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• W83695495 abstract "Function-Follows-Form Transformations in Scientific Problem Solving Todd W. Griffith Nancy J. Nersessian and Ashok Goel Computer Science Department Bucknell University Lewisburg, PA 17837 tgriffth@bucknell.edu College of Computing Georgia Institute of Technology Atlanta, Georgia 30332-0280 {nancyn,goel}@cc.gatech.edu Abstract This paper presents a pattern of reasoning called “function- follows-form” (FFF) uncovered through a study of scientific problem solving. In the study we modeled eleven “think-out-loud” problem-solving protocols taken by John Clement (1989). Our work involved computationally modeling the reasoning processes of eleven scientists each attempting to solve the same problem about springs. We describe experiments with two computational systems, ToRQUE and ToRQUE2, which were used to model salient reasoning found in the protocols, and we show how the use of function-follows-form reasoning patterns enables exploration and conceptual change. Introduction Our research identifies and elucidates a pattern of reasoning we call function-follows-form (FFF) reasoning. We have shown that this pattern of reasoning plays an important role in exploratory problem solving, and may lead to significant change to a subject’s mental models. Here we present specification of FFF resulting from experiments with two successive computational systems called ToRQUE and ToRQUE2. The study involved modeling the problem solving of eleven scientists each attempting to solve the same problem about springs. We used “think-out-loud” protocols collected by John Clement (1989) and performed experiments testing the fidelity of our computational model with the protocols. This research represents a melding of disciplines with the goal of understanding complex scientific problem solving. We have combined techniques from history and philosophy of science, cognitive psychology, and artificial intelligence to study the problem solving of scientists. The focus of our effort discussed here was to capture the salient aspects of problem solving for each of the scientists in the form of a general competence model, encoded in a computational system (i.e. ToRQUE2). Background As a first attempt at developing an interpretation of scientific problem solving Nersessian and Greeno (1992) examined an extensive expert problem-solving protocol obtained in a “think-out-loud” interview conducted by John Clement (1989). In particular, they were interested in the second protocol (S2), because it exhibited many of the characteristics of James Clerk Maxwell’s problem-solving practices in the construction of the electromagentic field concept. As they interpret this protocol, the subject uses what they call “constructive modeling” to satisfy himself that his initial answer to a problem was the correct answer. They saw this process as primarily one of arriving at a model that is of the same kind with respect to the salient features of the spring problem. They argue that while this example is much more constrained than historical cases of scientific discoveries, it is still complex enough to require dealing with the many quite difficult modeling issues historical discoveries present. Clement's own analysis of S2's reasoning focuses on a process he calls modeling via “bridging analogies”. He characterizes this process as one in which the subject “produces models via a successive refinement process of hypothesis generation, evaluation, and modification or rejection” (p.358, Clement 1989). It is the specific nature of the construction and “successive refinement” process that led Nersessian & Greeno to interpret S2’s reasoning as a form of constructive modeling, and subsequently led to our computational theory of generative modeling (Griffith et al 1996, Griffith et al 1997, Griffith 1999). The Problem According to Clement, S2 was a computer scientist who had some training in physics. He had also passed comprehensive examinations in mathematics in the area of topology, which is highly significant to our interpretation of the protocol session. In the protocol, S2 is asked to solve the following problem about springs: “... a weight is hung from a spring. The original spring is replaced with a spring made of the same kind of wire; with the same number of coils; but with coils that are twice as wide in diameter. Will the spring stretch form its natural length more, less, or the same amount under the same weight? (Assume the mass of the spring is negligible compared to the mass of the weight.) Why do you think so?” In our interpretation, S2 began the problem-solving session with an intuitive understanding that the stretch of a spring is due to its flexibility. Then he derived a new understanding that a spring maintains constant slope when stretched through torsion in the spring’s wire. So, although this is a more modest outcome of scientific reasoning than evidenced in historical cases, for S2 it was an instance of highly creative problem solving leading to conceptual change. To" @default.
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• W83695495 title "Function-Follows-Form Transformation in Scientific Problem Solving" @default.
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