College students' epistemological belief in their academic performance of mathematics has been documented and is receiving increased attention. However, to what extent and in what ways problem solvers' beliefs about the nature of mathematical knowledge and thinking impact their performances and behavior is not clear and deserves further…

This paper reports one aspect of a larger study which looked at the strategies used by a selection of grade 6 students to solve six non-routine mathematical problems. The data revealed that the students exhibited many of the behaviours identified in the literature as being associated with novice and expert problem solvers. However, the categories…

High school students (n=295) were administered variants of the student-professor problem to ascertain whether errors could be traced to implicit versus explicit relationships between the variables. Concludes that implicit variable relationship problems were harder than explicit variable relationship problems. A follow-up study to explore why is…

The purpose of this study is to analyze the relationship between student behaviors and the growth of mathematical ideas (using the Pirie-Kieren model). This analysis was accomplished through a series of case studies, involving middle school students of varying ability levels, who were investigating a combinatorics problem in after-school…

Investigates the mathematical behavior of 30 college students in a problem situation that requires them to find the inverse of a given compound element in an environment of LOGO turtle graphics. Results from interviews indicate that, in searching for the inverse, students tend to invert the elements but not the order. (MDH)

This paper describes insights on how to promote mathematical reasoning in problem solving based on the mathematical experiences of participants in a long-term study in which the students engaged in strands of well-defined, open-ended mathematical investigations, as a context for research on the development of particular concepts and ways of…

Investigated why, contrary to expectations, group performance in a written test of problem solving was not better than individual performance. Examined protocols of students solving problems in groups and concluded that in much of the group discussion, students passed over right ideas in favor of simpler, but erroneous, ideas. (14 references) (MDH)