Lists several problems that have proven to be successful in getting students to think about topics and notions they thought they knew. Indicates that students have not only solved the conundrums (often with help), but also developed them further into research projects. (Author/ASK)

Describes the Treisman model which involves supplemental workshops in which college students solve problems in collaborative learning groups. Reports on the effectiveness of Math Excel, an implementation of the Treisman model for introductory mathematics courses at Oregon State University over five academic terms. Reveals a significant effect on…

Discusses experiences teaching mathematics courses in a lecture-free, discussion-based seminar format at all levels of the traditional undergraduate mathematics curriculum. Presents methods for motivating, instructing, and supporting student efforts toward independent reading of mathematical text. Provides a non-scientific assessment of the…

An interdisciplinary activity in which students can see how a famous author, Leo Tolstoy, metaphorically applied the integration steps from calculus to illustrate his ideas about how history should be studied is described. The activity provides a startling and energizing conclusion to a unit on applications of integration and provokes students'…

Topics such as linear and nonlinear equations and inequalities, compound inequalities, linear and nonlinear absolute value equations and inequalities, rational equations and inequality are commonly found in college algebra and precalculus textbooks. What is common about these topics is the fact that their solutions and graphs lie in the real line…

This paper describes a sequence of lessons from two Calculus I classes for teaching the epsilon-delta definition of a limit. In these lessons, the author elicited students' misconceptions and perceptions of this definition through a reading/writing lesson and then used these student ideas to design a lesson aimed at addressing these misconceptions…

This article is a discussion of some geographical problems related to geographic and population centers of the U.S. The focus is on modeling, using concepts from calculus.

In their sections on inverses most precalculus texts emphasize an algorithm for finding f [superscript -1] given f. However, inspection of precalculus and calculus texts shows that students will never again use the algorithm, which suggests the textbook emphasis may be misplaced. Inverses appear primarily when equations need to be solved, which…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

To identify and describe the basis upon which instructors make curricular and pedagogical decisions, we have developed an artifact-based interview and an analysis technique based on multilayered concept maps. The policy capturing technique used in the interview asks instructors to make judgments about concrete instructional artifacts similar to…

Calculus has become the center of a heated debate within the mathematics community. There are those who question the very centrality of calculus in the mathematics curriculum. Evidence indicates that many current calculus courses are not serving students well. In addition, computers and advanced calculators can now do many of the manipulations…

The aims of the study were to explore the effects of teaching heuristics in a calculus course and to generate hypotheses about related changes in heuristic usage and problem solving performance. Thirty college students in two classes participated and a Solomon four-group research design was used. Students from one group in each class were…

A slight rewording can often transform a routine exercise into a nonroutine one. Three problems (with solutions) from first-year college calculus are presented to illustrate how the technique can be used and how it is applicable to any course. (JN)

This study examined quantitatively the effects of varying retention intervals (RI) within a 4 X 4 block schedule on knowledge retention of Algebra 2 skills and concepts. Specifically, the study contrasted the mean scores of students having an RI of 0, 8, and 12 months on a pre-review, post-review, and end-of-course test in precalculus. The study…

This paper describes a model for effective incorporation of technology into the learning experience of a large and diverse group of students in first-semester first-year tertiary mathematics. It describes the introduction of elementary use of MATLAB, in a course offered both on-campus and at a distance. The diversity of the student group is…