This paper sets forth some salient results in the algebra of circulant matrices which can be used in time-series analysis. It provides easy derivations of some results that are central to the analysis of statistical periodograms and empirical spectral density functions. A statistical test for the stationarity or homogeneity of empirical processes…

This note uses some elementary concepts in linear algebra to prove some well-known results in two- and three-dimensional geometry.

This article describes an activity for secondary school students that may constitute an appropriate opportunity to discuss with them the idea of proof, particularly in an algebraic context. During the activity the students may experience and understand some of the roles played by proof in mathematics in addition to verification of truth:…

Using Newton's method as an intermediate step, we introduce an iterative method that approximates numerically the solution of f(x) = 0. The method is essentially a leap-frog Newton's method. The order of convergence of the proposed method at a simple root is cubic and the computational efficiency in general is less, but close to that of Newton's…

This article illustrates the fact that unless tempered by algebraic reasoning, a graphing calculator can lead one to erroneous conclusions. It also demonstrates that some problems can be solved by combining technology with algebra.

Implications of the no-news no-change approach and student perceptions extends beyond the Monty Hall problem to two other situations in which the underlying concepts are similar.

We describe the design of a sequence of spreadsheet-based pedagogic tasks for the introduction of algebra in the early years of secondary schooling within the Purposeful Algebraic Activity project. This design combines two relatively novel features to bring a different perspective to research in the use of spreadsheets for the learning and…

The mathematics students are given a task to understand the fundamentals of liner functions by analyzing the height of the football stadium bleachers, as studying mathematical relationships in real-world contexts can enhance a student's knowledge of mathematics. The study of the stadium seating problem helps students to understand quadratic,…

The existing vector formalism method for thermodynamic relationship maintains tractability and uses accessible mathematics, which can be seen as a diverting and entertaining step into the mathematical formalism of thermodynamics and as an elementary application of matrix algebra. The method is based on ideas and operations apt to improve the…

In grade 8 (the only grade in which subgroup trends were analyzed by achievement level), California students made gains across the board in reading at the basic, proficient, and advanced levels for racial/ethnic subgroups, low income students, and boys and girls. In math, there were some declines at the basic achievement level. In terms of…

In grade 8 (the only grade in which subgroup trends were analyzed by achievement level), Arkansas showed across-the-board gains--improvements in reading and math at the basic, proficient and advanced levels for all racial/ethnic subgroups, low income students, and boys and girls. The gains were quite large in most instances, especially at the…

Competence in algebra is linked to access to higher education, employment in better-paying jobs, and, increasingly, the ability to earn a high school diploma. For many students with learning disabilities, developing proficiency in algebra represents a challenging, but necessary goal. Teachers of students with learning disabilities need access to…

Outreach mathematicians are college faculty who are trained in mathematics but who undertake an active role in improving primary and secondary education. This role is examined through a study where an outreach mathematician introduced the concept of complex variables to junior high school students in the United States with the goal of stimulating…

This study examined the relationship between teacher assessments and grade eight New Jersey NCLB mathematics testing. It also examined how curricular changes affected student achievement for one New Jersey junior high school on the NCLB mathematics test. The research considered teacher assessments and the New Jersey grade eight NCLB mathematics…

Assumptions: In mathematics learning, one of the considerations in the graphing calculator (GC) use is to understand students' attitude toward calculators. Rationale: This presentation describes design of an assessment instrument of students' attitude toward graphing calculator. Objectives: A pilot study that assessed the effectiveness of the…