What do we have so far Basic biology of the nervous system Motivations Senses

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McEvoy, Aoife, Contributing Editor has reference to this Academic Journal, PHwiki organized this Journal What do we have so far Basic biology of the nervous system Motivations Senses Learning Perception Memory Thinking in addition to mental representations What do we have so far All of these topics give a basic sense of the structure in addition to operation of our mind What kinds of tasks does our mind engage in Language Problem Solving Decision Making Others Problem Solving: Definition A problem exists when you want to get from here (a knowledge state) to there (another knowledge state) in addition to the path is not immediately obvious.

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What are problems Everyday experiences How to get to the airport How to study as long as a quiz, complete a paper, in addition to finish a lab be as long as e recitation Domain specific problems Physics or math problems Puzzles/games Crossword, anagrams, chess A Partial Problem Typology Well-defined vs. ill-defined problems: Problems where the goal or solution is recognizable-where there is a right answer (ex. a math or physics problem) vs. problems where there is no “right” answer but a range of more or less acceptable answers. Knowledge rich vs. knowledge lean problems: problems whose solution depends on specialized knowledge. Insight vs. non-insight problems-those solved “all of a sudden” vs. those solved more incrementally-in a step by step fashion. Contents of Memory Does the contents of memory influence how easy a problem is Knowledge rich problems Require domain knowledge to answer, physics problems Knowledge lean problems Can use a general problem solving method to solve, dont need a lot of domain knowledge

Some Problem Examples Tower of Hanoi Weighing problem Traveling salesman (100 cities = 100! or 10200 or each electron, 109 operations per sec. would take 1011 years!!) but 100,000 cities within 1% in 2 days via heuristic breakup (reduce search!) Missionaries & Cannibals Flashlight: 1, 2, 5, 10 min. walkers to cross bridge 21 link gold necklace/21 day stay Subway Problem Vases (or 3-door)

Early findings Zeigarnik effect, 1927 Participants were given a set of problems to solve On some problems, they were interrupted be as long as e they could finish the problem Participants were given a surprise recall test They remembered many more of the interrupted problems than the uninterrupted ones Moss et al. (2007) recent RAT results: open goals

Early Findings: Prob. Solv Set Luchins water jug experiment, 1942 Participants were given a series of water jug problems Example: You have three jugs, A holds 21 quarts, B holds 127, C holds 3. Your job is to obtain exactly 100 quarts from a well Solution is B  A  2C Participants solved a series of these problems all having the same solution Early Findings: P.S. Set Luchins water jug experiment, 1942 New problem: Given 23, 49, in addition to 3 quart jugs. Goal is to get 20 quarts. Given 28, 76, in addition to 3 quart jugs, obtain 25 quarts Some failed to solve, others took a very long time Mental set People who solved series of problems using one method tended to over apply that method to new similar appearing problems Even when other methods were easier or where the learned method no longer could solve the problem Prob. A B C Goal 1 21 127 3 100 2 14 163 25 99 3 18 43 10 5 4 9 42 6 21 5 20 59 4 31 6 23 49 3 20 7 15 39 3 18 8 28 76 3 25 9 8 48 4 22 10 14 36 8 6

Early Findings:Functional Fixedness Dunckers c in addition to le problem, 1945 Problem: Find a way to fix a c in addition to le to the wall in addition to light it without wax dripping on the floor. Given: C in addition to le, matches, in addition to a bow of thumbtacks Solution: Empty the box, tack it to the wall, place c in addition to le on box Have to think of the box as something other than a container People found the problem easier to solve if the box was empty with the tacks given separately Early Findings:Funct. Fixedness Dunckers c in addition to le problem Maiers two-string problem 1930

Functional Fixdness: Conclusion Functional Fixedness Inability to realize that something familiar as long as a particular use may also be used as long as new functions But is this really a bad thing We learn in addition to generalize from our experience in order to be more efficient in most cases Is it really a good idea to sit around trying to figure out how many potential uses a pair of pliers has How often do mental sets in addition to functional fixedness save time in addition to computation General Problem Characteristics What characteristics do all problems share Start with an initial situation Want to end up in some kind of goal situation There are ways to trans as long as m the current situation into the goal situation Can we have a general theory of problem solving General Theory of Problem Solving Newell & Simon proposed a general theory in 1972 in their book Human Problem Solving They studied a number of problem solving tasks Proving logic theorems Chess Cryptarithmetic DONALD D=5 + GERALD ROBERT

General Theory of Problem Solving Verbal Protocols Record people as they think aloud during a problem solving task Computational simulation Write computer programs that simulate how people are doing the task Yields detailed theories of task per as long as mance that make specific predictions General Theory of Problem Solving Problem spaces Initial state Goal state(s) Operators that trans as long as m one state into another An Example Tower of Hanoi Given a puzzle with three pegs in addition to three discs Discs start on Peg 1 as shown below, in addition to your goal is to move them all to peg 3 You can only move one at a time You can never place a larger disc on a smaller disc

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Another ex.: Detour Problems Missionaries in addition to cannibals problem Six travelers must cross a river in one boat Only two people can fit in the boat at a time Three of them are missionaries in addition to three are cannibals The number of cannibals on either shore of the river can not exceed the number of missionaries Problem Space

Operators How do we choose which operators to apply given the current state of the problem Algorithm Series of steps that guarantee an answer within a certain amount of time Heuristic General rule of thumb that usually leads to a solution Algorithm Examples Columnar algorithm as long as addition Add the ones column Carry if necessary Add the next column, etc. People dont have a simple algorithm as long as solving most problems 4 6 2 + 2 3 4 8 5 Common Heuristics Weak Methods Hill climbing Just use the operator which moves you closer to the goal no matter what What about problems where you have to first move away from the goal in order to get to it (detour problems) Fractionation in addition to Subgoaling Break the problem into a series or hierarchy of smaller problems

Conclusions Problem solving is an everyday activity We can use findings from problem solving to further our underst in addition to ing of the mind in addition to its processes We can use our knowledge of the minds structure in addition to operation to underst in addition to elements of problem solving Different types of problems in addition to different contributions to problem difficulty

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