In educational practice, a test assembly problem is formulated as a system of inequalities induced by test specifications. Each solution to the system is a test, represented by a 0-1 vector, where each element corresponds to an item included (1) or not included (0) into the test. Therefore, the size of a 0-1 vector equals the number of items "n"…

This article presents situations involving perimeter, area, volume and mass, and the misconceptions often encountered with these measurements. The author suggests possible interventions that teachers can use to correct these misconceptions and help students to better understand these properties.

The Hill cipher is the simplest example of a "block cipher," which takes a block of plaintext as input, and returns a block of ciphertext as output. Although it is insecure by modern standards, its simplicity means that it is well suited for the teaching of such concepts as encryption modes, and properties of cryptographic hash functions. Although…

The authors explore the importance of "range" and its relationship to continuously differentiable functions that have inverses when their graphs are reflected about lines other than y = x. Some open questions are posed for the reader. (Contains 5 figures.)

The basic rules of elementary algebra can often appear beyond the grasp of many students. Even though most subjects, including calculus, prove to be more difficult, it is the simple rules of algebra that continue to be the "thorn in the side" of many mathematics students. In this paper we present a result intended to help students achieve a…

We present a derivation for the coordinates of the centre of mass--or centre of gravity--of a homogeneous triangular plate by using scaling and symmetry. We scale the triangular plate by a factor of 2 and divide its area into four plates identical to the original. By symmetry, we assert that the centre of mass of two identical masses lies at the…

This article presents a problem that can help high school students develop the concept of instantaneous velocity and connect it with the slope of a tangent line to the graph of position versus time. It also gives a method for determining the tangent line to the graph of a polynomial function at any point without using calculus. (Contains 1 figure.)

This article describes how students at North Central College do-si-doed their way to a deeper understanding of fractals, fractions, and abstract algebra. As part of the college's "Verandah" curriculum, David J. Schmitz, an associate professor of mathematics, led seven undergraduates, mostly math majors and minors, through an adventure in "math in…

The purpose of the study was to determine the technical adequacy of the Core Skills Algebra curriculum-based measure for students enrolled in algebra I courses at the high school level. Due to the dearth of curriculum-based measures available to educators at the secondary school level, the Core Skills Algebra curriculum-based measure was developed…

Through an examination of the underserved urban population, this paper takes a look at how the use of games and simulations may provide a means of closing a gap in education which has lingered for several decades. Discussion on how this engagement might look as both a class learning algebra through game programming and gameplay is reviewed. As…

A high school education, which includes access to advanced math courses, has a positive effect on students. Math classes taken in high school show a relationship to higher salaries and college graduation rates. However, the high-stakes accountability system in California, redesigned in 2003 to meet the requirements of the No Child Left Behind Act…

The purpose of this study is to understand how a policy that provided college-prep coursework for low-skill students may affect instructional organization within schools, and how such effects on instructional organization may have unintended consequences on academic outcomes of high-skill students who were not targeted by the policy. The author…

Despite increasing accountability requirements and a national call for transparency in public policy, Mid-Atlantic Region state education agencies indicate that they have little information about what instructional materials districts adopt. This report describes first-year results of an ongoing project to generate and share information on core…

This book examines the five key elements (meaningful use of symbols, mindful manipulation, reasoned solving, connection algebra with geometry, and linking expressions and functions) identified in "Focus in High School Mathematics: Reasoning and Sense Making" in more detail and elaborates on the associated reasoning habits. This volume is one of a…

This paper presents the results obtained from a study comparing the strategies used by 1,070 Chinese students and 1,002 Singaporean students from primary grade 6 to secondary year 2 in solving three fraction-related problems. It is part of the author's Ph.D. study, which involves more word problems on speed. The Chinese students performed better…