Offers perspectives on mathematics education from an instructional design viewpoint through an overview of the conflicting ideological paradigms and three case studies illustrating those models. Presents a personal narrative of the importance of social and cultural realities as a professional engineer. (54 references) (MDH)

Two studies of the effectiveness of supplemental instruction (SI) for college-level calculus courses are reported. In each, achievement was compared for students whose discussion groups were conducted using the supplemental instruction (SI) model and those whose discussion groups were conducted with traditional content-only focus. In both cases,…

This article examines constructivism in terms of the learner, the content, teacher-student interactions, motivation, and assessment; evaluates mathematics standards and their sensitivity to students with mild/moderate disabilities; and identifies 19 instructional components derived from constructivism, focusing on teacher behaviors, teacher…

A tiered objectives model is recommended that teachers can use in mixed-ability classrooms to raise students' mathematics achievement. Guidelines for developing tiered activities include: identify objectives, create a set of activities for teaching each objective, identify the next level of increasing complexity, and group students according to…

This document addresses issues raised during the Research on Teaching Mathematics Conference, examining them in view of the central tenets of the Institute for Research on Teaching at Michigan State University. It explains why teacher judgment is the focus of IRT research and discusses the concept of "the wisdom of the practitioner,"…

This article uses a cognitive problem-solving model to explore the application of hypermedia authoring software to mathematics in general and to mathematical problem solving in particular. Hypermedia is presented as a method of exploring alternative solution processes to remediate or prevent learning problems. (JDD)