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,…

Three issues concerning the relationship between research and practice are addressed. (1) A certain "prototype mathematics classroom" seems to dominate the research field, which in many cases seems selective with respect to what practices to address. I suggest challenging the dominance of the discourse created around the prototype mathematics…

Within mathematics education, classroom teachers, educational researchers, and instructional designers share the common goals of understanding and improving the teaching and learning of mathematics. Teachers work to help students learn; researchers study how people learn and teach mathematics; and designers develop instructional materials to…

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…

In this paper, we draw on a 16-month study funded by the Learning and Teaching Support Network in the UK and entitled "Mathematicians as Educational Co-Researchers." The study's aims were two-fold. Primarily we intended to explore mathematicians' reflections on issues identified in the literature as highly topical in the area of teaching and…

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…

The reversal phenomenon was studied with nearly 1,000 Australian students in grades 9-12. The insertion of a multiplication sign in an equation tended to lower the incidence of reversals, but switching from initial letters to other letters made little difference. (MNS)

Examples of relatively novel computer software environments from the representation perspective are described. Even more novel approaches to curriculum reform to cultivate higher-order thinking skills are then discussed. (MNS)

Presents a constructivist view of mathematics, mathematics teaching, and mathematics achievement, and differentiates this view as an alternative to the typical traditional perspective of these terms. Discusses the roots of this approach in contemporary information-processing psychology. (TW)

Reports on a seminar conducted by the Massachusetts Institute of Technology which was designed to help teachers develop their understanding of learning and teaching arithmetic. Describes some of the sessions and the activities and includes some of the dialogue exchanged within the group during the sessions. (TW)

This paper describes a 4-month-long experiment in computer-based learning called Instructional Software Design and presents aspects of the software evaluation. Results included greater mastery of LOGO and fractions by the experimental class than for either control class and greater acquisition of metacognitive skills. (Author/CW)

Provides a brief summary of current research in mathematics education at the college level. Explores the current needs of college-level faculty. Suggests ways of coping with the apparent perception that some of the best contemporary research is useless or irrelevant from the practitioner's point of view. (22 references) (JJK)

Presents a model of the tutoring process that takes into account the evolving tutor/student relationship and the subject matter concerns that the tutor is helping the student master. Reports illustrative data from case studies from which the model is derived. (15 references) (MDH)

Discusses dilemmas teachers may face when shifting their concept of teaching or tutoring from explaining or telling to a constructivist perspective of facilitating the development of students' knowledge structures. Examines teachers' decisions during a 20-minute segment of dialogue between a student and teacher while studying linear functions. (14…

Examines the potential role for Computer Algebra Systems (CAS) when teaching courses as functions, calculus, and linear algebra to students with low prerequisite algebra skills. A study reports the rationale, planning, and implementation of a functions course integrating Maple CAS into instruction. (MDH)