Problem Solving and Creative ThinkingDan Weijers

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1、Problem Solving and Creative ThinkingProblem SolvingWhat is a Problem?A problem arises when a living creature has a goal but does not know how this goal is to be reached. A problem exists whenever one cannot go from the given situation to the desired situation simply by action. K. Dunker, On Problem

2、 Solving, (1945) p. 1What is Problem Solving?Problem Solving is the process of working out or discovering how to reach such a goal.What is creative thinking?Creative thinking is the process of generating novel ideas and alternative courses of action, no matter how good those ideas and alternatives m

3、ight be.Creative thinking should not be seen as an alternative to critical thinkingWhen you have recognised a problem, then you should employ creative thinking to produce some options for solving the problem, then you should employ critical thinkingIf you havent come up with enough options to begin

4、with, then your critical thinking decision procedure might produce the wrong result a dangerous result!Creative Thinking, Critical Thinking, and Problem SolvingCreative thinking supports critical thinking While critical thinking focuses on step-by-step, linear processes aimed at arriving at a correc

5、t answer, creative thinking begins with possibility, multiple ideas, and suspended judgement. It might be said that creative thinking supports the ideas with which critical thinking works. Thus, even though these two kinds of thinking work in different ways, they actually support one another and aim

6、 at the same ultimate goal, which is to solve a problem At the beginning of the process, creative methods are used to examine the problem environment, generate ideas, and make associations. Then the analysis and judgment faculties are brought into play, and the possibilities are analyzed for a possi

7、ble solution. Robert Harris, CB pp. 115-6 Who is this man?ArchimedesGreat inventor, mathematician etc.The Screw The LeverArchimedesHelped protect Syracuse from the Romans in the siege of 213BCThe MirrorThe ClawArchimedes puzzleDid the smithy replace some of the kings gold with silver?How did Archime

8、des find out?(Not Archimedes style to torture the smithy)Solution to Archimedes puzzle. The solution, which occurred when he stepped into a public bath and caused it to overflow, was to put a weight of gold equal to the crown, and known to be pure, into a bowl which was filled with water to the brim

9、. Then the gold would be removed and the kings crown put in, in its place. An alloy of lighter silver would increase the bulk of the crown and cause the bowl to overflow. Vitruvius, De Architectura And the wreath was impure!Creative thinking! It was very useful to Archimedes He was well respected an

10、d treated in Syracuse Marcellus, the Roman general, ordered his life to be spared when Syracuse finally fell But his obsession with maths was ultimately his downfall! Can we be like Archimedes? Can we learn to be creative thinkers?4 Methods for Generating Ideas1. Associative Techniques2. Analytic Te

11、chniques3. Brainstorming4. Role PlayingAssociative Techniques1. Compare something familiar to something unfamiliar.a) Close analogy e.g. apples and pearsb) Remote analogy e.g. Pringlesc) Forced analogyForced Analogy 1 The problem: recreating that dazzling 360 degree panoramic holiday view The forced

12、 analogy: a wreath The answer!Forced Analogy 2 The problem: vertigo The forced analogy: swimming The answer!Forced Analogy 3 The problem: Carrying lots of shopping when its raining The forced analogy: a tennis player The answer!Analytic Techniques2.Breaking a problem down into smaller partsE.g. How

13、can I make the All Blacks win the Rugby World Cup?Vital components of the problem:Henry: Just one: ensuring the ABs perform to their capacity Hence the 4 Rs of Henrys regimeRestRotationRelationships within team are friendlyReally discreet signaling during matchesAnalytic TechniquesUnfortunately (as

14、we know), Henry didnt analyse the problem thoroughly.He missed a vital component of the problem:The Barnes Factor Analytic TechniquesGood analytic techniques will help to ensure that all of the important components of the problem are addressedBrainstorming3. Deliberately set about coming up with alt

15、ernatives, and write them all down, no matter what.No idea is a bad idea (at least just yet)Edward de Bono 6 hats green hat timeOne company generated 2,200 ideas in one day!Roleplaying4.Roleplaying. Attempt to simulate aspects of the problem and proposed solutions. Try to imagine details of the rele

16、vant outcomes after your choice has been made, and attempt to put yourself in the shoes of other people.A good method for gathering information and gaining perspectiveE.g. Theoretical vs. practical lecturingE.g. Customers-eye-view of displaysE.g. Hand-out-of-the-car-window aerodynamicsBut Archimedes

