presented w/this prob and asked to generate solution Group 2: also given an additional problem (attack dispersion story): Solution aid -The solution to the 2nd problem helps to find solution to 1st problem 2. REsults: Participants were not good at making the connection between the two problems unless a ___ was given

1. similarities 2. hint

Expertise and analogical reasoning All subjects were asked to categorize 'mathematically related' problems (Silver, 1981) 1. Good problem solvers grouped based on __ 2. Poor problem solvers based on __ Similar results for Chi et al. (1982) with physics problems 3. ___ categorized by *objects,* like spring problems or inclined-plane problems (surface features) 4. __ categorized on basis of physics *principles* needed to solve them (deep structure) a) better able TO ACCESS WHAT ASPECTS OF PROB ARE IMPT IN FINDING WHAT STRATEGY TO USE

1. structure 2. content 3. novices 4. experts

Creativity: Solutions that are not only correct, but also novel and useful 1. Is creativity a fx of the process or the end point? a) Weisberg: "The myth of genius" says... a) WE JUST CARE THAT THE RESULT IS NOVEL AND WORKS WELL 2. Nobody comes up with something completely novel, yours just appear to be more creative bec it's not obvious where it came from 3. More creative output: show differences in process (expertise, highly motivated to come up w solution)

1. the end point

*Experts spend more time analyzing problems:* 1. Often have a *Slow start* on a problem because they spend time trying to ___ the problem rather than immediately trying to solve it 2. However, experts are better problem-solvers in their *___ only* AND they are *less open to ___ ways of looking at problems* 3. Being an expert might be a disadvantage when a problem requires ___ thinking a) less __ problem solvers

1. understand 2. field; new 3. flexible a) creative

4 card prob Expertise and reasoning - Only 5 of 128 subjects correctly selected the D and 7 cards - most picked D and 3 (Watson & Shapiro,1971) 1. People make mistakes because they seek information that would ___ the rule rather than information that would ___ it -Would using more realistic materials related to everyday knowledge make the task easier? 2. what might facilitate experts being better at solving this?

1. verify> falsify 2. memory

Gestalt psychology -Insight - sudden discovery of a solution *Should people be able to report how near they are to a solution?* Experimental evidence: -Subjects were given insight problems (like the triangle) or noninsight problems (algebra) 1. Non-insight problems require steady __ toward a solution *All subjects were asked to indicated how close they were to the solution (1= cold; 7 = hot) whenever a tone sounded* Results 2. Insight problems: ratings of warmth were low until 3. Non-insight problems: ratings __ warmer as closer to goal. 4. supports the idea that we can come to insight using trial and error

2. just before solution found. 3. gradually

Expertise and reasoning 1. A task that has ___ or __ content can be very difficult, compared with the same task with familiar content

abstract; unfamiliar

Solving a problem by using a solution to a related problem

analogies

2 strings, put can't hold onto both at same time -have to put pliaras on one end to weigh it down to swing it to grab other string 1. FX FIXEDNESS: only thought you could use the pillars to ___ something instead of another use (as a weight)

cut

Must discover the relations among the parts of the problem

inducing structure

overcoming functional fixedness One way to overcome: _____: if a I need to get something I want but don't have it, I'm more motivated to find another way (think outside)

necessity

Gestalt psychology 1. ___ leads to* insight* - sudden realization of a problem's solution The triangle points to the top. How can you move only 3 dots to make it point to the bottom?

restructuring

What is a Problem? WHAT ARE THESE AN EX OF 1. Example: ___ extrapolation or ___ -Determine which element comes next 1 2 8 3 4 6 5 6 .... A B M C D M .... • Whats the pattern? There is a fixed relationship 3rd number is going down by 2, so next number would be 4? EFN next

series; analogies inducing structure