Exam 4 First Problem Solving

Exam 4 First Problem Solving - Problem Solving(Part 1...

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Unformatted text preview: Problem Solving (Part 1) Research on problem solving • What makes a problem a problem? • How do we go about the process of solving problems? • Are some processes better and more efficient? • What sorts of cognitive processes facilitate or impede problem solving? What is a problem? ill-defined-not clear, not sure what you have to do to find the answer • A situation in which there is an obstacle between a present state and a goal – It is not immediately obvious how to get around the obstacle – Well-defined vs. ill-defined problems Gestalt approach How we see the problem is how well we solve it, not easy and you face obstacles along the way • Representing a problem in the mind • Problem solving involves restructuring the problem’s representation • Obstacles to problem solving 1 Problem Solving (Part 1) Representing a problem in the mind • The solution to a problem depends on how it is represented – Kohler’s “circle” problem – “What’s happening” problem Representing a problem in the mind Found that some people would represent problem in a description that could be depicted visually which takes longer to come to solution. • Kohler’s “circle” problem Representing a problem in the mind • "What's happening" problem People incorrectly represent as a person in a house but home in this sentence actually means home base. Must reconstruct the representation in your mind. – There is a man at home. That man is wearing a mask. There is a man coming home. What is happening? 2 Problem Solving (Part 1) Restructuring and insight • Changing the problem’s representation is associated with insight – Sudden realization of a problem’s solution – Metcalfe & W iebe (1987) • Metacognition and insight Metcalfe & Wiebe (1987) • Asked participants to make “warmth” judgments every 15 seconds while working on problems – 1 (cold) to 7 (hot), indicating closeness to solution – Noninsight and insight problems Insight problems • Nine-dot problem – Connect these nine dots with four connected straight lines. Do not lift your pencil when you draw the four lines. 3 Problem Solving (Part 1) *insight Metcalfe & Wiebe (1987) • Results – Metacognition differed for the two types of problems • ______ occurs suddenly Obstacles to problem solving • Functional fixedness – Duncker (1945) candle problem – Maier (1931) two-string problem (in book) • Mental set – Luchins (1942) water-jug problem Functional fixedness • Functions or uses of objects tend to remain fixed – Duncker candle problem 4 Problem Solving (Part 1) Duncker candle problem Attach candle to wall only using the objects in the room, candle, matches, and thumbtacks. Attach candle to wall so that it burns properly Duncker candle problem • Only 43% of people found a solution Solution: attach a box to the wall and stand candle up in it(box from matches or thumbtacks) – Difficult to see multiple uses or functions of the match/tack boxes Duncker candle problem • Adamson (1952) Proves that there are way to overcome functional fixedness and think more flexibly, problem is, how do we do that on our own? s o lv in g – Put tacks outside of box to reduce fixedness on “container” function % 100 80 60 40 20 0 in box out of box Placement of Tacks 5 Problem Solving (Part 1) Mental set • Tendency to use a previously successful problem solving approach – Luchins water-jug problem Manipulated easier solution in later problems Luchins water-jug problem Luchins water-jug problem 6 Problem Solving (Part 1) Luchins water-jug problem *A+C *A-C *less • Problems 1-8 can be solved using B-A-2C – Problem 7 can be solved more easily (____), as can problem 8 (____) • Results – People who solved all of the problems were __________ to solve problems 7 and 8 with the simple solution • Keep trying the same solution used previously Newell & Simon’s approach • Problem solving as a search that occurs between posing of the problem and its solution – Tower of Hanoi problem http://mazeworks.com/hanoi/index.htm Tower of Hanoi problem 7 Problem Solving (Part 1) Methods of problem solving • A person has to search the problem space to find a solution – Means-end analysis – Algorithms – Heuristics Means-end analysis • Reduce the difference between the initial and goal states – Create subgoals, each of which moves the solution closer to the goal state – Sometimes involves moving backward Algorithms • Always produce a solution – e.g., x + 5 = 9 – Search entire problem space (exhaustive) • e.g., anagram solving • Is effective when problem space is small GPI (= 6 possible combinations) • Can be inefficient and time consuming RAHDLE (= 720 possible combinations) 8 Problem Solving (Part 1) Heuristics We use heuristics ("Look for valid letter combination") • Shortcuts that provide a best-guess solution, but do not guarantee a solution • Why is 1st anagram easier? 9 ...
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