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Lecture 2

Study Guide Week 2-5

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University of Toronto St. George
John Vervaeke

Week 2 Review three kinds of theories which are all inter-connected and inter-meshed Descriptive Does it exist? Can it be studied scientifically? What are the appropriate conceptual fameowrks Normative Generated by rational reflection, layout certain norms that can be used to obtaining truth Explicit or implicit theory? Is it ecologically or externally valid? Prescriptive How can one design and teach? Often a driving motivation for many psychological researches Best methods for enhancing learning and transfer Today The search inference framework Computational tradition: thinking=info processing, which is best understood as computation Newell & Simon (1957) Gestalt tradition: long debate w the search inference Problem solving = a new search through problem space Baron (1994) search for 3 kinds of things 1. Possibilities 2. Goals: the criteria by which you can evaluate possibilities 3. Evidence: belief or potential belief that helps you determine how well a possible X can actually achieve a goal Inference is the used of evidence to alter beliefs about possibility, goal, and evidence Judgement is the evaluation of the interconnections between goals and possibility The nature of search: they argue that problems formally represented by 4 kinds of elements 1. Description of initial state 2. Goal state 3. Set of operators, which are actions that can be altered 4. Path constraints, additional constraints on the solution beyond the goal (eg. Finding the solution using the fewest steps) A solution = a sequence of operators that can transform the initial state into the goal state while obeying path constraints Problem solving method = a procedure for finding a solution F =the search space. F = the number of operators as any step and D = the number of steps Combinatorial explosion In order to solve the problem, one has to formulate the problem as such that most of the search space is excluded General Problem Solver (GPS) Try to develop a GPS that can shed light on how ppl actually solve problems Research failed because of 2 fundamentally flawed assumptions 1. Problems are in some sense the same and form a unified category, which means that they share a certain essential features 2. Formulating the problem is an easier job than solving the problem Why is 1 wrong? Often, how one solves a set of problem doesnt transfer to how they solve other problems Why is 2 wrong? There are 2 kinds of problems: well-defined and ill-defined. Ill-defined problem means that the representation of all elements (eg. Path constraints and operators) are incomplete, thus require reformulation first Mutilated chess board: almost everyone solves it topographically in the beginning, but once reformulated, then the problem was solved in 3 steps Insight: Is it a real psychological construct? Is there even a thing called insight? The distinction between algorithm and heuristic Algorithm: A completely reliable routine or procedure that can be carried in a finite number of steps to solve a problem Heuristic: A rule of thumb that do not guarantee a solution but often help in dealing w a problem Most of our problem solving skills cannot be algorithmic (logical) in nature Heuristic search: since heuristic doesnt guarantee a solution, then mistakes are unavoidable Bias is just a heuristic that showed up in the wrong context Trial & Error: a myth, human beings dont actually engage in trial and error Hill climbing heuristic: You have some way of knowing whether you are getting closer to the goal (eg. Hill climbing method in dosage prescription by doctor) Metaphor: the strategy isnt really realistic, nor is it that powerful and useful Means-ends analysis: 1. Comparison between current and goal state: identify salient differences between them (how to identify salience?) 2. Select operator to reduce difference (which requires well-defined operators) 3. Apply operator if possible. If not, select a new subgoal under which the operators can be applied However, this is recursive because of the problem of infinite regression. The number of attempts at sub- goal is an ill-defined problem 4. Return to step 1 Productive Heuristics = heuristic procedures that can be used to resolve a problem Provocative Heuristics = tickling memory or insight
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