Describes the Interactive Mathematics Program (IMP), a four-year curriculum that teaches algebra, geometry, and trigonometry together in a problem-solving process emphasizing logical analysis, inference, and deduction. Because the program presents mathematics in real-world contexts, teachers need time for consultation and planning. (LMI)

Investigates the probability of winning the largest prize at Bingo through a series of five simpler problems. Investigations are conducted with the aid of either BASIC computer programs, spreadsheets, or a computer algebra system such as Mathematica. Provides sample data tables to illustrate findings. (MDH)

Describes how the computer algebra system Mathematica can be used to enhance the teaching of the topics of sequences and series. Examines its capabilities to find exact, approximate, and graphically generated approximate solutions to problems from these topics and to understand proofs about sequences. (MDH)

Presents and discusses assumptions for a general-mathematics problem-solving curriculum that incorporate the belief that all students can do algebra, geometry, and trigonometry, that mathematics must be presented in problem situations, and that students should work cooperatively. Worksheets provide exemplary problem-solving activities. (MDH)

Describes an algebra course organized around the concept of function and based on intensive use of technology. Includes an explanation of the assessment sequence used to explore students' use of familiar representations and procedures to reason logically and to solve and communicate about unfamiliar tasks. (DDR)

Produces algebraic solutions by reducing the problems to equations and arithmetic solutions that do not use variables. Investigates how the arithmetic solution helps students better understand the problem before they approach it algebraically and how logic used in solving the problem arithmetically can be directly linked to the algebraic…

This article reports the results of a questionnaire applied to secondary school students (n=35) to explore efficiency in the resolution of equations in the domain of whole numbers and the spontaneous responses to problems leading to negative solutions. The most significant results obtained with the questionnaire are the lack of knowledge of the…

Discusses a classroom presentation using a Tonka toy truck's forward and backward motion that (1) develops a graphical representation of the truck's one-dimensional motion; (2) creates graphs representing constant velocity; (3) leads students to a definition of average velocity; and (4) introduces the concept of instantaneous velocity. (MDH)

Focuses on two types of symmetry, rotation and reflection, their underlying structure as a mathematical group, and their presence in the designs of diverse cultures. Illustrates patterns created by applying these symmetry operations that offer students a visual image which forms the axiomatic basis of algebra. (KHR)

Discusses errors made by remedial intermediate algebra students in factoring polynomials in light of student definitions of factoring. Found certain beliefs about factoring to logically imply many of the errors made. Suggests that belief-based teaching can be successful in teaching factoring. (16 references) (Author/MKR)

Presents a technique used during the first five minutes of class that elicits from students written responses to questions of their understanding of mathematical content or their attitudes toward their mathematics class specifically, or mathematics in general. Provides sample questions from algebra, geometry, and general mathematics. (MDH)

Activities for gifted math students at North Carolina's Governor's School East are described, including college-level coursework in linear algebra, group theory, probability, and computer programing; guest speakers; small group work; competitive events; committee work; and completion of a challenge course at a nearby camp. (JDD)

Suggests an approach to teaching vectors that promotes active learning through challenging questions addressed to the class, as opposed to subtle explanations. Promotes introducing vector graphics with concrete examples, beginning with an explanation of the displacement vector. Also discusses artificial vectors, vector algebra, and unit vectors.…

Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)

Describes a prototype package that uses algorithms created within the symbolic algebra system Axiom, numerical routines from the NAG Libraries together with the easy-to-use facilities of modern graphical interfaces. Considers the implementation of different techniques, both symbolic and numeric, for the analysis and calculation of interpolating…