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…

Hypothesizes that the construction of visual models, resolution of these visual models with numeric models and, in many cases, rejection of commitments such as the belief in one true velocity, are necessary for students to form integrated mental models of relative motion events. Studies high school students' relative motion problem solving.…

The spontaneous use of analogies in problem-solving occurs when a subject first spontaneously shifts his attention to a situation (B) which differs in some significant way from an original problem situation (A), and then tries to apply findings from B to A. This paper describes research on the process with 10 scientifically trained subjects…

Data indicate that relatively advanced science-oriented college students can experience serious difficulties in symbolizing certain meaningful relationships with algebraic equations. Reversal errors in formulating equations were seen to stem from two main sources: (1) a syntactic word order matching process and (2) a semantic static comparison…

This project had three major goals: (1) investigate the extent to which introductory physics students misuse or misunderstand formulas; (2) catalogue the typical ways in which they do this; and (3) begin the larger task of identifying key types of knowledge that successful problem solvers use to give formulas meaning. Exploratory interviews and…

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…

Errors students typically generate while trying to translate problems into and out of algebraic notation are reviewed. Translation skills and pupil difficulties with them are seen as areas deserving further research. (MP)

Presents transcripts of freshmen engineering majors solving elementary physics problems to examine some limitations of formula-centered approaches to problem solving. Although students use formulas successfully, the qualitative conception of the underlying physical situation is weak. Results from written tests indicate that this phenomenon may be…

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.…

Describes basic problem-solving skills and presents a protocol of a student solving a problem. Discusses some of the difficulties in obtaining a correct solution. Lists basic prompts for problem solving. (YP)

Presents evidence for students' qualitative and quantitative difficulties with apparently simple one-dimensional relative-motion problems, students' spontaneous visualization of relative-motion problems, the visualizations facilitating solution of these problems, and students' memories of the online computer simulation used as a framework for…

Teaching students to think mathematically or to apply mathematics to the solution of real-world problems has become a national priority. This paper explores a method of developing the basic problem-solving skills in a remedial mathematics course at the college freshman level. The first part of this paper describes some basic problem-solving skills…

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.…