In this paper we examine the roles that metonymy may play in student reasoning. To organize this discussion we use the lens of a structured derivative framework. The derivative framework consists of three layers of process-object pairs, one each for ratio, limit, and function. Each of the layers can then be illustrated in any appropriate context,…

This paper reviews the presentation of problem solving and process aspects of mathematics in curriculum documents from Australia, UK, USA and Singapore. The place of problem solving in the documents is reviewed and contrasted, and illustrative problems from teachers' support materials are used to demonstrate how problem solving is now more often…

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…

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…

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)

Reports a case study to evaluate whether basic concepts of fractal geometry are teachable to elementary school children and to determine the effectiveness of having an elementary school student present a lesson to inservice and preservice teachers. Concludes that simple concepts of fractal geometry appear appropriate for the elementary school…