Links the use of Computer Algebra Systems (CAS) to an existing classification scheme for mathematical tasks called the MATH Taxonomy. Illustrates through concrete examples how the goals of teaching and learning mathematics can be set using this classification together with the CAS. (Author/MM)

In many countries, the traditional processes of algebra have received criticism from educational reformers. Current reform policies, national frameworks, and local implementing statements have encouraged an algebra-for-all curriculum for students. After years of effort to improve the teaching of algebra, studies indicate that students usually do…

Takes the concept of using a geometrical or visual approach to teach algebraic concepts and extends it to connect with the section on binomial expansion by using three dimensional objects. (ASK)

Investigates secondary mathematics teachers' concept definitions, mathematical understanding, and pedagogical content knowledge of slope. Indicates that geometric ratios dominated teachers' concept definitions of slope, and teachers' descriptions of classroom instruction included physical situations more often than functional situations. (Contains…

Describes the use of an application for TI-83 and TI-92 calculators called the Symbolic Math Guide (SMG) for teaching and learning the laws of exponents in algebra. Discusses ways in which the SMG can be used for teaching, review, and testing. (MM)

Not too many years ago the author started out to study the students' own perspectives on their experience with the intent to answer the question, "How do college remedial math students define success, and what are they striving for in their math classes?" The author did not quite manage to answer such a grand question, but did gain some very…

The advent of powerful Computer Algebra Systems (CAS) continues to dramatically affect curricula, pedagogy, and epistemology in secondary and college algebra classrooms. However, epistemological and pedagogical research regarding the role and effectiveness of CAS in the learning of algebra lags behind. This paper investigates concerns regarding…

Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the…

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

This article presents a brief biography of Johann Carl Friedrich Gauss. Gauss was born on April 30, 1777, in the German city of Braunschweig (Brunswick). He was the only child of Gebhard Dietrich Gauss and Dorothea Benze. Neither of Gauss's parents had much education, his father could read and write, but earned his living doing menial jobs such as…

This study examined how 4 middle school textbook series (2 skills-based, 2 Standards-based) present equal signs. Equal signs were often presented in standard operations equals answer contexts (e.g., 3 + 4 = 7) and were rarely presented in nonstandard operations on both sides contexts (e.g., 3 + 4 = 5 + 2). They were, however, presented in other…

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of…

Despite the ready availability of computer algebra packages, from a pedagogical point of view, the authors still feel that integration should be taught extensively the classical way, by means of carefully selected examples which combine as many fundamental techniques as possible for their evaluation. Furthermore, whenever possible, these examples…

The ubiquity of calculators led to many "computational abuses", when numbers substitute for substance. On the other hand, it resulted in decrease in number oriented dexterity of students. The latter led to a disdain for even simple calculations to work about unfamiliar mathematical problems. As a reaction to the former, the reputation of…