Loading
Notes
Study Reminders
Support
Text Version

Problem Solving Approaches

Set your study reminders

We will email you at these times to remind you to study.
  • Monday

    -

    7am

    +

    Tuesday

    -

    7am

    +

    Wednesday

    -

    7am

    +

    Thursday

    -

    7am

    +

    Friday

    -

    7am

    +

    Saturday

    -

    7am

    +

    Sunday

    -

    7am

    +

Problem Solving Approaches
Hello and welcome to Introduction to Cognitive Processes, I am Ark Verma and in this weekof the course, we are talking about Problem Solving.So, in the last lecture I talked to you a little bit about particular strategies ofsolving problems, heuristics and algorithms ah in today's lecture we will move slightlyfurther and, look up at some traditional approaches ah to problems when you talk about researchfrom the gestalt approach and will talk about research from the information processing approachnow the gestalt approach.If you remember in history of psychology, if you have taken a course in psychology earlierah the gestalt psychologists like Wolfgang Kohler Koffka and those kind of people, ahthey basically believed in a particular theory and the theory could be just summed up inone of the things, in one of the statements and the statement was like the whole is morethan the sum of it is parts.So, the idea is you have to look at the holistic picture and, the holistic picture ah givesyou much more information things put together give you much more information, then theyare tiny bits you know independently or separately.Now ah the gestalt psychologists were not only interested in perception, but they alsodid a lot of work in areas like learning and memory in problem solving, ah they also wereinterested in ah working about attitudes and beliefs and so, on and so forth.So, ah today we will just ah talk a little bit about their contribution towards problemsolving research.Now the gestalt approach to problem solving, basically ah emphasizes on two things, itemphasizes on the fact that how are you representing the problem in your head, ah if you have tobegin solving a problem, you have to figure out a way of representing the problem in yourhead correctly, remember we have talked about this a little bit in the first lecture onproblem solving and, today we will just try and do some more demonstrations ah that isah basically going to you know help you see the importance of representations.ah Also ah the gestalt psychologists believethat solving a problem ah would involve a degree of reorganization, or restructuringthis representation, it is not like that you can build a very inflexible and immovablerepresentation of a problem and you are going to solve it 100 percent time.A lot of times ah you will be required to change your representation, you will be requiredto repre ah restructure your representation, ah in order to be able to solve the problemyou know it is it is more like you have to look at the problem from different characterand you know from different angles, ah or you have to know you know shuffle the problemaround ah put it in such a way that makes it easier for you to solve the problem.So, these are the two ah major aspects that kind of in some sense summarize or highlightthe gestalt approach to ah solving problems, let us see ah how it really works.So, the first thing is representing the problem in mind.Now solving a problem the gestalt psychologists believed that solving a problem is very ahclosely influenced, by how it is represented in the persons mind, how you are looking atthe problem well ah you know almost there define in some sense, how you are going tosolve that particular problem.And we can just demonstrate this by a very simple example and, this example was a problemposed by Wolfgang Kohler back in 1929.Now, this is the problem and you can look at this figure the figure is borrowed fromGoldstein's book, ah but you can look at this circle here, you are seeing that there isyou know triangle there the line the ah the diagonal of the triangle is ah called thehypotenuse of the triangle is called x.And then ah what has been asked is if the length of the circles radius is r ah whatis the length of the line x, what do you have to tell is you have to tell the ah you knowlength of line x ah and you have to compute it.So, one of the ways to represent this problem is that a circle with the vertical and horizontallines, that divide the circle into four quadrants, with a small triangle in the upper left quadrant.So, with a small triangle in the upper left quad this is how you can verbally describeit.Now is this definition is this ah statement of the problem ah going to be very helpfulah for you to solve this problem, you can just use this problem slide, you can go backto this ah statement and, let us try and figure out whether it is helpful whether you canyou know solve this problem in such a way, after you spend a couple of minutes, afteryou spend a couple of minutes dealing with the problem in such a way.ah What you can also do is you can change thelast aspect of the problem and, instead of a triangle you could just say that a smallrectangle in the upper left quadrant is there and, the diagonal of the triangle is x, whichis running between the two corners ah look at this triangle as ah basically a rectanglethat is having the quadrant ah as ah two sides the boundaries of the coordinate has two sides.So, once you realize that this diagonal is actually the radius of the circle and, thatboth diagonals of the you know trying of the rectangle are of same length, you can veryeasily conclude that the length of x is actually going to be equal to the length of r.So, very easy ah to solve this particular problem, just by restructuring the way youwere looking at the problem.So, the important aspect here is the solution could just be arrived at very quickly, byfirst perceiving the object ah completely and, then representing it in a slightly differentway, this is what is referred to as restructuring.So, we