Summarizes the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards document and suggests 10 implications for college mathematics. (MKR)

Outlines a three-step approach to proof writing: exploration, explanation, and formalization. Provides a detailed example of its use. Offers reflections on this approach and adaptations to it. (Author/MKR)

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)

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)

Focusing on student learning rather than the deductive presentation of mathematics is stimulus not only to discover theorems and proofs but also to generate meaning of definitions and axioms before their formal articulation. Provides worksheets that enable an intuitive grasp to precede formal definition in the field of elementary group theory for…

Describes a course that integrates the teaching of finance theory and mathematics. Concludes that this marriage of mathematics and finance reflects the current state of the investments profession and produces a deeper understanding of both fields. Contains 18 references. (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)

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)

Examines the various issues surrounding the implementation of journal writing in an undergraduate linear algebra course. Identifies the benefits of incorporating journal writing into an undergraduate mathematics course, which are supported with students' comments from their journals and their reflections on the process. Contains 14 references.…

Prospective secondary teachers can explore mathematics at their own level by using the law of cosines to establish connections between topics that are usually taught separately such as cosine of the difference of two angles, Cauchy's inequality, determinants, sine of the difference of two angles, triangle inequality, and inner product of two…

Introduces the necessary game-theoretic background and explains how game-theoretic experiments of the Matching Pennies game can be used as a classroom activity to develop intuition about saddle points. (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)

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)

Compares experiences in two calculus courses for non-science majors: a traditional business calculus course and a course using materials from the Calculus Consortium based at Harvard. The latter program is recommended. (MKR)