L18Problems.6slides - Issues: (a) Representing problems (b)...

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1 Page 1 1 Issues: (a) Representing problems (b) Methods & common flaws in problem solving (c) Expertise 1. Problems and problem representation Well-structured vs. ill-structured problems Stages in problem solving The importance of problem representation 2. Common flaws in problem solving Analogies Hindrances to forming appropriate representations 3. Problem solving methods Algorithms and heuristics Heuristics: Hill climbing, means-ends analysis, working backward 4. Expertise Very domain specific (chess study) Power law of practice Characteristics of expertise 2 A Problem consists of some initial state in which a person begins and a goal state that is to be attained, plus a non-obvious way of getting from the first to the second. Initial State Goal State Methods 3 4 Polya (1957) Form a representation Construct a plan Execute plan Checking/Evaluation Reformulate 5 Problem Solving Concepts: Initial & Goal states. Intermediate States. Representation of problem. Operators: actions that move between states Problem Space: Whole range of possible states and operators, only some of which will lead to goal state 6 n = 4p, and p = n - 30 Initial state n = and p = Goal state Substitute for p Divide by 4 Divide by 30 Problem space whole range of possible states and operators, only some of which will lead to the goal state The price of a notebook is four times that of a pencil. The pencil costs $.30 less than the notebook. What is the price of each? Substitute for n Subtract 4p from both sides: p = 4p - 30 -3p = -30 Divide, substitute Operators Intermediate states 40 10
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2 Page 2 7 O O O O O O O O O There are 9 dots arranged in a square below. Using no more than 4 lines, connect all the dots without lifting your pencil. 8 Initial & Goal States well defined Operators: Four connected lines Representation: Graphical layout Problem space: all possible lines you can draw O O O O O O O O O 9 O O O O O O O O O 10 For many problems, the representation may make it easier or harder to solve. Algebra problems easier as equations Geometry problems easier graphically Decision problems easier when relevant information is laid out in a grid 11 One morning, exactly at sunrise, a Buddhist monk began to climb a tall mountain. A narrow path, no more than a foot or two wide, spiraled around the mountain to a glittering temple at the summit. The monk ascended at varying rates of speed, stopping many times along the way to rest and eat dried fruit he carried with him. He reached the temple shortly before sunset. After several days of fasting and meditation he began his journey back along the same path, starting at sunrise and again walking at varying speeds, with many pauses along the way. His average speed descending was, of course,
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This note was uploaded on 12/26/2009 for the course PSYCH 240 taught by Professor Gehring during the Fall '08 term at University of Michigan.

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L18Problems.6slides - Issues: (a) Representing problems (b)...

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