Greg Francis 5/27/081Problem solvingIIE 269: Cognitive PsychologyGreg FrancisLecture 35What does that “aha” feeling mean?Problem solving A hallmark of intelligence often used as a definition of intelligence Seem to get something from nothing We will not explain exactly how it happens but we can look at some characteristics ofproblems and problem solving» what makes for an easy (or hard) problem?» what makes for a good (or bad) problemsolver?Topics We will look at a number of factorsthat influence our ability to solveproblems expertise analogy set effects» priming» incubation» functional fixedness insightExperts Some people learn how to solve particulartypes of problems What makes an expert different from anovice? Experts know how to describe problems other than that, there seems to be nofundamental difference (even for geniuses!)An example of experts Take second year physics students(novices) and ask them to classify a bunchof physics problems they tend to group them by surface similaritiesAn example of experts Have experts (PhDs) classify the sameproblems grouped according to how to solveGreg Francis 5/27/082Chess experts Show subjects a chess board and then clear it have subjects recall positions of the chess pieces on theboard Experts do much better than novices but only when the arrangement of pieces on the boardmade sense in an actual game random arrangements were poorly recalled by bothexperts and novicesExpert schemas In general, experts have lots of problemsolving schemas specific to their domain ofexpertise given such and such; do such and such allows them to organize information in a way thatallows for easy recall and easy use Expertise in one domain does not transfer toanother except for especially useful skillsAnalogy: Attack-Dispersion Story The many roads to a dictator’s fortress aremined so that small groups of men maypass, but a large group will be destroyed. Ageneral knows that his army can defeat thefortress if he can get his entire army toattack at once, but he cannot take his armydown a single road all at once without losingtoo many men. What should he do?Solution The general should split up his army intomany smaller units each unit takes a separate road to converge onthe fortress simultaneously and defeat thedictatorfortressAnalogy: Parade-dispersion A dictator wants to show off his army so hetells a general to plan a parade of the army. Hedemands that the general insure that the armyis seen and heard across the entire kingdomsimultaneously. The dictator also demands thatthe parade be the most impressive ever at thefortress. Splitting up the army would allow it tobe seen everywhere, but would make thedisplay at the fortress unimpressive. What should the general do?Analogy The solution is the same split up the army and have them converge tothe fortress from different parts of the kingdom Glick & Holyoak (1980) subjects read stories like these and wereasked to solve the problems even when shown one solution and told that itcould be applied by analogy to another subjects used analogies only 20% of the timeGreg Francis 5/27/083Analogy Analogies are actually very difficult to apply need to identify what is common between twoproblems Analogies are often applied after twoproblems are solved and well understood it is then easier to see what is common One of the problems handed out can besolved by analogy to these two problemsSet effects “Set” refers to “mind set” (or something likethat) negative set: bias toward solving a problem makesit more difficult positive set: bias toward solving a problem makesit easier You can be biased by lots of things problem statement previous methods of reaching solution general knowledgePast experience Buddhist monk problem One morning, exactly at sunrise, a Buddhist monk began toclimb a tall mountain. The narrow path, no more than a footor two wide, spiraled around the mountain to a glitteringtemple at the summit. The monk ascended the path with anaverage speed of 3 mph. He reached the temple shortlybefore sunset. After several days of fasting and meditationhe began his journey back along the same path, starting atsunrise and walking an average speed of 5 mph. Is there aspot along the path that the monk occupied on both trips atprecisely the same time of day?Self-imposed limits Nine dots problem Draw four straight lines, passing through all nineof these dots, without lifting your pencil from thepage.Set effects: Representation Mutilated chessboard 62 squares remain can 31 dominoes cover them? Easy solution!Set effects: Priming Safren (1962) Unscramble the following anagrams 12.2 seconds per word7.4 seconds per wordKOBO CTURK STTECHUOC ANCYD DRINEFKMLI GRAUS RECMAFOEFCE TEESW IKRDNGreg Francis 5/27/084Set effects: Incubation Cheap necklace problem Opening a link costs $2 Closing a link costs $3 Go from given to goal state for no more than $15Set effects: Incubation Silveira (1971) Control: Work on problem for half an hour 55% solve problem Exp A: Work on problem for half an hour in15 minute sections, half-hour distracter task 64% solve problem Exp B: Work on problem for half an hour in15 minute sections, 4 hour distracter task 85% solve problemSet effects: Incubation Subjects often get stuck using an approachthat goes nowhere (set) After a break they are more likely to try adifferent approach Brainstorming tries to avoid set effects byallowing free “dreaming” of solutions most of the ideas are worthless, but the approachis still beneficialSet effects: Functional fixedness How can you tie two strings together? Dunker (1945) “MacGyver”Insight Intuitively, we sometimes feel as if we have astrong insight into a problem and its solutionbecomes obvious the “aha” feeling is it real? what does it correspond to? Using problems like the “Bronze coin” andthe “Tree planting” problems subjects judge their progress with a “warmth”ratingInsight Warmth stays mostly steady, right up toproposing a solution the “aha” feeling02468101230 20 10 0Time before giving solution (sec)WarmthCorrectIncorrectUnfortunately,the feeling doesnot indicate acorrect solutionGreg Francis 5/27/085Conclusions Effects on problem solving Expertise Analogy