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;…

This study originated from the realization that many community college students have significant difficulties with the concepts related to linear functions and their graphs even though these topics are included in the mathematics curriculum from about third grade onward. It is an attempt to identify possible gaps in the math standards in this…

Using a qualitative case study approach, this research explored the perceptions of middle school students on the role of their mathematics teacher in their success or failure to achieve in his mathematics classroom. Also, the study examined the teacher's perceptions of his role in the students' achievement. Further, the research explored the…

This article summarizes the creation and implementation of a concurrent support class for TRS 92--Intermediate Algebra, a developmental mathematics course at Fort Lewis College in Durango, Colorado. The concurrent course outlined in this article demonstrates a statistically significant increase in student success rates since its inception.…

The purpose of this study was to explore the utility of a dynamic assessment (DA) of algebraic learning in predicting third graders' development of mathematics word-problem difficulty. In the fall, 122 third-grade students were assessed on a test of math word-problem skill and DA of algebraic learning. In the spring, they were assessed on…

The results from a year-long study to investigate the technical features of easyCBM mathematics screening measures for first grade are presented. Measures were designed based on the National Council of Teachers of Mathematics Curriculum Focal Point standards, which for Grade 1 include (a) Number and Operations and Algebra, (b) Number and…

This study investigated the impact of mathematics curriculum (standards based vs. traditional) on the performance of sixth and seventh grade students with disabilities on multiple-choice and open-ended assessments aligned to one state's number and operations and algebra standards. It also sought to understand factors affecting student performance…

We describe our approach to incorporating a civic engagement component into a quantitative literacy (QL) course and the resulting gains in student learning, confidence, and awareness of local civic issues. We revised the existing QL course by including semester-long group projects involving local community issues that students could investigate…