Chapter 11: Problem-Solving and Creativity

Some Questions of Interest What are some key steps involved in solving problems? What are the differences between problems that have a clear path to a solution versus problems that do not? What are some of the obstacles and aids to problem-solving? How does expertise affect problem-solving? What is creativity, and how can it be fostered?

Problem-Solving Cycle Discuss resource allocation, monitoring problem solving and evaluating success as completing the process. You can also elaborate on the arrows to demonstrate how one may cycle through several strategies before achieving the final goal or solution.

Problem Representation what information is relevant and what is irrelevant People pay attention to the wrong information People need to focus on the right information

Strategy Formation Select a strategy to solve the problem Analysis: Breaking into subgoals EX: Study for exam subgoals Read textbook and class notes Identify most relevant topics Create study questions and answers on note cards Learn all concepts on note cards Test self with note cards Recycle through learning and testing until mastery is achieved

Strategy Formation Divergent thinking Convergent thinking Generate multiple solutions to problem Convergent thinking Narrow down to best answer

Organization of Information Organize to aid solution Symbols Matrixes Diagrams Let L = Lucy, S = Sean, 2L=3S, S=10   Mango Peach Steak Alex x Jarod Henry

Types of Problems Well-structured problems Clear path to the solution Math problems Anagrams

How do you get them all to the other side? Three hobbits and three orcs come to a river and find a boat that holds two If the orcs ever outnumber the hobbits on either bank, the hobbits will be eaten How do you get them all to the other side? This is a well structured problems

Strategies to Solve Problems Algorithms Systematic procedure guaranteed to find a solution Heuristics Useful rule of thumb based on experience Efficient but does not guarantee a correct solution

Heuristic: Means-End Analysis Compare your current state with the goal and choose an action to bring you closer to the goal Break a problem down into smaller subgoals EX: Win at Monopoly Start by buying properties, continue to buy until you get a set, buy houses, then buy hotels, wait for others to land on spaces, etc. May not work if subgoals cannot be identified  

Heuristic: Working Forward Start at initial state and work to goal state EX: Math problems (2 + 6)/(4 x 1) = ? Complete the math inside parenthesis first, then divide the quantities to get to solution

Heuristic: Working Backward Figure out the last step needed to reach your goal, then the next-to-the-last step, and so on EX: You have lost your keys Try to remember the last time you used them and work backward Work backward from goal state

Heuristic: Generate and Test Trial-and-error strategy Create possibilities, test them, and discard the ones that are incorrect EX: Your car will not start Wait a moment and try again, may be flooded Check to see if there is gas, if no success Check to see if the battery is charged… etc. This may not be the most efficient strategy Tower of Hanoi Visit http://www.mazeworks.com/hanoi/ for an interactive trial and error example. Move all the discs from the left peg to the right one. Only one disc may be moved at a time. A disc can be placed either on an empty peg or on top of a larger disc. The goal is to move all the discs using the smallest number of moves possible. You may also watch the computer solve the Tower of Hanoi if you like.

Tower of Hanoi Move all the discs from the left peg to the right one. Only one disc may be moved at a time. A disc can be placed either on an empty peg or on top of a larger disc. The goal is to move all the discs using the smallest number of moves possible. If you are connected to the internet, you can click the blue base bar and open a web page that allows you to try the tower of Hanoi game. The website is Mazeworks at http://www.mazeworks.com/hanoi/. You may also watch the computer solve the Tower of Hanoi if you like. 15

Types of Problems Ill-structured problems Dimensions of problem are not specified or easy to infer Finding an apartment Writing a book

Gestaltist View of Insight Sudden rearrangement of elements creates “insight” Apparent sudden solution to a problem some time after the problem has been presented Wertheimer- humans and insight Kohler Animal model of insight Sultan stacked boxes to get banana

Non-Gestaltist View of Insight Insight: A prisoner was attempting escape from a tower. He found in his cell a rope that was almost long enough to permit him to reach the ground safely. He divided the rope in half and tied the two parts together and escaped. Algebra: (3x2 + 2x = 10)(3x) = ? Participants indicated how close they were to solution every 15 seconds 1 being very cold to 7 being very warm

Neuroscience and Insight fMRI studies found right hippocampus is active during problem-solving another found spike in right anterior temporal lobe just before insight neural correlates measured before an individual sees a problem can predict if insight will occur Prior to viewing of a problem, participants who had activation in the frontal lobes would later generate an insightful solution

Obstacles to Problem-Solving Mental set Functional fixedness Stereotypes

Mental Set Seeing a problem in a particular way instead of other plausible ways due to experience or context May cause you to adopt an ineffective strategy and prevents problem-solving May make assumptions without realizing it May find it hard to approach the problem in a new way

