Cognitive Psychology

1. Cognitive Psychology Problem Solving I

2. Problem solving - The cognitive process through which information is used to reach a goal that is blocked by some obstacle • Many ranges of problems from simple, everyday ones to life-or-death ones • Examples • What is 233 - 17 • What is the best way to get our troops out of Iraq? • Is it possible for someone to win a coin flip 1 million straight times? • Everyday stuff

3. Tower of Hanoi • http://www.dynamicdrive.com/dynamicindex12/towerhanoi.htm

4. What is the next number in the sequence: • -1, 2, -4, 8, -16, 32, __ • 1, 4, 9, 16, 25, 36, 49, __ • Three missionaries and three cannibals come to a river. A rowboat that seats two is available. If the cannibals ever outnumber the missionaries on either bank of the river, the missionaries will be eaten. How shall they cross the river?

5. Three features of problem solving • Initial state – the starting point of the problem • Also the knowledge and resources you have at the beginning • Goal state • Obstacles – restrictions that interfere with the move towards the goal state • Path constraints – limitations that rule out some options in problem solving • Money • Time • Ethical concerns

6. Types of Problems • Well-defined vs. ill-defined • Well-defined – clear and understandable. The initial state, goal state, and obstacles are understood. • Ex. Crossword puzzles • Ex. Solving an anagram • Ill-defined – unclear and abstract • Ex. Draw a picture • Ex. Go have fun

7. Routine problems vs. nonroutine • Routine problems – can be solved by applying well-practiced procedures • Non-routine problems – novel strategies are required. • With practice, problems become routine • Experts vs. nonexperts

8. Approaches to Problem Solving • E. L. Thorndike and the Behaviorists • Thorndike’s puzzle box

9. For Thorndike and the behaviorists, problem-solving was all about associative learning. • Trial-and-error learning • The Law of Effect – the shaping of behavior - behavior having good consequences tends to be repeated whereas behavior that leads to bad consequences is not repeated • Example: • Advantages and disadvantages to approach

10. Kohler and the Gestalts • Gestaltian perception – we inherently arrange information and put it into patterns • Ex. Law of closure, similarity, etc. • We naturally try to organize information • As we rearrange the material, often the solution simply emerges from that process • Insight – the rapid restructuring of the problem that results in a solution • Little light that goes off • Advantages and disadvantages to approach

11. Newell and Simon • Problem solving as information processing • Computer analogy • Step by step progression towards the goal state • General Problem Solver (GPS) • Minimize the differences between the initial state and the goal state • Does so by breaking problem up into subgoals • Problem space – mental representation of the problem, the initial state, goal state, and all of the possible subgoals.

13. Representation problem • Perhaps the most important step in problem solving is understanding the problem. • The representation problem – the challenge of how best to formulate the nature of the problem. • Possibilities • Symbols • Matrix • Diagrams • Hierarchical tree diagram • Visual images

14. Symbols – very commonly used. Especially in Math problems • Ex. Elizabeth visits her friend Andrew and then returns home by the same route. She always walks 2km/h when going uphill, 6km/h when going downhill and 3km/h when on level ground. If her total walking time is 6 hours, then what is the total distance she walks in km? • Using symbols puts the problem into more familiar and simple (mathematically at least) terms

15. Matrix – a chart that shows all possible combinations of items • Ex. Five people are in a hospital. Each person has only one disease, and each has a different disease. Each person occupies a separate room; the room numbers are 101 through 105. • 1. the person with asthma is in room 101 • 2. Ms. Lopez has heart disease. • 3. Ms. Green is in room 105 • 4. Ms. Smith has tuberculosis • 5. The woman with mononucleosis is in room 104. • 6. Ms. Thomas is in room 101. • 7. Ms. Smith is in room 102. • 8. One of the patients, other than Ms. Anderson, has gall bladder disease. • Question: What disease does Ms. Anderson have, and in what room is she?

16. Diagrams – many types • Hierarchical tree diagrams – simply places objects or components of an object into a hierarchy.

17. Example: The Buddhist monk problem – • Exactly at sunrise a Buddhist monk set out to climb a tall mountain. The narrow path was not more than a foot or two wide, and it wound around the mountain to a beautiful, glittering temple at the mountain peak. The monk climbed the path at varying rates of speed. He stopped many times along the way to rest and to eat the fruit he carried with him. He reached the temple just before sunset. At the temple he fasted and meditated for several days. Then he began his journey back along the same path, starting at sunrise and walking as before, at variable rates of speed with many stops along the way. However his average speed going downhill was greater. Will there be a spot along the path that the monk will pass on both trips at exactly the same time of day? Why or why not?

19. Problem Solving Strategies • Many strategies we use to solve a problem. Some good, some bad. • Trial and error • Algorithms • Heuristics • Insight • Analogy • Mental imagery

20. Trial and error – simply try a number of solutions and hopefully one of them will work. • Problems: what to try? • Can be very inefficient • Algorithms - A method that if followed exactly will guarantee a solution. • Examples: Multiplication tables; most forms of math • Following directions when putting together a new toy. • Computers use algorithms • Problems: • the algorithm has to be followed exactly to work. • Most problems do not have an algorithm available.

