This study investigates 3 preservice secondary mathematics teachers' understandings of limits of sequences and their changing conceptions of limit during and after instruction involving interactive, dynamic sketches embodying the formal definition of the limit of a sequence. Manipulating a coherent visual representation of the formal definition in…

Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…

This paper investigates the effects of a computer algebra system (DERIVE) on students' comprehension and computational skills in Brief Calculus, a first course for non-mathematics majors. Research results indicate better conceptual understanding by the group using DERIVE without the loss of pen-and-paper computational ability. (KHR)

This paper describes two uses of the software package TEMATH (Tools for Exploring Mathematics) with calculus students: (1) as a demonstration tool in the classroom to visually explore with students the many mathematical models introduced in a first year calculus course; and (2) as a part of a lab where students use a set of laboratory explorations…

This submission contains the Proceedings of the 2010 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Simon Fraser University in Burnaby, British Columbia. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims…

Investigates how animation is used to improve students' comprehension of the limit concept in an experimental course in which the main topics are approximation and interpolation by Taylor polynomials. Uses Mathematica software to generate the dynamic graphics, visualize the process of convergence, and give meaning to the definitions. Analyzes…

The subject of q-calculus is a rich source of learning activities that address concept formation, exploration, variation, rich training and proof. This paper is a survey of the subject that shows how high school students using a computer algebra system can explore the field and prove some results. (Contains 7 figures.)

Explores what kinds of calculus-related insights seem to typify calculus-related reasoning. Introduces "qualitative calculus" in which learning is focused on synthesis. Discusses the resemblance and difference between traditional calculus and qualitative calculus, advantages of learning qualitative calculus, and how understanding qualitative…

Discussed are possible reasons behind the inconsistencies in the learning of calculus. Implicated are students' beliefs, mathematical paradigms including concept image and concept definition, language use, and curriculum sequencing. (KR)