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)

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)

Common student attitudes toward reform methods are conveyed through the thoughts of a student leaving a multivariable calculus exam and musings range over textbooks, homework, workload, group work, writing, noncomputational problems, instructional problems, instructional styles, and classroom activities. (Author/ASK)

Describes an activity designed to help students develop a good foundation from the beginning of the transition from multivariate calculus to linear algebra. (MM)

Presents a murder mystery in the form of five Calculus I worksheets in which students must apply mathematics to determine which of the suspects committed the murder. Concludes that effort was made to create scenarios that realistically lend themselves to the use of mathematics. (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)

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)

Multiplicative calculus is based on a multiplicative rate of change whereas the usual calculus is based on an additive rate of change. Describes some student investigations into multiplicative calculus, including an original student idea about multiplicative Euler's Method. (Author/ASK)

Describes a 'Moore Method' course whose purpose is to teach students to create and present in class mathematically correct proofs of theorems. Discusses grading, class discussions, ways to help students, and the extent to which to encourage cooperative learning. (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)

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)

Proposes a calculus curriculum combining formative knowledge, mathematical foundations, and instrumental knowledge in mathematics. Discusses each of these components, the organization of a core calculus course, and the use of problem solving in calculus instruction. (10 references) (MKR)

Improved writing and higher grades of first-semester calculus students (n=25) were the result of a variety of written assignments used in the course. Includes sample writing assignments. (MKR)

Several mathematicians have expressed their criticism of calculus instruction and some have developed innovations. This paper reviews the criticism and innovations and then questions the approach and the emphasis of the reformers. (Contains 34 references.) (Author)