A way for students to refresh and use their knowledge in both mathematics and physics is presented. By the study of the properties of the "Runge-Lenz" vector the subjects of algebra, analytical geometry, calculus, classical mechanics, differential equations, matrices, quantum mechanics, trigonometry, and vector analysis can be reviewed. (KR)

Presented are two teaching methods: an algorithm for determining area; and identifying cubic polynomials with three integral zeros, integral maximum and minimum points, and integral inflection points at the advanced placement calculus level. Examples for each are given. (CW)

Emphasis on problem solving and mathematical modeling has gained considerable attention in the last few years. Connecting mathematics to other subjects and to the real world outside the classroom has received increased attention in mathematics programs. This article describes an application of simple differential equations in the field of…

The author discusses the definition of the ordinary points and the regular singular points of a homogeneous linear ordinary differential equation (ODE). The material of this note can find classroom use as enrichment material in courses on ODEs, in particular, to reinforce the unit on the Existence-Uniqueness Theorem for solutions of initial value…

How did it happen that both full-time and adjunct faculty at Scottsdale Community College embrace a standards-based curriculum from beginning algebra through differential equations? Simply put, it didn't just happen. Not only did it take well over a decade, but it was also the result of a sequence of initiatives, decisions, discussions, targeted…

Over the past two decades, calculus reformers have called for the use of alternative pedagogical techniques to promote student learning. Some mathematics instructors have responded by developing a set of student projects intended to hone thinking skills and improve the mathematical writing skills of calculus students. Drawbacks to this strategy…

What is a routine question? The focus of this paper is routine questions and time (in years) since a hitherto routine question was last attempted by the solver. The data comes from undergraduate students' work on solving two calculus questions. The data was selected for reporting purposes because it is well documented and because it threw up…

We examine the behavior of the curvature function associated with most common families of functions and curves, with the focus on establishing where maximum curvature occurs. Many examples are included for student illustrations. (Contains 18 figures.)

In this paper, results of a questionnaire about continuity of functions are analysed. The tested students attend Novi Sad grammar school. The aim of this test was to check the student's theoretical and visual knowledge of continuous functions at the end of their high school education. The questions were given with and without the graphs of…

Problem solving in mathematics incorporates abstract thinking skills, number logic skills, and a nearly endless list of other factors. One problem-solving task required in university-level mathematics courses is integration. This study investigated instructor presentation of a specific problem-solving strategy and whether it impacted performance…

This study investigated students' conceptual and procedural understanding of calculus within the context of an engineering mechanics course. Four traditional calculus students were compared with three students from one of the calculus reform projects, Calculus & Mathematica. Task-based interviews were conducted with each participant throughout…

This workbook was designed to be used as a study aid in any course covering the various techniques of indefinite integration. Many students are able to master each individual technique, but upon encountering an integral on an exam, they often have difficulties in determining which technique to use. By working through all of the exercices in this…

This yearbook is a collection of 14 articles covering a wide range of topics. The first argues that arithmetic is "a general mode of thinking," not a "tool subject." The need and use of mathematics for the average citizen is the basis for the second chapter, and the following chapter continues in this vein by attempting to show…

Discusses some alternatives to calculus as an advanced high school course which will prepare students for college level work, improve their background in algebra, geometry and trigonometry, and introduce new and interesting material of a more advanced nature. (Author/RK)

This article summarizes research conducted in Gifted Algebra I and Gifted Precalculus classes in a public, suburban high school in spring 2002, which investigated the importance of reading and writing in understanding mathematical principles. The classroom teacher supplemented traditional numerical problem solving with vocabulary quizzes, reading…