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…

We report on a two-year NSF-funded project to strengthen connections among science, technology, engineering, and mathematics (STEM) disciplines. One component of this project was to produce some initial data on the effectiveness of Interdisciplinary Lively Applications Projects (ILAPs) in teaching science and engineering undergraduates. ILAPs are…

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…

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…

The broad aim of this research is to characterize the views of proof held by college calculus students and their two types of teachers mathematics graduate students and professors. The analysis is based on an examination of the ways in which people in all three groups produce and evaluate different types of solutions to a proof-based problem from…

This paper presents implementation details related to the freshman integrated curriculum at Texas A&M University. Specifically, the need for strong integration between physics, calculus, engineering problem solving, engineering design graphics, and English is emphasized. The paper presents a brief summary of the design and pilot implementation…

This document is concerned with developing an understanding of problem solving by providing tasks to help students with their problem solving strategies. These tasks were used by Vermont teachers during the pilot years of the High School Mathematics Assessment and were selected by attendees of the June, 1995 Research Scoring meeting. Tasks are…

A tool to aid elementary calculus students in the computation of unusual limits is reviewed. (MP)