talked about the representation part and this is how the restructuring of thatrepresentation ah would lead you to ah ah effective and a quick solution.So, this is the solution, if you wanted ah graphic aid this is how you look at it andyou see that r and x are exactly equal to each other.Another important concept in the gestalt theory of ah solving problems in this aspect of insight,now the gestalts believed that sudden realization of a problem, you know there are a lot oftimes people have a sudden realization of a problems solution, ah they assume that peoplesolving ah you know particular problems, were sometimes experiencing insight, because thesolution seems to come to them all for sudden.So, they will be thinking thinking thinking thinking and suddenly all of a sudden they,will just say that ok now the solution is there.So, there is no gradation you know there is no we are talking about the initial stateand the goal state in the last lecture, there is no progression from an initial to the goalstate here, if suddenly that you are at the initial stage and one minute passes and youare at the goal state, without this proper methodological planning.This is also referred this has also been referred to as the ah moment, or the ah experiencethat suddenly you get a solution of a particular problem.Now Metcalfe and Wiebe basically, they did this ah research they wanted to differentiatebetween insight problems where, the solution will come up you know almost instantly andthere is no proper method towards the thing and a non insight problem.And their basic assumption their starting point of their experiment was that there shouldbe a basic difference in how participants feel, when they are working on an insightproblem versus when they are working on an non insight problem.So, what they did was they predicted that participants working on an insight problem,in which the answer is supposed to appear suddenly, should not really be very good atpredicting how near to a solution they are.On the other hand participants working on an non insight problem which involves a moremethodological process, a methodical process ah would be more likely to know that wheneveryou know to know how far or how closer to the final solution they are.So, this is ah what the two kinds of groups are and this is what they are you know assumptionis.So, they tested this hypothesis they wanted to test this hypothesis by giving participantsinsight problems, I will just show you ah the examples and non insight problems.And while these people were working on these insight problems, ah they were asked to makewarmth judgments.So, warmth judgment is like the closer you are to a solution the higher your warmth ratingwill be.So, if you are very close to a solution, your ah you know your warmth rating on a 1 to 7scale could be 6 or 7 even ah when you are far from the solution your warmth readingwould be somewhere between 1 2 and 3 and something like that.So, while they were working on ah solution and, they were supposed to you know give thisah judgment of warmth every 15 seconds and, this is what they ah what the task was now.Let us go to the problems ah 2 of the insight problems are presented here, you can lookat these figures ah again borrowed from Goldstein's book, ah you can see there is in the figurea there is a triangle problem and, ah the triangle problem basically says that in thefewest steps possible ah so, the idea is basically that show how you can you know move the threeof the circles to get the triangle to ah point to the bottom of the page, you can look atthe triangle triangle is pointing towards the top of the page, you just have the choiceof ah moving 3 ah of the triangle 3 of the circles that constitute the triangle and youmove these three circles in such a way that the triangle starts pointing to the bottom.That is one the other problem is the chain problem.So, there is a woman who has four pieces of chains ah each chain, has 3 you know linksand the the thing is that she wants to join these pieces, in a single ah you know chainin a single closed loop of chain.Now what what the problem here is that to open a link ah is going to cost 2 cents, andto close a link is going to cost 3 cents.She has only 15 ah 15 cents and how is she supposed to achieve this in just 15 cents.Now, these are the two insight problems you have to kind of think over them think, orthan think over there and it is highly probable that suddenly you will just get the solutionin one set, there is no ah step by step hierarchical ah approach to solving these problems, youcan kind of pause this and you know attempt to solve ah these things.For the non insight problems they just picked up high school algebra problems.So, problems like say 1 by 5 of x plus 10 is equal to 25 and you have to solve for xagain very straight forward, but there are steps in there you know you can move fromah 1 step to the next step to the next step and 2 or 3 or 4 steps would actually leadyou to the final solution.So, the results of their experiments indicated that the median warmth rating for all of theparticipants during the just you know during the minute, just before the solution is there.So, they kind of showed this and, ah for the insight problems it was ah observed that thewarmth ratings remain ah at a very low 2 or 3, until just before the problem is solved.Notice that I will show you the results very quickly notice that just 15 ah seconds belowthe solution the median rating is very cold it is a relatively cold it is around 2 or3, in contrast for the in contrast for the algebra problems the rating is increasinggradually.So, this is these are the results you can just see here, ah the red line is the insightproblem and the dotted line is the algebraic problem, you can see here, that the you knowthe change from ah minus 15 to when the solution is achieved is a rather steep in case of theinside problem, but it is a relatively gradual relatively step by step in case of algebraicproblems.So, this demonstration basically