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…

As of 2008, approximately 40% of eighth grade students in the United States enroll in Algebra I (National Council of Teachers of Mathematics, 2008). Although research has shown that students have more opportunities to take advanced mathematics courses by taking eighth grade Algebra I, in the United States, approximately only one-third to one-half…

In 2002/03, the Charlotte-Mecklenburg Schools initiated a broad program of accelerating entry into algebra coursework. The proportion of moderately-performing students taking 8th grade algebra increased from less than half to nearly 90%, then reverted to baseline levels, in the span of just six age cohorts. We use this policy-induced variation to…

The purpose of this study was to discover what teaching strategies were utilized by Special Day Class (SDC) teachers to prepare their 9-12 grade students to pass a course in Algebra 1 and the mathematics section of the California High School Exit Exam (CAHSEE). This study used a mixed methodology involving a quantitative survey and qualitative…

This research study assessed the effectiveness of a three-dimensional mathematics game, DimensionM, through a pretest-posttest control group quasi-experimental design. Participants consisted of 437 eighth graders. The classrooms were randomly assigned either to the treatment group that utilized DimensionM as a supplement to regular classroom…

Montgomery County Public Schools (MCPS) is more than a school system, it is a community. It's a community of people working together to provide Montgomery County students with an education that prepares them for success today, tomorrow, and in the years to come. That is MCPS' core purpose: to prepare students to thrive in their future. The Annual…

The 2015 edition of the "Annual Condition of Education Report" includes a rich set of information about the status of Iowa's K-12 education system. The report provides valuable feedback about Iowa's students, educators and school districts across a number of statewide measures. They include changes in student populations and…

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…