During the first 12 weeks of an applied calculus course, two classes of college students studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Three weeks were spent on skill development. Students showed better understanding of concepts and performed almost as well on routine skills.…

Sophomore and junior students in the College of Engineering at Cornell University have been taught engineering mathematics using new computer software that performs exact symbolic algebraic and calculus operations. Describes this software, the computer-based mathematics laboratory, changes in the teaching/learning environment, and short- and…

In this paper, we discuss the (potentially positive) pedagogical role of intrinsic limitations of computational descriptions for mathematical concepts, with special focus on the concept of derivative. Our claim is that, in a suitable approach, those limitations can act for the enrichment of learners' concept images. We report a case study with a…

The starting point for this study was the resistant nature of prior knowledge in conceptual change from natural numbers to rational numbers observed in our previous study. Thus, in this study the effects of deliberately teaching the abstraction of the density of numbers on the number line was tested in a quasi-experimental study at the beginning…

Massively parallel programming languages, like StarLogo, provide a rich environment for introducing differential equations to students with an unsophisticated mathematical background. This paper describes the basic software for stimulating and monitoring various population dynamics. Simple differential equations that describe the observed dynamics…

Investigated students' (N=110) understanding of elementary calculus using clinical interview method. Analysis of responses to tasks concerning differentiation and rate of change led to detailed data concerning degree of understanding attained and common errors/misconceptions. Implications for mathematics instruction are discussed. (This is a…

Three teaching ideas are discussed: the improvement of ditto reproduction, and exploration of congruent triangles, and an intuitive introduction to the concept of limit. (MP)

Refutes the assumption that large classes must be impersonal, characterized by lecture style, and presented in a theorem-proof-example format. Discusses successful strategies for space use, classroom management, and collecting student feedback. (DDR)

Provides pathological examples for which graphing calculators sometimes give surprising, misleading, or incorrect results. Investigates some of the more interesting of these examples encountered while using the TI-85 in a variety of undergraduate courses including calculus and matrix theory. (DDR)

Describes a successful course in mathematical biology at Dartmouth College. The course targets premedical students and biology majors rather than mathematics majors, and requires only one semester of calculus as prerequisite. Real world problems form the basis of student work. (Author/KHR)

Presented are two exercises on the differential geometry of curves. A generalization dealing with smoothness conditions is given that relates the two exercises. Included are the definitions, theorems, propositions, and proofs. (KR)

Presented is a Poisson derivation using explicitly stated assumptions and exact functional equations. The assumptions are homogeneity, independence, and negligibility. Included are the derivations and proofs using L'Hopital's rule for each assumption. (KR)

The following ideas are presented: (1) working together in calculus, including a handout for a jigsaw lesson; (2) a lesson on water and ecology from the USSR using the collective teaching technique; (3) the Israeli Havruta "Companionship" method for peer teaching; and (4) an origami lesson outlined and illustrated. (JD)

Discusses a way to help children retain the desire to understand mathematical ideas and to carry out routine procedures. Describes a method using computers to teach linear equations and calculus. Eight references are listed. (YP)

Discussion of the use of computers for presentations in the classroom focuses on their use in a calculus course to explain graphs of functions. Topics discussed include the importance of managing the group process in the classroom; environmental considerations; and projectors and screens. (LRW)