Discusses common misconceptions in algebra, including: grouping symbols and order of operations; equations, inequalities, and expressions; and domains. Offers recommendations to help students avoid these mistakes. (MKR)

In this note, an integrated form of some significant means with two variables is provided, and some chains for mean value inequalities are obtained. At the same time, a concise family of algebraic functions appears, which satisfy Mitrinovic's requirements.

Illustrations on how algebra students can detect patterns and form conjectures are presented. In constructing algebraic proofs, students can see the crucial connections between whole-number operations and algebra and can proclaim, "Yes, it's always true."

A semigroup G is a group if it has a left identity and every element has a left inverse. The purpose of this note is to weaken this condition further in two different ways. A semigroup G with an identity e is a group if every element x in G has an inverse. It is well known that this statement can be weakened. A semigroup G with a left identity e…

In this paper the power of the [gamma] algorithm for obtaining the dual of a given cone and some of its multiple applications is discussed. The meaning of each sequential tableau appearing during the process is interpreted. It is shown that each tableau contains the generators of the dual cone of a given cone and that the algorithm updates the…

In this article, an alternative multiplication method for rhotrices is proposed. The method establishes some relationships between rhotrices and matrices. This article has discussed a modified multiplication method for rhotrices. The method has a direct relationship with matrix multiplication, and so rhotrices under this multiplication procedure…

Consider the family of monic polynomials of degree n having zeros at -1 and +1 and all their other real zeros in between these two values. This article explores the size of these polynomials using the supremum of the absolute value on [-1, 1], showing that scaled Chebyshev and Bernstein polynomials give the extremes.

In the last After the Bell column, the importance of algebraic thinking was discussed, with respect to a common practice used in scientific inquiry-the importance of rates. This column discusses the importance of functions in preparing students for empirical and experimental inquiry. Functions are not only a necessary mathematical tool for…

Several ways for solving inequalities have been suggested in the literature, among them graphical, verbal and algebraic solutions. A new look at solving inequalities via use of the intermediate value theorem is presented here, and this method may prove to be straightforward for many students.

Six proofs are given for the fact that for each integer n [greater than or equal to] 2, the nth root function, viewed as a function from the set of non-negative real numbers to itself, is not linear. If p is a prime number, then [Zeta]/p[Zeta] is characterized, up to isomorphism, as the only integral domain D of characteristic p such that D admits…

This article describes the connection between a novel puzzle and uses of algebra to generalize the fewest moves to solve it.

This article presents an alternative to the traditional method of multiplying polynomials, FOIL. The method can be used with any size of polynomial.

The purpose of the study is to present research focused on validating the four algebra cognitive models in Gierl, Wang, et al., using student response data collected with protocol analysis methods to evaluate the knowledge structures and processing skills used by a sample of SAT test takers.

Virtual Learning Environments (VLEs) are becoming increasingly popular in online education environments and have multiple pedagogical advantages over more traditional approaches to education. VLEs include 3D worlds where students can engage in simulated learning activities such as Second Life. According to Claudia L'Amoreaux at Linden Lab, "at…

This article presents a case study of a two-year pilot to increase pre-collegiate math course success rates at a large community college. The EnableMath pilot involved the use of computerized software that allowed students to practice math problems in a lab during class time. Additional components of the program included the administration of the…