When learning, students yearn for meaning, challenge, and relevance. Integrated learning fulfills these desires by limiting the compartmentalization of learning--providing a more coherent learning environment. Too often, mathematics and the physical sciences are taught as separate entities. Yet, many commonalities exist, especially between…

The purpose of this study is to design a constructivist learning environment that helps learning the limit concept. The study is a pretest-posttest quasi-experimental research. The control and the experimental groups were chosen from the students attending a calculus course. Worksheets were used to assess students' learning of the limit concept.…

In this research report we examine knowledge other than content knowledge needed by a mathematician in his first use of an inquiry-oriented curriculum for teaching an undergraduate course in differential equations. Collaboratively, the mathematician and two mathematics education researchers identified the challenges faced by the mathematician as…

In this study the effectiveness of an arrow diagram which can help students apply the Chain Rule was investigated. Different variations of this diagram were used as mnemonic devices for applying the Chain Rule. For the investigation two instruments were developed, diagnostic test and post-test. The diagnostic test was developed to determine the…

Technologies play a prominent role in current reforms of school and collegiate mathematics. This study examined ways in which first-semester calculus students still showed the influence of a graphing-intensive college algebra course they had studied one or two semesters earlier. Students (n=18) at a large research university were asked to solve a…

This book brings together papers by scholars from around the globe on the historiography and history of mathematics and their integration with mathematical pedagogy. Of the three articles in Part 1, "Historiography and Sources", one identifies research trends in the history of mathematics, the second discusses the centrality of problems, and the…

This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical…

Mathematics textbooks embody a particular set of assumptions about mathematics or the mathematics intended for students at a particular level. An epistemological analysis of textbooks can provide some context for understanding, for example the difficulties many students encounter when moving from high school to collegiate mathematics. In this…

The fundamental results of integration theory are shown to follow from an axiomatic definition of the integral as a real valued function whose domain is a subset of the set of real valued functions of a real variable. (SD)

A systematic approach to general orthogonal co-ordinates, suitable for use near the end of a beginning vector analysis course, is presented. It introduces students to tensor quantities and shows how equations and quantities needed in classical problems can be determined. (Author/LS)

Presents a technique, using the method of variation of parameters for solving differential equations, for introducing Green's function early in an undergraduate curriculum. Presents various examples. (Author/MLH)

This is part two of a three-part SMSG calculus text for high school students. One of the goals of the text is to present calculus as a mathematical discipline as well as presenting its practical uses. The authors emphasize the importance of being able to interpret the concepts and theory in terms of models to which they apply. The text…

This is part three of a three-part manual for teachers using SMSG high school text materials. Detailed solutions are given to all the exercises in the text. Chapter topics include: (1) area and the integral; and (2) differentiation theory and technique. (MP)