Suggests that the lack of motivation in mathematics courses often demonstrated by undergraduates can be remedied in part by a better explanation of the intrinsic value of studying mathematics. Offers suggestions for maximizing success such as previewing topics, attending class regularly, and knowing how to read the text and how to study for exams.…

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.…

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…

Although data is often used to estimate parameters for models in calculus and differential equations, the models themselves are seldom justified. Uses the data itself to motivate mathematical models in introductory mathematics courses. Illustrates various regression and optimization techniques. (Author/ASK)

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)

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)

Describes a reading and writing course about the fourth dimension that involves readings selected from both mathematical and non-mathematical literature, frequent class discussion, several invited speakers from disciplines other than mathematics, and some hands-on and group activities. (Author/ASK)

Describes a house-buying active learning project designed to motivate students in lower level college mathematics courses. Discusses the mathematical content, implementation, evaluation, and benefits of the project. (Author/ASK)

Describes an algorithm for planning college-level mathematics lessons based on the identification and achievement of student learning objectives. Discusses the ways in which this algorithm can help novice instructors to include opportunities for active learning in their lessons. (Contains 50 references.) (Author/ASK)

Describes the specific courses in a sequence along with how the writing has been implemented in each course. Provides ideas for how to efficiently handle the additional paper load so students receive the necessary feedback while keeping the grading time reasonable. (Author/ASK)

Presents problems to find the integrals of logarithmic and inverse trigonometric functions early in the calculus sequence by using the Fundamental Theorem of Calculus and the concept of area, and without the use of integration by parts. (Author/ASK)

Describes an experiment using applications and projects to motivate students in college algebra. Provides a few illustrative examples of the applications/projects used and shares some student comments. (Author/ASK)

Error estimates for tangent line approximations and for numerical integration are found using special cases of the error formulas for Taylor's Theorem and the Trapezoidal Rule, respectively. Proofs of these theorems rely on a modification of Rolle's Theorem. (Author/MKR)