The theory of error-correcting codes and cryptography are two relatively recent applications of mathematics to information and communication systems. The mathematical tools used in these fields generally come from algebra, elementary number theory, and combinatorics, including concepts from computational complexity. It is possible to introduce the…

The study investigated whether online professional development courses with different levels of support have different impacts on teacher outcomes. Variations of an online course for middle school algebra teachers were created for four experimental conditions. One was a highly supported condition, with a math education instructor, an online…

It is argued that algebra is a gateway to a rich high school curriculum and later success at a four-year college. Therefore, everyone should take algebra and take it as early as possible. In this article, the author contends that it is a fallacious argument that infers causation from correlation. He believes that the kids who take algebra early…

This article draws out many mathematical ideas connected with a familiar game often used by middle school teachers. (Contains 5 figures and 1 table.)

Solving algebraic word problems involves multiple cognitive phases. The authors used a multitask approach to examine the extent to which working memory and executive functioning are associated with generating problem models and producing solutions. They tested 255 11-year-olds on working memory (Counting Recall, Letter Memory, and Keep Track),…

To deeply understand proportional reasoning, students must be able to differentiate proportional situations from nonproportional situations. Unfortunately, the emphasis on the use of proportional strategies in middle-grades mathematics has led students to develop a disposition to associate certain characteristics of problem formulation with the…

Dutch universities complain that freshmen in studies such as chemistry, physics, economics and mathematics do not master the required algebraic skills. In the worldwide discussions on mathematics education, mastery of algebra is also a prevalent issue. Often a distinction is made between basis procedures and algebraic reasoning, so-called symbol…

This qualitative study examined the experiences of three eighth-grade prealgebra teachers as they planned student sensitive lessons for their ethnoculturally diverse students. The teachers worked in a lesson study group with a diversity consultant, an ESL (English as a second language) teacher who had a variety of multicultural experiences from…

Schools are institutions in which students' course taking creates series of linked learning opportunities continually shaped by not only curricular structures but demographic and academic backgrounds. In contrast to a seven-step normative course sequence reflecting the conventional hierarchical structure of mathematics, analysis of more than…

This document presents the proceedings of the 19th Annual Research Forum held June 26, 2014, at Wake Forest University in Winston-Salem, North Carolina. Included are the following 17 action research papers: (1) Using Voices to Change Minds: Oral Performance and Poetry in the English Classroom (Erika Bunpermkoon), (2) Imagining Audiences: The Use…

Students were asked to find all possible values for A so that the points (1, 2), (5, A), and (A, 7) lie on a straight line. This problem suggests a generalization: Given (x, y), find all values of A so that the points (x, y), (5, A), and (A, 7) lie on a straight line. We find that this question about linear equations must be resolved using the…

This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…

Some might argue that the true ability to think, perceive, and analyse mathematically is the ability to solve problems. Others might say that it has more to do with advanced applications of procedures in particular contexts. The author would like to put a slightly different spin on this by viewing it, at least partly, in terms of one's ability to…

Several activities that are based on the ancient method of false position, also called false assumption, are presented in this article as a way to motivate students to find the solution of literal equations in beginning algebra.

In the teaching of calculus, the algebraic derivation of the derivative (gradient function) enables the student to obtain an analytic "global" gradient function. However, to the best of this author's knowledge, all current technology-based approaches require the student to obtain the derivative (gradient) at a single point by…