Reports on a study of students' responses to two types of questions on final examinations in calculus. Concludes that the two kinds of understanding--pointwise and across time--are clearly distinguishable. Discusses the differences between these two types of understanding. (ASK)

Examines how components of the concept of function (variable, domain, and range) and the process-object duality in its nature emerge as highly relevant to student learning in various mathematical contexts related to linear and abstract algebra. (Contains 22 references.) (ASK)

Reports on a study on the construction of examples and counter-examples in a college-level calculus course. Verbal and written productions of the students were classified as one of activity, expression, content, and correctness. Finds two types of strategies, global and local. Analysis also distinguishes between "winning" and…

Describes the use of time-lapse photographs of a running cat as a model to investigate the concepts of function and derivative in a college calculus course. Discusses student difficulties and implications for teachers. (MKR)

Examines the value of concept maps as instruments for assessment of conceptual understanding, using the maps to compare the knowledge of function that experts and two groups of students (N=28)--traditional and nontraditional--enrolled in university calculus classes hold. Discusses the differences between the student and expert groups as well as…

Rate of change has its basis in everyday experience like growth and motion and is a fundamental organizing idea for relationships between varying quantities. In this paper three types of rate of change knowledge for functions are discussed: global, interval, and point-wise. Each of these types of rate of change knowledge can be examined using…

Outlines an attempt at integrating web-based activities into a precalculus course at a large university in which discussion of the development of the activities is initially provided. Investigates the effects of the use these activities in four classrooms. Focuses on the use of the activities by two instructors, only one of whom received…

This paper describes student difficulties in first-year calculus classes and suggests some instructional strategies to address these difficulties. Participants in this study were 200 low socio-economic background freshmen majoring in business in Brazil. Results show that the main difficulties are related to lack of understanding of algebraic…

Reports on part of a study that was conducted with individual students (n=5) and five groups of students who worked together in the first course of experimental calculus classes. The goal of the study was to discover how the concept of inverse function can be learned. (26 references) (DDR)

Presents a study to describe and understand the thinking processes of students in a computer environment while undertaking mathematical tasks related to the differentiation of functions defined on real numbers. Describes two different approaches, the visual and the algebraic approach, in the thinking processes of calculus students. (Contains 19…

This document contains nine research papers presented at the Joint Special Session on Research in Undergraduate Mathematics Education at the annual meeting of the American Mathematical Society and the Mathematical Association of America (San Francisco, California, January 1991). Paper titles are: "The Teaching and Learning of College…

This paper documents how eight high school students in a precalculus class enhanced with graphing calculators think about functions. Three models of thinking about functions emerged from students' function images observed over a period of 9 months. In the graph model, students believed that functions are essentially graphs; in the equation model,…

There has been much recent discussion concerning the content of the standard calculus course for students majoring in mathematics and the sciences. Some of this discussion has focused on the available textbooks. One weakness noted in some of these books involves the definitions of limit and continuity for functions of several variables. A…

Describes an approach to the design of learning environments around a computer algebra kernel. Presents two environments to help students learn precalculus. Provides students with symbolic, graphic, and numeric tools as well as functionalities to help them build proofs. (Author/KHR)

Describes an experimental study in which two sections of calculus were taught using the same materials, except one section was enhanced with the computer algebra system Mathematica. Results indicated that the students in the technology group had advantages to understanding certain key topics in calculus such as limits, derivatives, and curve…