Describes an exploration into the concept of the rate of convergence in a university classroom. It is well known in mathematics that this concept leads to a modern construction of infinitesimals and their orders. (Author)

Explores the extent and nature of students' calculator usage as determined from examination scripts in the Western Australian Calculus Tertiary Entrance Examination. Discusses errors made and understanding called upon for seven questions. Discusses instruction and assessment of skills associated with graphical interpretation. (Author/KHR)

Presents results from a national survey of two-year colleges regarding placement practices for calculus. High school records were the most important factor, followed by placement test results and college entrance examination scores. (DMM)

The overwhelming tendency of textbooks to ignore the midpoint-rectangle method of approximating a definite integral is noted. Examples are given, with stress on the accuracy of the method. (MNS)

Proposes a calculus curriculum combining formative knowledge, mathematical foundations, and instrumental knowledge in mathematics. Discusses each of these components, the organization of a core calculus course, and the use of problem solving in calculus instruction. (10 references) (MKR)

Responses to rate-of-change problems were collected during and after 24 hours of conceptual calculus instruction given to first-year university students. Analysis revealed three categories of error in which variables were treated as symbols to be manipulated rather than quantities to be related. Contains test questions. (Author/MKR)

Improved writing and higher grades of first-semester calculus students (n=25) were the result of a variety of written assignments used in the course. Includes sample writing assignments. (MKR)

Uses parametric equations and a graphing calculator to investigate the connections among the algebraic, numerical, and graphical representations of functions. (MKR)

Discusses using dimensional analysis in beginning calculus to help the students determine if the correct exponents and factors are being used. Suggests that dimensional analysis may be very useful but must be used with care. (MVL)

Describes a test using 155 third-year undergraduates in 15 different institutions to examine the extent to which certain core first-year material is retained and understood. Includes an analysis of the answers given by students to each question as well as some of their comments. Students' misconceptions indicate that foundations laid in the first…

Compares the attitudes about mathematics of students from traditionally taught calculus classes and those taught in a "reformed" calculus course. Reports that one to two years after, reform students felt significantly more that they understood how math was used and that they had been required to understand math rather than to memorize formulas.…

Analysis of the constraints and potential of the artefact are necessary in order to point out the mathematical knowledge involved in using calculators. Analyzes and categorizes observations of students using graphic and symbolic calculators into profiles, illustrating the transformation of the calculator into an efficient mathematical instrument.…

The graphing calculator affords the student in analysis a powerful tool to extend visualization, which was previously limited to textbook illustrations and time-consuming constructions. Provides illustrative examples used in initial classroom presentations of several topics including convergence and in student explorations of these topics. (ASK)

Presents an activity to introduce the concepts of average rate change and instantaneous rate of change of a function and to explore the relationship between the value of the exponential function and its instantaneous rate of change. (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)