17、 was not just a creative thinker.He was also a prolific problem solverSo, how can we harness these 4 idea creation techniques to help us solve problems?Ideas should be generated after the problem has been properly understood and representedSolving real problems is a two step process:ProblemModelSolu

18、tionThe Main MessageIn order to generate potentially fruitful ideas, and thereby make it more likely that you solve your problem, make sure you represent the problem in the right way. C BAOne and only one of the switches (A, B & C) on the outside of the room turns on all of the lights (x, y & z) in

19、the roomFrom outside, you cannot see into the roomThe wiring is hidden from viewYou are not allowed to damage any of the propertyIs there a way of knowing for sure which switch turns the lights on?Once you enter the room, you cannot leave again to rearrange the switches x y zThe Lights ExampleSwitch

20、es:Possible arrangements: A11110000 B11001100 C10101010 1 on, 0 offThe Lights ExampleSolving real problems is a two step process:ProblemModelSolutionThe Main MessageIn order to generate potentially fruitful ideas, and thereby make it more likely that you solve your problem, make sure you represent t

21、he problem in the right way. The Bird-Train Problem (Posner, 1973)Station 1 and Station 2 are 50 miles apart on a straight train trackTrain 1 leaves Station 1 at the same time that Train 2 leaves Station 2Both trains travel at 25 miles per hour toward the other stationThe bird starts directly above

22、Train 1 and flies above the track until it reaches Train 2. Then it flies back to Train 1 etc.The bird flies at 230 miles per hourHow far has the bird flown by the time the trains meet?The Bird-Train Problem (Posner, 1973)Solving real problems is a two step process:ProblemModelSolutionThe Main Messa

23、geIn order to generate potentially fruitful ideas, and thereby make it more likely that you solve your problem, make sure you represent the problem in the right way. The Drop Block ProblemWhat will happen to the block of wood when the person lets go of it?The Drop Block ProblemThe block will drop do

24、wn as it is drawn to earth by gravity The Drop Block Problem so long as the person is on earth. The Drop Block ProblemIt will float up if the person is under water. The Drop Block ProblemAnd it will go nowhere (or a little bit sideways?!) if the person is in space. Solving real problems is a two ste

25、p process:ProblemModelSolutionThe Main MessageIn order to generate potentially fruitful ideas, and thereby make it more likely that you solve your problem, make sure you represent the problem in the right way. So, how can I best represent a problem?Suggestion 1: Drop presuppositions that arent expli

26、cit in the original statement of the problemThe Nine Dot Problem (Maier, 1931)Can you connect all of the dots with just 4 straight lines?You cannot take your pen off the paperYou cant use a ridiculously big penThe second line must start where the first line finished. The third line must start where

27、the second line finished etc.Imagine the dots are drawn on a flat an immovable surfaceThe solutionSolution to The Nine Dot Problem (Maier, 1931)How can I best represent a problem?Suggestion 1: Drop presuppositions that arent explicit in the original statement of the problem.A Terrible AccidentThere

28、was a terrible accident on the motorway coming into WellingtonA man was killed on impact and his son was rushed to hospital with life-threatening injuriesAt the hospital, the surgeon saw the boy and said: “I cant operate, thats my son”What is going on here?Many of us assume that surgeons have to be

29、male, making us come up with crazy answers for a simple questionHow can I best represent a problem?Suggestion 1: Drop presuppositions that arent explicit in the original statement of the problem.How can I best represent a problem?Suggestion 1: Drop presuppositions that arent explicit in the original

30、 statement of the problem.Suggestion 2: Make sure you represent everything explicit in the original statement of the problem. On a street somewhere:Ted: All three of my sons celebrate their birthday today. Canyou tell me how old each one is? (Ted is a bit weird)Fred: Yes, but you have to tell me som

31、ething about themTed: The product of their ages is 36.Fred: I need more infoTed: The sum of their ages is equal to the number of windowsin the building next to usFred: I need more infoTed: My oldest son has blue eyes.Fred: That is sufficient! Can Fred really know how old Teds sons are? How?2 old hig

