The Mobius strip, torus, and Klein bottle are used to graphically and analytically illustrate the differences between orientable and non-orientable surfaces. An exercise/laboratory project using the non-orientable Boy surface is included. (Contains 11 figures.)

In this article, the author proves a theorem about polynomial zeros, but the focus is on how the theorem is integrated into a QuickBASIC computer program, and how that program answers the questions of the theorem--a unification of mathematics and computer programming. For a given polynomial, how can one overcome assorted problems in finding zeros…

Rhymes are often useful teaching devices for small children, and can even become a creative resource for teaching mathematics. The students and their teachers can change many of them to better fit their environment and/or extend the rhyme so that higher numbers are involved. A number of rhymes and folk tales lend themselves to more detailed…

This article illustrates how a computer algebra system, such as Maple[R], can assist in the study of theoretical fluid mechanics, for both Newtonian and non-Newtonian fluids. The continuity equation, the stress equations of motion, the Navier-Stokes equations, and various constitutive equations are treated, using a full, but straightforward,…

This classroom scholarship report is based on the teaching experience using Davydov's mathematics curriculum, which was developed in the former Soviet Union. While "from arithmetic to algebra" is the normally accepted instructional sequence in school mathematics, Davydov's curriculum is laid out "from algebra to arithmetic," focusing on algebraic…

This study examines a math journal writing assignment comparing how high school (grades 10 through 12) algebra students who performed well and students who performed poorly on traditional mathematics tests constructed their corresponding journal entries. Statistically significant differences found indicated that students who performed well on the…

Computer software that shows students visual models of mathematical concepts--and lets them manipulate those models by doing math--has a certain intuitive appeal. Now, recent research on SimCalc Mathworlds, one of the pioneering examples of such software, is providing some of the best evidence so far that the approach can lead to gains in student…

"Saxon Math" curricula and materials are available for grades K through 12, with the content and skills designed to meet National Council of Teachers of Mathematics (NCTM) standards and various state standards. This WWC report focuses on middle school math curricula, defined as all Saxon Math curricula for grades 6 through 9. The…

Montgomery County Public Schools (MCPS) "Special Education at a Glance." which includes a copy of the "Guide to Planning and Assessing School-Based Special Education Programs." provides in a single document, information about the special education population at each Montgomery County (Maryland) public school, including…

This paper describes a 2-year collaborative action research project in which the focus was to investigate the effects of the use of "Hands-On Equations" mathematics manipulatives in an algebra class on students' confidence, interest in, and ability to solve and retain understanding of algebraic equations. The first phase centered on documenting…

This study investigated the development of students' abilities to see connections between algebraic equations and life-situated relationships during an extended problem solving experience. The design problem required students to analyze some aspect of their socio-physical environment for cause and effect and to generate a dynamic model using the…

Background information on the history and rationale for Tech Prep introduces the description of a study that examines the perceptions of students enrolled in Applied Mathematics 1 and Applied Mathematics 2 courses which are based on the Center for Occupational Research and Development's (CORD) applied mathematics curriculum. The primary goal is to…

This study examined effects of cultural and curricular variables on algebraic reasoning in early and middle adolescence. Four algebra curricula in England and Russia were included in the design. Two age groups were included in the samples: 10- to 14-year-olds, and 14- to 16-year-olds. Algebraic reasoning processes were examined using a written…

Exploring whether deductive reasoning can develop adequately without special instruction, this paper presents two studies that examine the development of meta-components of deductive reasoning, first in algebra, and second in verbal reasoning. The first study examined students' understanding of logical necessity in algebraic tasks in different…

This paper speaks to the challenges, risks, and rewards of teaching about linear functions in a technology-rich environment from a constructivist perspective by describing a Foundations of Algebra class, which was designed and taught to junior high school students in such an environment in the summer of 1991. The design and implementation of the…