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…

States that we are duly obligated to view student input from two perspectives: from what we see of their attitudes and from what they show us, frequently indirectly, of their learning. Describes student reactions to calculus reform, both positive and negative, and proposes better assessment measures that conjoin attitudinal and learning data. (PVD)

Addresses the assertion that the teaching of calculus using reform techniques puts students at a disadvantage when they must take subsequent math or science courses that are not instructed using the reform techniques. Answers the question of whether one method of instruction in calculus is better than another with regard to students' grades in…

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

A study involving 1,244 eighth-grade females who were high achievers in algebra, investigated characteristics of those who ended up taking calculus (n=474). Results showed differences between the two groups in mother's education, socioeconomic status, and educational aspirations. However, when applying all factors together, they did not predict…

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)

Compares outcomes of traditional and reform calculus courses in terms of students' retention of basic concepts and skills after the passage of time. Concludes that reform students retain better conceptual knowledge and traditional students retain better procedural knowledge. Demonstrates that reform calculus students understand concepts before…

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Questions students raise about the meaning of zero to the zero power present an opportunity for mathematics teachers to involve students in active participation in exploring mathematical relationships. Calculators are the needed tool to make this exploration accessible to students. How they can be used is described. (MNS)

Illustrates exploration of composition of functions, translations, and inverse functions on a graphing calculator. Includes reproducible student worksheets. (MKR)

Presents a strategy for graphing conic sections on the polar plane without using a table of values by beginning with information gained from the graphs of circular functions. (MKR)

Attempts to answer and generalize the question: When is the numerical derivative obtained on the graphing calculator greater than the actual derivative, and when is it smaller? Discusses symmetric difference. (MKR)

Describes the experiences and conclusions of a long-range program to revitalize undergraduate instruction in mathematics utilizing state-of-the-art workstations and the computer algebra system, Maple, and includes two examples of this type of instructional improvement. Focuses on computer-intensive calculus. (MKR)

Presents a solution to the problem of finding the probability that a needle would cross a crack in a tile floor when dropped. (MKR)

Utilizing composition of elementary functions as prototype of dynamical system, notions of periodic points and their orbits in relation to concept of shift map are used to illustrate concept of continuity. A special case of Sarkovskii's theorem, dealing with period-3 point, is presented with proof relying solely upon Intermediate Value Theorem and…