Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)

A procedure for generating quasigroups from groups is described, and the properties of these derived quasigroups are investigated. Some practical examples of the procedure and related results are presented.

Robots are used in all kinds of industrial settings. They are used to rivet bolts to cars, to move items from one conveyor belt to another, to gather information from other planets, and even to perform some very delicate types of surgery. Anyone who has watched a robot perform its tasks cannot help but be impressed by how it works. This article…

Proofs that the area of a circle is nr[superscript 2] can be found in mathematical literature dating as far back as the time of the Greeks. The early proofs, e.g. Archimedes, involved dividing the circle into wedges and then fitting the wedges together in a way to approximate a rectangle. Later more sophisticated proofs relied on arguments…

Polynomial loglinear models for one-, two-, and higher-way contingency tables have important applications to measurement and assessment. They are essentially regarded as a smoothing technique, which is commonly referred to as loglinear smoothing. A SAS IML (SAS Institute, 2002a) macro was created to implement loglinear smoothing according to…

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

We present a comprehensive proof of the theorem that relates the weights and nodes of a Gaussian quadrature rule to its degree of precision. This level of detail is often absent in modern texts on numerical analysis. We show that the degree of precision is maximal, and that the approximation error in Gaussian quadrature is minimal, in a…

Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…

Background/Context: From two decades of research on the grading practices of teachers in secondary schools, researchers discovered that teachers evaluated students on numerous factors that do not validly assess a student's achievement level in a specific content area. These consistent findings suggested that traditional grading practices evolved…

Remedial mathematics at the college level has evidenced strikingly low retention and passing rates. It has been shown that at least 25% of the variation in student performance is explained by students' affective variables such as attitudes, study skills, and mathematics anxiety. This study endeavored to address affective variables by: (a)…

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

This two-group, pretest-posttest, quasi-experimental study compared secondary students' learning of Algebra II materials over a 4-week period when identical instruction by the same teacher was delivered through either embedded blended learning (treatment group; n?=?32) or a live-lecture classroom (control group; n?=?24). For both groups,…

This report summarizes Austin Independent School District's Title I, Part A program for 2014-2015. AISD annually receives federal NCLB Title I funds, based on the percentage of low-income students in the district's attendance zones, for the purpose of improving educational programs.

Tasks that develop spatial and algebraic reasoning are crucial for learning and applying advanced mathematical ideas. In this article, the authors describe how two early childhood teachers used stories as the basis for a unit that supports spatial reasoning in kindergartners and first graders. Having mathematical experiences that go beyond…

The author's teaching goal is always to make certain that his students, children and adults alike, have some reason for joining him on his mathematical journeys. The lesson he describes in this article provides him with the unusual opportunity to call attention to strategies that have had a long history and remarkable results. With careful…