ah you know it tells us something about the differencebetween what in how insight versus non insight problems are achieved are solved.Moving on the gestalt psychologists believed that restructuring was usually involved insolving insight problem.So, they said that if you have to ah you know solve an insight problem, you have to do alot of shuffling of their representation, you have to do a lot of restructuring.So, they kind of started to focus on devising these kind of problems their strategy wasto devise a such kind of problems and situations and make it difficult for people to achievethe restructuring that is needed.So, that they are kind of ah it is not methodologically possible to do it and, they are kind of onlyinsight ah solvable problems.And they hope to ah investigate how people are solving these problems and by investigatingthat, they hope to learn about the processes that are involved in problem solving, andby the kind of obstacles that you know come when people are trying to solve problems.So, here again there is a solution to the triangle problem, you can see that this 23 dots three circles have been moved ah and, you can already ah see that there is a trianglestarts pointing to the bottom of the page.This is ah one of the solutions the other solution is here, ah again you just have toah use 15 cents ah and, you can just need to open three links and close ah three linksto basically be able to achieve this.So, 3 3 is 9 ah in the closing part is 3 2s a 6 and 9 plus 6 is 15.So, you are kind of doing it in just 15 moves 15 cents.So, ah this is the kind of obstacles I was talking about.So, the kind of obstacles ah that you know come up that kind of ah are present, whenpeople are solving problems ah are ah and, then there is a variety of obstacles thatare there, but one of the very common obstacle one of the very common problems you will ahsee in people, who are very ah you know they are not very good at solving problems is thatah of a fixation and fixation basically is somebodys tendency is peoples tendency tofocus on a specific characteristic of the problem that keeps them from arriving at.Suppose for example, you are basically just fixed at one kind of way, or one method ofsolving a particular problem, you are not very open you are not really willing to restructurethe probably not we ah really willing to think in more innovative ways and, then it is highlyprobable that you will be stuck with the same problem for a long time ok. ah On the contrary,if you are reflexible if you are open to looking at ah the problem from different perspectives,you might be able to reach the solution ah in a much more faster way.So, and a demonstration is due so the the if you remember the very old candle problem.So, ah this candle problem was first proposed by Karl Duncker in 1945 and the candle problemserves as a demonstration of how functional fixedness, or how fix in a fixation to a particularway of doing things can hamper somebody's problem solving abilities.ah Just to give you a cue, ah if you remember,there is a candle, there is a matchbox and, there are these pins tacks, ah as you maycall it.And the ah problem is basically to be able to you know fix the candle to the wall insuch a way that no ah wax falls on the ground.So, this is basically the problem statement and these are the three kinds of materialsthat are given.So, what dunker did was they he did this experiment with two groups of people two groups of participants,one group was presented with a small cardboard box containing the materials candle stacksand matches and the other group was presented with the same materials, but outside the boxeseverything was outside and the boxes were empty.So, what they found was ah when they compared the performance of the two groups, they foundthat the first group found solving this problem in a much more difficult than the second group.Now how is it happening what is the problem here, why is first row finding it more difficult.If you just look back at this thing ah and I am sure a lot of you would have come acrossthis problem and a lot of you know the solution already, the idea is that you just attachthe empty part of the box ah to the wall using the text and, this keep the candle in thematch box.So, that whenever even when the wax is melting, it just falls within the box that is prettymuch what the ah solution of the problem is, but the first group are basically ah not beingable to see this extra use of the match box, they are just ah thinking that match box isused to contain and matchbox cannot be you know stuck to the wall.So, this functional fixedness this fixation ah with using the box in only one particularway, is actually hampering their approach to solving this problem.Adamson in 1952 ah repeated the same repeated Duncan's experiment and you also got the sameresult, participants who were presented with empty boxes, were twice as likely to solvethe problem as compared to participants, were presented with boxes as containers because,boxes as containers is kind of priming and you know ah reaffirming the fact that boxescan only be used as containers and, cannot be used to attach to the wall.So, this is this is just a demonstration of how people think in very fixed very inflexibleways to approach problems and, sometimes kind of you know they are far worse for it.There could be another demonstration of the same ah concept and this demonstration comesfrom Maier's ah to string problem and the problem is ah is this.So, there are 2 strings attached to the ceiling and, ah there is a chair and there is a pairof pliers and, the idea is that the person has to tie these 2 strings together.The strings are created such that it is very difficult to be able to hold two of them together.So, how would somebody solve it, this is difficult ah and you know it basically required somesort of innovative thinking to solve this, I am just pausing here for a minute you canactually reason out how to do it.Moving on let us say solve this problem, the participants