How would you use 3 jars with the indicated capacities to measure out the desired amount of water? Problem Jar A Jar B Jar C Desired 1 29 3 2 20 21 127 100 14 163 25 99 4 18 43 10 5 9 42 6 59 31 7 23 49 8 15 39 28 76

Functional Fixedness An inability to assign new functions and roles to elements of a problem

Transfer Negative transfer Positive transfer Solving prior problem makes it more difficult to solve later problem Positive transfer Solving earlier problem helps to solve later problem

Gick & Holyoak (1980) Results Control group that only tried to solve the radiation problem A group previously given the analogous general/fortress problem and solution A group given the general/fortress problem and told that its solution would help solve radiation problem

Incubation Time away from a problem provides new insights or otherwise facilitates the problem-solving process Release from a problem-solving set, or functional fixedness Retrieval of new information by changing context Recovery from fatigue

Neuroscience and Planning during Problem-Solving Frontal lobe active in problem-solving Prefrontal cortex active in planning Greater bilateral prefrontal activation with incorrect than correct responses Both problem-solving and planning ability decline following traumatic brain injury

Intelligence and Problem-Solving Participants who score higher on traditional intelligence tests take longer to encode the terms of the problem (global planning) are faster at forming and implementing strategies for the details of the task (local planning)

Expertise Not a general ability Experts have extensive knowledge that is used to organize, represent, and interpret information Thus affecting their abilities to remember, reason, and solve problems

Chess Experts Experts vs. beginners Under what condition did the experts remember more? Check student’s understanding of the graph by having them look at graphs and explain the results found. Fig. 11.13: When experts and novices were asked to recall realistic patterns of chess pieces, as in panel a, experts demonstrated much better performance, as shown in panel b. However, when experts and novices were asked to recall random arrangements of chess pieces, as shown in panel c, experts performed no better than novices, as shown in panel d.

Beer Experts?? Beer experts Beer novices Two-year beer training program in France Beer novices No prior training Tasted a series of 8 different beers Assessed memory of beers between experts and novices Experts remembered more

Experts Differ from Novices Better schemas Well-organized knowledge in specific domain Less time to set up problem Select more appropriate strategies Faster at solving problems Are more accurate

Computer “experts”? The Turing test What questions would you ask? ELIZA: http://www-ai.ijs.si/eliza/eliza.html Alison: http://www.blivion.com/alison/ MeBot: http://mrholden.tripod.com/mebot/ Several downloadable chatterbots: http://www.simonlaven.com/ http://www.loebner.net/Prizef/loebner-prize.html As the site says, “The Loebner Prize is the first formal instantiation of a Turing Test.” It provides additional information on the prize, rules for the contest, and winners of previous contest.

Creativity Process of creating something that is original and worthwhile

Test of creativity 2 minutes- 4 is about average, 8 is very good, 12 is rare, and only 1 in 1,000 people think of 16 uses

Improving creativity? What is a product or service that needs to be improved? select 10 common nouns at random from the dictionary task is to figure out ways to change and improve the product/service use the 10 stimulus words to stimulate thinking.

Theories of creativity Psychometric view Emphasis is on the measure of the product a person creates—creativity test scores The process approach Nothing innately special about people Hard work and dedication leads to creativity Personality approach Way of looking at things Intrinsic motivation is important

Environment Approach Csikszentmihalyi (1996) Must examine historical and social context in which product is made When one achieves balance with context, one achieves flow Flow is the enjoyment we experience when we are engaged in mental and physical challenges that absorb us

A Synthesis Examined case studies of creative people Albert Einstein (logical-mathematical) Pablo Picasso (spatial) T.S. Elliot (linguistic) Mohandas Gandhi (interpersonal) Most had strengths in more than one intelligence and weaknesses in others First become a master; then creativity is possible Gardner (1993)

What is necessary for creativity? Synthetic ability To see problems using novel perspectives and not be bound by conventional thinking Analytic ability To recognize the importance of ideas and focus energy on those worth pursuing Practical-contextual To be able to convey and sell the importance of the ideas to others Sternberg, R. J., Kaufman, J. C., & Pretz, J. E. (2002). The creativity conundrum. New York: Psychology Press.

Neuroscience of Creativity Prefrontal regions are active Brodmann’s area 39 is active These areas were measured while partiicipants had to make up a story: either using semantically related words or unrelated words (presumarbly more creative task) Area 39: part of the parietal cortex in the human brain. BA39 encompasses the angular gyrus