An activity in which students obtain a growth curve for algae, identify the exponential and linear growth phases, and calculate the parameters which characterize both phases is described. The procedure, a list of required materials, experimental conditions, analytical technique, and a discussion of the interpretations of individual results are…

Presents a mathematical problem that, when examined and generalized, develops the relationships between power and efficiency in energy transfer. Offers four examples of simple electrical and mechanical systems to illustrate the principle that maximum power occurs at 50 percent efficiency. (MDH)

Short essay questions are introduced into the calculus course as a technique to involve students with their own learning. Provides (1) instructions to the student for writing the report; (2) results of using the technique; and (3) reasons for using writing in mathematics classes. (MDH)

Working in groups on weekly themes, students discover calculus concepts through assigned readings and written reports. Provides an outline of the course content for two courses and how the courses are organized. An appendix contains the complete text of two themes on curve sketching and applications of the definite integral. (MDH)

Explains the reasons for low U.S. score results on the Third International Mathematics and Science Study (TIMSS) and compares them with students from other nations. Swedish high schools scored highest on the science test, which is attributed to their curriculum. Suggests that the majority of students are taught science that is irrelevant for their…

This paper describes Test Analysis, an alternative assessment method which shifts the responsibility for learning and grading to the student. Students perform a written analysis of their corrected tests, especially errors, prior to receiving a final grade. Improvements in student attitudes toward tests and performance on them are reported from…

Describes the development and implementation of a Web-based calculus course at Texas A & M University. Discusses the course design, layout of content and the contrast with textbook structure, results of course surveys that included student reactions, and how students learn form Web-based materials. (Author/LRW)

Sfard and Thompson (1994) state that what matters most is that educators develop ways of thinking, teaching, and learning mathematics. This study introduced constructive habituation, a new strategy developed to aid both students and teachers in the thinking, teaching, and learning of mathematics. Constructive habituation attempts to unite…

The experience tutoring a student who is blind in four semesters of university calculus is discussed. The mechanics, instructional strategies employed, and the challenges encountered are examined as they relate to teaching mathematics. It was found there are important similarities and also differences as compared to sighted students in teaching…

In the study reported here, I examined the diagrams that mathematically capable high school students produced in solving applied calculus problems in which a diagram was provided in the problem statement. Analyses of the diagrams contained in written solutions to selected free-response problems from the 1996 BC level Advanced Placement Calculus…

In a previous paper, we showed the importance of using low-level commands of a CAS in order to enhance the students' conceptual insight into mathematics. In this paper, we wish to emphasise a different use of a CAS, which makes possible the exploration of new topics, when the necessary theoretical results have still not been acquired, and avoids…

An experienced mathematics teacher in a rural high school in the United States was studied as she first implemented a reform calculus curriculum. Her instruction was compared to her previous practice using a curriculum not constructed with the reform movement in mind. Despite her early attempts to make her instructions more student-centered, the…

To help students understand the real-world applications of calculus, our calculus students all take part in a lab. This is not another "computer lab" but a lab where the students perform experiments and then collect and analyze the data. The students are able to verify for themselves many of physical claims that are left as theory in…

This article describes a calculus project that exposes students to the concept of retirement annuities in both the saving and withdrawal phases, via revenue streams represented by integrals. Students use modeling skills to solve several related problems as the assumptions of the original problem are changed, and the project requires them to use a…

Heuristic training alone is not enough for developing one's mathematical thinking. One missing component is a mathematical point of view. This study reports findings regarding outcomes of a historical approach calculus course to foster Taiwanese college students' views of mathematical thinking. This study consisted of 3 stages. During the initial…