Recounts teaching mathematics to junior high school students in France in the context of seventeenth-century mathematics history. Examines extracts of original works by Leibniz on the origin of calculus and of Huygens on continued fractions. Investigates historical puzzles and a variety of mathematical problems arising out of the texts. (MDH)

Maintains that certain concepts in mathematics are difficult to learn because of problematic continuity from prior knowledge to new concepts. Focuses on the problems of conceptual change connected with the learning of calculus and the shift from rational to real numbers. Summarizes the results of a study involving secondary students. (MJP)

Discusses how applications from microbiology and sociology can be used to involve students. Presents a physical context for critical concepts in a first-semester calculus course. (Author/ASK)

The Merit Workshop Calculus Program, based on Treisman-style workshop calculus, was intended to address the problems of low success rates of students from underrepresented populations and the failure to retain these students in mathematics- and science-based majors. Concludes that the program had a positive impact for both genders and several…

In this essay, the authors suggest that there is another, different and more ancient way of looking at the moral and social role of the teacher and the processes of education in which she is involved. This alternative perspective draws on older, more imaginative and complex sources of meaning than the latest Gallup poll or the latest adjusted…

The importance of visual representation, usually a geometric figure presented in words and in mathematical symbols that is frequently found on high-stakes standardized tests is evaluated. The study shows that mathematics teachers can help prepare students to solve mathematical problems containing a figure not drawn to scale by looking for and…

Courses below calculus need to be refocused to emphasise conceptual understanding and realistic applications via mathematical modelling rather than an overarching focus on developing algebraic skills that may be needed for calculus. Without understanding the concepts, students will not be able to transfer the mathematics to new situations or to…

The subject of q-calculus is a rich source of learning activities that address concept formation, exploration, variation, rich training and proof. This paper is a survey of the subject that shows how high school students using a computer algebra system can explore the field and prove some results. (Contains 7 figures.)

Near the conclusion of their final term in the calculus sequence at The United States Military Academy, cadets are given a week long group project. At the end of the week, the project is briefed to their instructors, classmates, and superior officers. From a teaching perspective, the goal is to encapsulate as much of the course as possible in one…

The Mobius strip, torus, and Klein bottle are used to graphically and analytically illustrate the differences between orientable and non-orientable surfaces. An exercise/laboratory project using the non-orientable Boy surface is included. (Contains 11 figures.)

Although the phase plane can be plotted and analyzed using an appropriate software package, the author found it worthwhile to engage the students with the theorem and the two proofs. The theorem is a powerful tool that provides insight into the rotational behavior of the phase plane diagram in a simple way: just check the signs of c and [alpha].…

This submission contains the Proceedings of the 2010 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Simon Fraser University in Burnaby, British Columbia. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims…

Advanced Placement Calculus examinations were administered to nearly 7,000 students in order to determine the impact of calculator use. Both experimental examinations had two sections. Section I items were designed so that a calculator was not needed, but approximately half of the students were permitted to use calculators. Section II items…

The failure to successfully complete gateway calculus courses often prevents ethnic minority students from pursuing science and engineering majors. Research suggests that this failure to succeed is caused more by social factors than by attributes related to ability. This article presents the findings of an evaluation study done of the Wisconsin…

This research focuses on the graphics calculator in calculus and its impact on students' abilities to work with graphical, numerical, and symbolic representations. Three courses are compared, two of which are taught with less emphasis on the use of graphing calculators. The format of the course emphasizing calculator use is more traditional than…