would need to actually what theyah needed to is to tie the plier to one of the strings and this create a pendulum andjust remove the string, when one of the string moves the participants could already be holdingone of the other strings and just link it using the pliers.So, the idea is you can just you know when these strings are moving towards each other,they are going to cover a lot of distance and, then they can come close to each other.Where you can actually tie them, two important things happened in this experiment 60 percentof the participants could not solve the problem because they focus on the usual function ofthe pliers and, did not think of using the pliers as weight, using which the stringscould be swung.When Maier said the string into motion accidentally you know just to give them a clue 23 out ofthe 37 participant who had not really solved the problems after even 10 minutes is us,proceeded to solve it within 60 seconds as soon as the clue was there, they saw thatok the strings could move and when they move they could come closer to each other, theycould actually solve this.So, in gestalt terms what is happening the solutions of the problems are occurring, whenthe participants are restructuring their representation of the problem and of also how to achievethe solution.Both the problems discuss were discussed because of peoples were basically difficult because,of peoples preconceptions.Their mental sets you know a preconceived notion about how to approach solving a problem,that is determined by a persons previous experiences.If your previous experiences are kind of you know in some sense making you very inflexibleah unable to you know look at different possible options, then there is a high chance thatyour problem solving strategy will be less effective more time consuming ah giving chanceof more errors etcetera.The gestalt psychologists were pioneers of problems research between 1920s and 50s, theydescribed a lot of problem ah problems and solutions and the kind of illustrated howmental states can influence problem solving and, how creating of new representations,or restructuring you know the given representations can contribute to getting solutions.Let us move on to a different approach now, ah the information processing ah you knowah approach the information processing paradigm, started ah long back around 1956 when AlanNewell and Herbert ah Simon, they described their logic theorist program.So, the logic theorist was basically a computer program which was designed to simulate humanproblem solving, this basically marked the beginning of a research program, that basicallythought that you know ah that problems could be solved using search mechanisms, you knowand it is not really unnatural to think of you know solving a problem as a search mechanism,we all the time we are using words like I am searching for a solution, or I am hittingthe dead end in my search for a solution.So, people generally do talk about it.So, what Alan Newell Herbert Simon did was this they conceived of ah solving a problemas searching for a solution and, in that sense they basically ah devised a way of lookingat how a problem has to be solved, in terms of an initial state I have been talking aboutthis ah again and again, an initial state which is conditions at the beginning of theproblem and, goal state that is the eventual solution of the problem.Now we will talk about this initial in goal state using the tower of the Hanoi problem.ah And if you know this is what the tower ofHanoi problem is there are 3 ah you know poles and one of the poles ah pole 1 has three pegsah arranged in ascending order of size and, the goal state is basically that you haveto move ah the pegs to the last pole to the last pillar using ah particular rules.And the rules are specified lists are to be moved one at a time from one back to anothera disk can be moved only, when there are no disks on top of it, and a larger disk cannever be placed or a smaller disk.So, this is the initial state is here, the goal state is here, the rules are definedand, now what you have to do is you have to move from the initial state to the goal stateusing these particular steps and, keeping in mind the following rules.Now this tower of Hanoi problem basically, ah you know was conceived by Alan Newell andHerbert Simon as ah you know a sequence of steps.So, the idea is that there is an initial sate and there is a goal state and, there haveto be a lot of intermediate steps and states.So, each step you take you end into an intermediate state and, then you know you are what youare doing is eventually, ah if you remember the means and heuristics eventually ah eachof these steps will take you closer to the goal state.So, the problem starts with initial states and you have to make these steps.Now the various states the intermediate states, here can be referred to as the problem space,I will just show you the problem space in a bit, ah this is what the problem space lookslike.These are all the possible initial states built together and what you have to do isyou have to start from 1 reach 8, which is a solution and just note ah a lot of timespeople would not have ah visualized all of the problem space.So, basically what they are doing is they are kind of moving ah in a sort of a definedah problem space, which by the way they are not really aware of what, they have to dois it is like almost moving in the dark moving from the initial to the goal state by takingsome intermediate steps.So, given all of the possible ways to reach the goal what the task of the problem solveris to figure out which moves to make and choose the correct sequence of steps.Because that is what is going to ah take them to the goal state in the shortest amount oftime, now according to Newell and Simon or the person has to do is the person has tosearch the problem space for a solution, what are the different possibilities that can beah ah considered what are the different moves I can make which of these moves will makethe distance