32、h school math club pals meet up after many years2 old high school math club pals meet up after many yearsAge of the first son: xAge of the second son: yAge of the third son: zSafe assumption: x y z36 1 118 2 112 3 1 9 4 1 9 2 2 6 6 1 6 3 2 4 3 3“The product of their ages is 36”:x y z2 old high schoo

33、l math club pals meet up after many years36 + 1 + 1 = 3818 + 2 + 1 = 2112 + 3 + 1 = 16 9 + 4 + 1 = 14 9 + 2 + 2 = 13 6 + 6 + 1 = 13 6 + 3 + 2 = 11 4 + 3 + 3 = 10“The sum of their ages is equal to the number of windows in the building next to us”x y z2 old high school math club pals meet up after man

34、y yearsHow can I best represent a problem?Suggestion 2: Make sure you represent everything explicit in the original statement of the problem. There are five houses, each of a different color and inhabited by men of different nationalities, with one unique pet, drink, and car. Some facts are given:1.

35、 The Englishman lives in the red house.2. The Spaniard owns the dog.3. The man in the green house drinks cocoa.4. The Ukrainian drinks eggnog.5. The green house is immediately to the right (your right) of the ivory house.6. The owner of the Oldsmobile also owns snails.7. The owner of the Ford lives

36、in the yellow house.8. The man in the middle house drinks milk.9. The Norwegian lives in the first house on the left.10. The man who owns the Chevrolet lives in the house next to the house where the man owns a fox.11. The Ford owners house is next to the house where the horse is kept.12. The Mercede

37、s-Benz owner drinks orange juice.13. The Japanese drives a Volkswagen.14. The Norwegian lives next to the blue house.Who owns the Zebra?House12345ColorDrinkCountryCarPetHouse12345ColorblueDrinkmilkCountryNorwegianCarPet762455826938895126331993645 9842967762455826938895126331993645 98442967How can I

38、best represent a problem?Suggestion 2: Make sure you represent everything explicit in the original statement of the problem. How can I best represent a problem?Suggestion 1: Drop presuppositions that arent explicit in the original statement of the problem.Suggestion 2: Make sure you represent everyt

39、hing explicit in the original statement of the problem. Suggestion 3: When thinking about how you could represent a problem, look for structural similarities between this problem and one you know the answer to.Structural SimilaritiesSuggestion 3: When thinking about how you could represent a problem

40、, look for structural similarities between this problem and one you know the answer to.This certainly works with IQ tests and brainteasersBut also with (real life!) problem solving in generalRadiotherapy treatment for stomach cancer- A structurally similar dictator analogy helped 1% 20%- The analogy

41、 with an answer helped 1% 75%Why should solving logic puzzles be relevant or important to me?An ability to solve logic puzzles is thought to be positively correlated with an ability to think creatively and solve problems of any kind.Whether or not such a correlation really exist, it is commonly beli

42、eved to exist.Employers care more about creative thinking and problem solving abilities in the workforce more than any other general skill.Creative thinking and problem solving abilities are among the most important skills sought after by universities.Hence, universities and employers will screen ca

43、ndidates on the basis of their ability to solve logic puzzles.ACTUAL MICROSOFT INTERVIEW QUESTIONSInterview Questions with a Determinate Answer1.You have twenty blue socks, twenty brown socks, and two black sock in a drawer in your room. If it is night time, and the room is completely dark, how many

44、 would you have to take out to be sure you have 2 of the same colour? 2.A mother sent her child to the lake and told him to bring back exactly 7 litres of water. She gave him a 5 litre bucket and a 3 litre bucket. How can the child measure out exactly 7 litres of water using nothing but the two buck

45、ets.3.Youve got someone working for you for seven days and a gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay your worker?ACTUAL MICROSOF

46、T INTERVIEW QUESTIONSImpossible Interview QuestionsAn Impossible Interview Question is one that has no single acceptable answer.1.How many piano tuners are there in the world?2.How long would it take to move Mount Fuji?Strategy: Dont freak out!Dont give a joke answer (e.g. depends if we get Chuck No

47、rris to help)Suggest a potential approachAsk them questionsHow to solve problems creatively:Make sure you represent the problem in the right way!i.Dont assume restrictions that arent stipulatedii.Do represent everything explicit in the questioniii. Do compare the structure of the problem with similar onesThen generate lots of creative ideas with:i.Associative techniquesii.Analytic techniquesiii. Brainstormingiv. RoleplayingSummary