Misconceptions which students have about the convergence of an alternating series are identified, and counterexamples are provided for each of the misconceptions. (DT)

Properties of solids generated by the rotation of some of the well-known solids about given axes are discussed. (DT)

Examples are given of difficulties that students have in determining extrema of real-valued functions of real variables. (DT)

An example is given of an application of calculus to biology in which a straightforward mechanical approach leads to a difficult situation, but the theory of beginning calculus leads quickly to a solution. (Author/DT)

Three modes of instruction were compared: regular classroom instruction, self-paced, and self-paced plus tutor. Results showed that in an introductory basic concepts of mathematics course, the two self-pacing methods were superior to the regular instruction, while in a calculus course the results were not as clear-cut. (DT)

This study compared a traditionally-taught calculus course with a self-paced one. Based on performance on a common final examination, students in the self-paced course did substantially better than those in the traditional course. (DT)

Algebra and calculus students have difficulties to express themselves in a statement of mathematical symbols and to comment on written mathematical statements to end with equivalent mathematical symbols statement. In this study, the reasons behind the meaning students load to the mathematical symbols and written mathematical statements was…

Many colleges and universities use a mathematics placement process to guide students to the appropriate entry-level mathematics course. The mathematics placement process presented here was developed over a four year period to make placement recommendations to Calculus I, Precalculus, and College Algebra. Placement recommendations are based on the…

An experimental calculus class was instructed by inquiry-style presentation incorporating heuristic problem-solving strategies. A control class was also instructed using an inquiry style, but with no emphasis on heuristics. Based on interviews, it is suggested that heuristic-oriented instruction can be an effective mode of teaching problem…

A model for securing student input for curriculum construction, including textbook writing, through observing small groups of students at work is described; its application to the topic of limits of sequences and implications for curriculum development in general are discussed. (DT)