As times change, so has the role of algebra in the educational program. The Interactive Mathematics Program (IMP) offers secondary students an opportunity to learn algebra in a college preparatory sequence that combines basic skills, problem solving, and conceptual understanding while integrating algebra into a problem-based program. Designed for…

Presents activities designed to engage students in an experiential and theoretical application of problems in precalculus and to study geometry, coordinate systems, rates, linear applications, and the concept of function. Illustrates problem situations and includes student worksheets and a teacher's guide. (KHR)

Assesses the ability of university students enrolled in an introductory calculus course to solve related-rates problems set in geometric contexts. Indicates that overall performance on the geometric related-rates problems was poor and the poorest performance was on steps linked to conceptual understanding. (Contains 34 references.) (Author/ASK)

In a well-known calculus problem, an open top box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. The task is to find the dimensions of the box of maximum volume. Typically, the length of the sides of the corners that produces the largest volume turns out to be an irrational…

This paper describes a modification of a popular TV game show, "American Idol[R]," conducted in an undergraduate calculus course. The focal point of this game show is to get students to interact in competitive self-assessment. Student competition is an effective device to engage students in the learning process. Placing students in the role of…

Techniques that can be used in solving various mathematical problems are illustrated by an optimization problem and the accompanying model and solution. (MP)

Presents three sample problems related to arithmetic and algebra, geometry, and calculus, indicating, in each case, similar problems that could be posed. Includes a discussion of positive benefits which result by asking students "Can you derive the result differently?" (JN)

This paper describes the design and initial data analysis of an ongoing study to determine the important elements, as perceived by faculty, of the learning and teaching of problem solving in the context of an introductory calculus-based physics course. To elicit instructors' beliefs that inform their instructional choices, an interview around…

This article (the 1971 Presidential Address to the Mathematical Association of U. K.) makes a plea that college teachers of mathematics should be better aware of the applications of mathematics in other subjects. As an example, the author describes the use of differential equations to solve certain vibrational problems in mechanical engineering.…

Considered are the main elements of computational chemistry problems and how these elements can be used to formulate the problems mathematically. Techniques that are useful in devising an appropriate solution are also considered. (Author/TG)

Lists several problems that have proven to be successful in getting students to think about topics and notions they thought they knew. Indicates that students have not only solved the conundrums (often with help), but also developed them further into research projects. (Author/ASK)

Twelve unusual problems involving divisibility of the binomial coefficients are represented in this article. The problems are listed in "The Problems" section. All twelve problems have short solutions which are listed in "The Solutions" section. These problems could be assigned to students in any course in which the binomial theorem and Pascal's…

In their sections on inverses most precalculus texts emphasize an algorithm for finding f [superscript -1] given f. However, inspection of precalculus and calculus texts shows that students will never again use the algorithm, which suggests the textbook emphasis may be misplaced. Inverses appear primarily when equations need to be solved, which…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

To identify and describe the basis upon which instructors make curricular and pedagogical decisions, we have developed an artifact-based interview and an analysis technique based on multilayered concept maps. The policy capturing technique used in the interview asks instructors to make judgments about concrete instructional artifacts similar to…