Presents a strategy for graphing conic sections on the polar plane without using a table of values by beginning with information gained from the graphs of circular functions. (MKR)

Attempts to answer and generalize the question: When is the numerical derivative obtained on the graphing calculator greater than the actual derivative, and when is it smaller? Discusses symmetric difference. (MKR)

Describes the experiences and conclusions of a long-range program to revitalize undergraduate instruction in mathematics utilizing state-of-the-art workstations and the computer algebra system, Maple, and includes two examples of this type of instructional improvement. Focuses on computer-intensive calculus. (MKR)

Presents a solution to the problem of finding the probability that a needle would cross a crack in a tile floor when dropped. (MKR)

Utilizing composition of elementary functions as prototype of dynamical system, notions of periodic points and their orbits in relation to concept of shift map are used to illustrate concept of continuity. A special case of Sarkovskii's theorem, dealing with period-3 point, is presented with proof relying solely upon Intermediate Value Theorem 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)

Described is an example of a piecewise defined function developed naturally as a consequence of the solution to the given problem statement, thereby allowing calculus students the uncommon opportunity to generate such an otherwise, seemingly contrived function. (JJK)

Several mathematicians have expressed their criticism of calculus instruction and some have developed innovations. This paper reviews the criticism and innovations and then questions the approach and the emphasis of the reformers. (Contains 34 references.) (Author)

In standard mathematical notation it is common to have a given symbol take on different meanings in different settings. Shares anecdotes of how this symbolic double entendre causes difficulties for students. Suggests ways in which instructors can clarify these ambiguities to make mathematics more understandable to students. (Author/ASK)

Genre analysis is a form of discourse analysis that can provide useful and sometimes surprising new perspectives on understanding teaching and learning. Uses two examples to illustrate the application of genre analysis in mathematics education. (Contains 23 references.) (ASK)

Reports on ongoing developmental research efforts to adapt the instructional design perspective of Realistic Mathematics Education (RME) to learning and teaching of collegiate mathematics using differential equations as a specific case. Focuses on the RME design heuristic of guided reinvention as a means to locate the starting point for an…

Describes how the meaning of a tool was constructed by students and their teacher, and how students used the tool to construct mathematical meaning out of particular tasks through a qualitative classroom-based study. Suggests that the nature of the mathematical tasks and the role, knowledge, and beliefs of the teacher influenced the emergence of…

Considers a trio of students who collaboratively discover a generalization while doing their calculus homework. Describes the argument as a play which portrays a relatively natural situation cleansed from unrefined mathematical language, errors, and tangential discussions unrelated to the mathematics of the situation. (ASK)

Presents problems to find the integrals of logarithmic and inverse trigonometric functions early in the calculus sequence by using the Fundamental Theorem of Calculus and the concept of area, and without the use of integration by parts. (Author/ASK)

Discusses a precalculus project in which students create a model United Nations to present and discuss the long-term prognosis for individual countries given data on population growth and food production. Students compare exponential and linear functions to determine whether starvation will occur and prepare oral and written presentations of their…