21. Heuristics – rules of thumb used to solve a problem. • Example: In Black Jack, when do you take another card? • Heuristic: stay at 15 or more. • Heuristics are fairly efficient and usually work fairly well. They do come at the cost of errors however. • Heuristics are used for both problem solving and decision making

22. Types of heuristics • Hill-climbing strategy – at each point, chose the option that moves you in the direction of your goal. • Named for hill-climbing analogy • How well does the hill-climbing strategy work? • Ex. Trying to find your way when you’re lost. • Problem – sometimes you have to go backwards to move forward

24. Means-ends analysis • A type of heuristic • Dividing the problem into smaller manageable parts and then solving each part until the entire problem is solved. • Example: studying for a test. Break it town into chapters, subsections of chapters, etc. • Example – cooking dinner tonight • First, identify the differences between the current state and the goal state. • Don’t have ingredients • Second, apply an operator to reduce the difference • Subgoal – go to store • Subgoal – go to bank for cash

25. Insight – solving a problem by finding a novel approach to it • Wallas (1926) – steps to problem solving • 1. preparation – relevant information is collected, initial solution attempts are made • 2. incubation – latent period. Stop thinking about the problem • 3. illumination – solution “appears”. Insight occurs • 4. verification – solution is checked for accuracy • Research shows that often, a period of incubation can improve problem-solving • Ex. Tip of the tongue phenomenon

26. Working backwards - start at the goal state and work backward toward the initial state • Ex. Tracing a maze • Works by eliminating many of the possible paths at the beginning. • Water lily problem • Water lilies are growing on Blue Lake. The water lilies grow rapidly, so that the amount of water surface covered by lilies doubles every twenty-four hours. On the first day of summer, there was just one water lily. On the ninetieth day of the summer, the lake was entirely covered. On what day was the lake half covered?

27. Analogy – apply a solution to a problem that has worked in similar situations in the past. • Depends on previous knowledge • Using analogies as a key to intelligence • Finding patterns in the structures of problems • Example - shoe is to foot as tire is to ? • Example – political comparisons

28. Research on analogies • People do not readily come up with them • When they are instructed to use an analogy, problem solving is improved dramatically. • Example: The tumor problem • Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach. To operate on the patient is impossible, but unless the tumor is destroyed, the patient will die. A kind of ray, at a sufficiently high intensity, can destroy the tumor. Unfortunately, at this intensity the healthy tissue that the rays pass through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but will not affect the tumor. How can the rays be used to destroy the tumor without injuring the healthy tissue. • Solution?

29. The general and fortress problem. • A small country was ruled from a strong fortress by a dictator. The fortress was situated in the middle of the country, surrounded by farms and villages. Many roads led to the fortress through the countryside. A rebel general vowed to capture the fortress. The general knew that an attack by his entire army would capture the fortress. He gathered his army at the head of one of the roads, ready to launch a full-scale direct attack. However, the general then learned that the dictator had planted mines on each of the roads. The mines were set so that small bodies of men could pass over them safely, since the dictator needed to move his own troops and workers to and from the fortress. However, any large force would detonate the mines. Not only would this blow up the road, but it would also destroy many neighboring villages. It seemed impossible to capture the fortress. However, the general devised a simple plan. He divided his army into small groups and dispatched each group to the head of a different road. When all was ready, he gave the signal and each group marched down a different road. Each group continued down its road to the fortress, so that the entire army arrived together at the fortress at the same time. In this way, the general captured the fortress and overthrew the dictator.

30. Mental imagery as a method of problem solving. • Improves representation • Particularly useful for spatial problems. • Problem – once a vivid mental image has been formed, we have difficulties adjusting it. • Fail to see novel approaches.

31. Impediments to problem solving • Fixation – using a prior strategy and failing to use a novel approach. • Mental Sets - We have a tendency to stick to the tried and true methods even when other strategies might be more efficient or useful. • Example: always taking the same route to work rather than trying another route that may be faster or less congested. • Also called Einstellung

32. Luchin’s jar problem • Capacity of jars        Amount to get      • A   B   C • 1.  21  127  3           100   • 2.  18   43 10             5 • 3.   9   42  6             21 • 4.  20   59  4             31 • 5.  23   49  3              20 • 6.  15   39  3              18 • 7.  28   76  3              25

33. The nine dot problem: connect the dots, with four straight lines, without lifting your pencil or pen.

34. Luchin’s water jar problem – we get used to using one strategy, and it impedes our ability to solve a problem that does not use that strategy • Nine-dot problem – our mental set imposes non-specified rules

35. Functional Fixedness - The tendency to fail in problem solving because of an inability to see novel uses for objects

36. Example of Functional Fixedness • Using only the objects shown in the picture, mount the candle to the wall

37. Solution • The thumbtack box can also be used as a shelf

38. Problem Solving: Obstacles Maier String Problem How can you tie the two stings together if you cannot reach them both at the same time?

39. Problem Solving: Obstacles Maier String Problem Use the pliers as a weight to create a pendulum motion.Avoid functional fixedness!

40. Other problem solving problems • Lack of motivation • Emotion – especially frustration

41. Experts vs. Novices • Chess playing expertise • Experts think further ahead • Memory for chess positions is better • No better if the board positions were impossible. • Increased ability to chunk • Use analogies much more. • Able to recognize meaningful patterns • Experts have a better organization of their knowledge • Less cognitive resources needed for tasks.