Since Polya, Wertheimer, and Hadamard's descriptions of qualitative reasoning strategies used by scientists and mathematicians, very little data have been collected on whether these strategies are actually used by experts. This study used video-taped thinking-aloud interviews to examine the problem solving strategies of professors and advanced…

Evidence from video tapes of experts thinking aloud and using analogies in scientific problem solving is presented. Four processes appear to be important in using an analogy: (1) generating the analogy; (2) establishing confidence in the validity of the analogy relation; (3) understanding the analogous case; and (4) applying findings to the…

This paper attempts to show that it is possible to analyze a problem solving protocol in which the subject spontaneously generates a series of analogies. The qualitative physics problem given to the subject describes a situation where that which is unfamiliar is often solved by relating it to several analogous situations that are more familiar.…

Some central issues in discussions of creative processes in science are: (1) the mechanism(s) by which hypothesis formation takes place; (2) the sources of new knowledge during hypothesis formation; and (3) the "Eureka" versus steady accumulation (accretion) issue concerning the pace of change during hypothesis formation. This paper…

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

This document focuses on evidence from problem solving case studies which indicate that analogy, extreme case analogies, and physical intuition can play an important role as forms of nonformal reasoning in scientific thinking. Two examples of nonformal reasoning are examined in greater detail from 10 case studies of "expert" problem solving.…

This paper presents evidence to indicate that spontaneously generated analogies can play a significant role in the problem solving process of scientifically trained individuals. In addition, it is suggested that these individuals exhibit more than one method for generating analogies. Ten scientists (representing physics, mathematics, and computer…

In this study 34 spontaneous analogies produced by 16 college freshmen while solving qualitative physics problems are analyzed. A number of the analogies were invalid in the sense that they led to an incorrect answer from the physicist's point of view. However, many were valid, and a few were powerful in the sense that they seemed not only to help…

When one encounters a problem that one has no adequate way of representing, a new mental model for the problem may have to be found. When a possible model is found, an important next step is to evaluate the validity of the model. In this document, examples of subjects finding and evaluating mental models used as problem representations are…