Montgomery County Public Schools (MCPS) "Special Education at a Glance," which includes a copy of the "Guide to Planning and Assessing School-Based Special Education Programs," provides in a single document, information about the special education population at each Montgomery County public school, including enrollment,…

Around 300 BC, Euclid wrote "The Elements", a major treatise on the geometry of the time, and what would be considered "geometry" for many years after. Arguably "The Elements" is the second most read book of the western world, falling short only to The Bible. In his book, Euclid states five postulates of geometry which he uses as the foundation…

Montgomery County Public Schools (MCPS) "Special Education at a Glance," which includes a copy of the "Guide to Planning and Assessing School-Based Special Education Programs," provides in a single document, information about the special education population at each Montgomery County (Maryland) public school, including…

This report presents results of the 2009 National Assessment of Educational Progress (NAEP) in mathematics at grades 4 and 8. The results from the 2009 assessment presented in this report are compared to those from previous years, showing how students' performance in mathematics has progressed over time. Results for students in the nation, the 50…

In this paper, using the Lambert series and other known results, the authors consider the computation of a class of series involving the powers of generalized Fibonacci and Lucas numbers, and obtain their approximate values.

In this article quadrilaterals with concurrent maltitudes are characterized. A generalization of the maltitudes is given, and a larger family of quadrilaterals for which an analogous property of concurrency holds is determined and studied.

Students' difficulty with reasoning and justification in the context of proofs in geometry has been well documented. Studies reveal that many of the ideas that students are asked to prove are known to be true, and therefore, the process of such proof is likely to remain meaningless and purposeless. The implication of this claim is that students…

This note provides a self-contained introduction to conics as loci of points equidistant from circles, lines and points, including a study of the loci of points equidistant from two circles, separated, intersecting or touching. (Contains 1 table and 8 figures.)

Between the 17th and 19th centuries, the Japanese government closed its borders to the outside world in an attempt to become more powerful. Foreign books were banned, people could not travel, and foreigners were not allowed to enter the country. One result of this isolation was the flourishing of sangaku--wooden tablets inscribed with intricately…

As time has progressed, the role of applied mathematics has become increasingly important. Indeed there are now more students enrolled in applied mathematics courses in senior high schools and colleges than in pure mathematics. Such courses become more relevant both to the student and to future employers, if the same constants and equations that…

The author of this article, while recently working through some problem sets on determining volumes by triple integrals in cylindrical and spherical coordinate systems, realized that, although the textbook he was using included many interesting problems involving spheres, cylinders and cones and the increasingly complex solids that arose from the…

Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…

Montgomery County Public Schools (MCPS) "Special Education at a Glance," which includes a copy of the "Guide to Planning and Assessing School-Based Special Education Programs," provides in a single document, information about the special education population at each Montgomery County (Maryland) public school, including…

Representative samples of fourth- and eighth-grade public school students from 21 urban districts participated in the 2011 National Assessment of Educational Progress (NAEP) in mathematics. Eighteen of the districts participating in the 2011 NAEP Trial Urban District Assessment (TUDA) participated in earlier assessment years, while three districts…

The purpose of this report is to examine results in mathematics for the ACT Educational Planning and Assessment System (EPAS) in schools nationwide. EPAS consists of three programs: EXPLORE[R] (for students in grade 8 or 9), PLAN[R] (for students in grade 10), and the ACT[R] test (for students in grade 11 or 12). The following questions are…