The purpose of this study was to determine if the use of a graphical teaching and learning approach via the graphing calculator enhances students' understanding of the formal definition of limit. College students in six sections of Calculus I participated by completing a test prior to the introduction of the definition, and completing a second…

Despite increases in the representation of African American and Hispanic youth in advanced math courses in high school over the past two decades, recent national reports indicate that substantial inequality in achievement remains. These inequalities can temper one's optimism about the degree to which the United States has made real progress toward…

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)

These syllabuses for grades 7-12 were written, evaluated, and revised by a team of writers from the Orange County Science Education Improvement Project (OCSEIP). OCSEIP is a cooperative enterprise of the University of California (Irvine), California State College at Fullerton, the Orange County Schools Office, and local districts throughout Orange…

Presented is an elementary approach to areas, columns and other mathematical concepts usually treated in calculus. The approach is based on the idea of average and this concept is utilized throughout the report. In the beginning the average (arithmetic mean) of a set of numbers is considered and two properties of the average which often simplify…