Little empirical investigation has been conducted on high school students and teachers using online instructional multimedia developed entirely from the classroom teacher's traditional live-lecture format. This study investigated academic achievement, engagement, preference, and curriculum development using screen-capture instructional…

It is widely publicized that student attitudes and achievement in math in the United States require improvement. U.S. students have shown lackluster mathematics achievement scores compared to their international peers in other developed countries. As a former high school math instructor, this author observed that the attitude of many high school…

Knowledge of the equal sign as an indicator of mathematical equality is foundational to children's mathematical development and serves as a key link between arithmetic and algebra. The current findings reaffirmed a past finding that diverse items can be integrated onto a single scale, revealed the wide variability in children's knowledge of the…

In recent years, the learning of algebra by all students has become a significant national priority (Moses & Cobb, 2001; National Council of Teachers of Mathematics, 2000). Algebra is considered to be a foundational topic in mathematics (Usiskin, 1988) and some have argued that an understanding of algebra is fundamental to success in today's…

The GeoGebra software is attracting a lot of interest in the mathematical community, consequently there is a wide range of experience and resources to help use this application. This article briefly outlines how GeoGebra will be of great value in statistical education. The release of GeoGebra is an excellent example of the power of free software…

The purpose of this paper is to describe the process by which a pair of undergraduate students, participating in a teaching experiment, reinvented (with guidance) the concepts of group and isomorphism beginning with an exploration of the symmetries of an equilateral triangle. The intent of this description is to highlight some important insights…

Some beginning students of statistics and econometrics have difficulty with traditional algebraic approaches to explaining regression and related techniques. For these students, a simple and intuitive diagrammatic introduction as advocated by Kennedy (2008) may prove a useful framework to support further study. The author presents a series of…

This note presents demonstrations of mathematics that emerges when problems are posed with respect to a combined 12 x 12 multiplication table showing multiplier and multiplicand. Through processes such as recognizing and extending patterns, specializing and generalizing particular functional relationships between the diagonal and row sequences are…

The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…

The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…

Early in their introductory college linear algebra class, the author's students learn to use a matrix to represent and solve systems of linear equations. Indeed, this simple idea is perhaps the foundational idea of the course. Nevertheless, the author was delighted to find that the study of linear systems can lead to surprisingly deep mathematics.…

Geometric algebra is based on two simple ideas. First, the area of a rectangle is equal to the product of the lengths of its sides. Second, if a figure is broken apart into several pieces, the sum of the areas of the pieces equals the area of the original figure. Remarkably, these two ideas provide an elegant way to introduce, connect, and…

This study investigated the extent to which student performance and teacher perception of student performance affect placement in eighth-grade mathematics classes for students with disabilities. Authors used the Early Childhood Longitudinal Study--Kindergarten dataset to investigate how each of the following factors predicted placement in…

Now entering into its 20th year of data collection, Trends in International Mathematics and Science Study, (TIMSS) is an international assessment of mathematics and science at the fourth and eighth grades. TIMSS 2015 is the most recent in the TIMSS series, which began with the first assessments in 1995 and has continued every four years--1999,…

Using an apparently simple problem, ''Design a cylindrical can that will hold a liter of milk,'' this paper demonstrates how engineering design may facilitate the teaching of the following ideas to secondary students: linear and non-linear relationships; basic geometry of circles, rectangles, and cylinders; unit measures of area and volume;…