This study focused on student achievement in ninth grade schools or academies compared to ninth grade students enrolled in traditional high schools. Student achievement was measured by standardized test scores. Other variables tested were gender and ethnicity. All students used in this study were enrolled in the ninth grade during the 2005-2006…

This paper posits the position that if higher education and secondary schools wish to increase students' college readiness, specifically in mathematics and critical thinking skills, continuous enrollment in secondary mathematics is one avenue worth exploring as opposed to increasing mathematics graduation requirements only in terms of Carnegie…

GRADES OR AGES: No mention. SUBJECT MATTER: Algebra. ORGANIZATION AND PHYSICAL APPEARANCE: The guide is divided into seven separately bound units. Unit headings are introduction, sets of numbers and axioms, open sentences in one variable, systems of linear open sentences, polynomials and factoring, rational numbers and expressions (A), and…

The purpose of this paper is to offer three alternatives to patterns or visualization used to justify division of fraction "algorithm" invert and multiply". The three main approaches are historical, similar denominators and algebraic, that teachers could use to justify the standard algorithm of division of fraction. The historical approach uses…

This article discusses the summability of some divergent series by Cesaro's method of successive arithmetic means. (MM)

The expectation that students be introduced to algebraic ideas at earlier grade levels places an increased burden on the classroom teacher to help students construct and justify generalizations. This study provides insight into the reasoning of 25 sixth-grade students as they approached patterning tasks in which they were required to develop and…

In this note the authors investigate ways to shorten the amount of work involved in using the Rational Roots Theorem to find the rational roots of a polynomial with integral coefficients. The first result is a proof of a fact that we had long suspected, but were never able to find the statement of in any of the college algebra textbooks we had…

The author offers a simple intuition that can be exploited to derive and to help interpret some canonical results in the theory of optimal commodity taxation. He develops and explores the principle that the marginal social welfare loss per last unit of tax revenue generated be equalized across tax instruments. A simple two-consumer,…

I report on the findings from research and literature on (a) use of symbols in mathematics, (b) algebraic/trigonometric expressions, (c) solving equations, and (d) functions and calculus. From these, some insights and implications for teaching and learning are derived.