ah ah lesser which of the moves will take me further from the solution whichof the moves will take me closer to the solution.Now how is the person how is the problem solver suppose to do it, the problem solver accordingto Newell and Simon, does what is called means ends analysis it is very similar to the meansand we have been talking about in the earlier lecture.So, what the problem solver does is it does a means ends analysis, that is it kind offigures out and you know figures out a way and the primary goal of this analysis is ahto be able to reduce the distance between the initial and the goal states.So, the idea is ah how how is this person going to do it, the person will again createsub goals or intermediate states and, he has to move from one intermediate stage to theother intermediate state, ah all the way ah towards the goal state and, the distance isah being reduced.So, you can see here.So, the participant basically has to move from 1 to 2 to 3 to 4 to 5 and, then towards9 and towards eight which is the final state.There could be ah different kinds of sub goals that people can actually make suppose andjust kind of borrowing and to demonstrate this.So, the sub goal one could be you know you have to first free up the largest.So, can you can move it to the big 3.So, the largest has to be moved first and, then you can just basically do it by you know,if you just look at here the idea is you have to first free the large disk.So, what you can do is you move ah one of the disks to you know you move the smallestdisk to peg 2, then ah you know you kind of move it ah further.So, that the large disk is free to move to the last peg.So, let me just read out the kind of steps.So, removing the small disk and placing it on the 3rd facts or smallest it goes to the3d peg, then remove the medium disk and move it to the 2nd peg and, then ah you know thiscompletes the sub goal of freeing the largest, you know the largest is free.Now you can move it wherever you want, but there is a rule that a larger disk cannotbe placed on top of a smaller disk.So, how will you do it?And the second thing is you have to know free of the 3rd peg because, this is where thelargest has to come.So, what you will do is you will pick up the smallest is from the peg 3 put it on peg 2,because peg 2 has the medium disk.Now on top of that you can pick the keep the smaller disk, once that is there peg 3 isfree now you can move this to the you can move this ah largest is from peg 1 to peg3, this is one way done.Now what you can do is you can just pick up the smaller disc keep it back and peg 1, youknow pick up the median disc keep it on peg 3 and, then ah bring the smallest is on peg3, this is basically a very quick ah solution to the tower of Hanoi problem, but it is;obviously, a complicated problem once you start, you know dealing with it in steps andstart figuring this one out.So, again this is just a description of how the problem has to be solved.So, once one reaches ah stage 5 in the problem face 1 can decide about how to ah achievethe sub goal four that is freeing up the medium size disc.So, once you have kind of done ah a particular steps and you kind of take a pause ah stepback see now how are you going to free this middle disc and, how are you going to moveit.We can ah and there are two possible options, you can move the small disc to peg 3, or ontopeg ah onto peg 9 that is stage 6 I will just go back here.So, when you are actually at sub goal 5 ah now what you have to do is you have to freeup the middle disc.So, you can either move it to ah peg 9 ah peg 3 or you can actually ah go to goal 6.So, again you kind of have to figure out what needs to be done to eventually reach the goals,that is pretty much what the ah thing ah that you have to do.Now these two possible choices the choices between moving the smallest is to a get backagain to pick 3 or onto peg you know or on do ah peg 9 ah and that will be the sub goal6.So, if you kind of have this idea that moving you know this to peg 3 is not really a goodidea because, it more blocks the medium sizes you will not put the medium size disc, buton top of the smallest disc.So, it is not really a good idea because, you know that will block the medium size is.So, what you have to do is you have to kind of move the smallest back to peg 1 as I wassaying, which makes it possible to move the medium size days to peg 3 and, then you canbring the smallest disc here.So, there is if you kind of you know take a step back and ah look at this much moreclosely, there are this sequence of steps that you have to take, each step is supposedto take you closer to the final solution.So, why is the tower of Hanoi problem important, you know the tower of Hanoi problem is importantbecause it demonstrates the usefulness of the means ends analysis, you know with thissetting of sub goals and the approach that needs to be applied and, this is what canapply to real life situations as well.If there are bigger problems at hand if they are more complicated problems at hand, whatyou really need to do is draft the problems into smaller smaller goals, and kind of youknow keep achieving those smaller goals in order to eventually reach the largest goal.That is pretty much how the means ends analysis would work out one of the main contributions,in that sense of the novel assignments you know approach is that it provides a way tospecify the possible pathways from the initial state to the goal state, you take this stepyou are moving further from the goal state, you take this step you are moving closer fromthe goal state, but research basically has shown that there is; obviously, more to theyou know a problem solving than just, specifying the problem space that is there are so, manyother things as well.So this is all from me about the information processing approach to problem solving inthe gestalt approach to problem solving, we will move to the next lecture, where we talkedabout some other approaches and some other aspects of problem solving.Thank you.