Results from a large-scale study of sixth-form and college students' understanding of elementary calculus and mathematical ideas underlying calculus are presented. Difficulties with speed, tables, linear graphs, curves and differences, the tangent as the limit, and the average rate of change are each discussed. (MNS)

We expand the theoretical perspective based on the notions of description and conflict, which was previously used to the learning of functions and calculus, to the learning of deductive geometry supported by Dynamic Geometry (DG) environments. Based on prior studies on functions and on the potential role of a DG software, we analyze a case study…

The metaphorical nature of first-year calculus students' reasoning about limit concepts is explored using an instrumentalist approach. Analysis of written and verbal language reveals that, while these students used motion terminology profusely when discussing limits, it was typically not intended to signify actual motion and did not play a…

The Cabri programming language is a dynamic geometry software used all around the world by many of teachers, students, and researchers in mathematics. This paper presents examples of using Cabri and graphing calculators as a tool to practice mathematics and provides ways that mathematics could be approached, taught, and received in a way…

This study explores computer-meditated tutoring and a traditional tutoring model that is carried out on a face-to-face basis and investigates whether there is a difference in high school students' mathematics achievement. In this study, there was no statistically significant difference between the face-to-face and the computer-mediated tutored…

This paper discusses the theories of conceptual change and how they explain the difficulties in mathematics learning, especially in enlarging the number concept. Two studies are presented, one of which examines the research questions: What is the role of prior knowledge in students' answers to questions about the density of rational and real…

This column contains brief notes on graphing in three dimensions; patterns in Pascal's triangle; plotting graphs by computer; and an application of the hypocycloid. (MM)

The symposium is seen to create an opportunity for students to understand the way mathematics is actually used in their own fields and to understand both their own potential as mathematics users and inherent difficulties in modeling. The symposium acts as a capstone for a two-semester, introductory calculus course. (MP)

This study, based on individual interviews with 100 students (aged 16 to 22 years), was designed to investigate understanding of elementary calculus (particularly integration and differentiation). Results indicated that items related to understanding integration as the limit of a sum were difficult even for good students. (Author/MP)

Discusses four computer-assisted-instruction programs used in a college-level mathematics course to introduce computer literacy and improve mathematical skills. The BASIC programs include polynomial functions, trigonometric functions, matrix algebra, and differential calculus. Each program discusses mathematics theory and introduces programming…

A science fiction approach is used to explore some unusual properties associated with the concept of infinity. (MP)

An easy way to construct a dodecahedron, interesting connections between conic sections in the Cartesian system and limacons in the polar coordinate system, and the use of u-substitutions in simplifying the integration of certain functions are all explored. A BASIC program is provided with the limacon-conic section discussion. (MP)

A number of general ideas intended to be helpful in analyzing differences in concept images among individuals are formulated. These ideas are applied to the specific concepts of continuity and limits, as taught in the secondary school and university. (MP)

An unusual alternative starting point for instruction in a beginning calculus course that focuses on Fixed Point Iteration (FPI) is presented. (MP)

An account is given of the introduction of multiple-choice and other forms of objective testing into the assessment of a first-year university elementary analysis class. (MP)