Summarizes an interdisciplinary undergraduate research project involving experimental physics and calculus and illustrates how mathematics was used to finesse incomplete experimental information and maximize physical quantity known as jerk. Describes how calculus can be applied in the "real world" where functions are not always given by nice…

Students in a freshmen calculus course should become fluent in modeling physical phenomena represented by integrals, in particular geometric formulas for volumes and arc length and physical formulas for work. Describes how to train students to became fluent in such modeling and derivation of standard integral formulas. Indicates that these lessons…

Shares a series of problems designed to provide students with opportunities to develop an understanding of applications of the definite integral. Discourages Template solutions, solutions in which students mimic a rehearsed strategy without understanding as the variety of problems helps prevent the construction of a template. (Author/ASK)

Present a study conducted at The Ohio State University and compares students from the calculus-reform course sequence Calculus and Mathematica with traditional students in two areas: (1) conceptual and procedural understanding of calculus; and (2) achievement in calculus-dependent courses. Investigates student achievement in calculus-dependent…

Explores a method of teaching called Peer Instruction. Describes how Peer Instruction was implemented in physics and summarizes the results. Discusses the way in which Peer Instruction was modified to be used in an introductory single variable calculus course. (Author/ASK)

Outlines ideas and exercises for two topics that accompany the standard treatment of integral calculus. Emphasizes intuition to help facilitate student comprehension of the definite integral as a limit of Riemann Sums. (Author/MM)

Presents a murder mystery in the form of six Calculus II review problems. Students must solve the six problems to determine the murderer, murder weapon, and time and location of the murder. (AIM)

Describes three labs designed to help students in a first course on ordinary differential equations with three of the most common numerical difficulties they might encounter when solving initial value problems with a numerical software package. The goal of these labs is to help students advance to independent work on common numerical anomalies.…

Addresses the problem of poor study habits in calculus students and presents techniques to teach students how to study consistently and effectively. Concludes that many students greatly appreciate the added structure, work harder than in previous courses, and witness newfound success as a consequence. (Author/ASK)

Studies the later course grades of students enrolled in freshman calculus taught using traditional texts through 1994-95 and the Harvard method which was fully adopted starting in 1995-96. Reports that, in some cases, the results were indistinguishable but some statistically significant patterns were found. (Author/ASK)

In standard mathematical notation it is common to have a given symbol take on different meanings in different settings. Shares anecdotes of how this symbolic double entendre causes difficulties for students. Suggests ways in which instructors can clarify these ambiguities to make mathematics more understandable to students. (Author/ASK)

Refutes the assumption that large classes must be impersonal, characterized by lecture style, and presented in a theorem-proof-example format. Discusses successful strategies for space use, classroom management, and collecting student feedback. (DDR)

Describes how constructing concept maps and writing accompanying interpretive essays can be used in a Calculus I course to improve students' understanding of important concepts and help teachers assess students' knowledge. This combined approach allows students to explicitly communicate their knowledge and a chance to view mathematics as a…

Describes a project involving a short car trip in which students experience an early opportunity to work in teams, think about mathematics, gather and analyze speed and distance data, and produce a report on their findings. Provides a typical-authored solution. (Author/ASK)

Presents an experiment to design a precalculus topic that would help prepare students for limits in differential calculus. Emphasizes the topic to enhance the interpretation of graphs and to be applicable in both technology-based and traditional precalculus courses. Uses graphing calculators to help students observe the results of their…