This article describes how to multiply binomials so that middle school students produce the equivalence (a + b)[superscript 2] = a[superscript 2] + 2ab + b[superscript 2] after reasoning about and representing problems. First, a two-dimensional array representation is used so that students can become comfortable with multiplication embedded in…

In this note, we present an improved Heaviside approach to compute the partial fraction expansions of proper rational functions. This method uses synthetic divisions to determine the unknown partial fraction coefficients successively, without the need to use differentiation or to solve a system of linear equations. Examples of its applications in…

Advanced mathematics courses have been developed and refined by the first author, using an action research methodology, for more than a decade. These courses use the computer algebra system (CAS) Maple in an "immersion mode" where all presentations and student work are done using Maple. Assignments and examinations are Maple files downloaded from…

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, "Using a sequence of number pairs as an example in teaching mathematics". Math. Comput. Educ., 39 (2005), pp. 198-205; Y. Shi, "Case study projects for college mathematics courses based on a particular…

In addition to data on overall performance since 1973, this article presents NAEP data on items that were recently released to the public. They are presented as examples of current student achievement in relation to achievement in the 1980s. Performance was stable or improving on most of the released items, with greatest improvement on items…

The introduction of the concept of the variable represents a critical point in the arithmetic-algebraic transition. This concept is complex because it is used with different meanings in different situations. Its management depends on the particular way of using it in problem-solving. The aim of this paper was to analyse whether the notion of…

Using a unique dataset, this dissertation analyzes the relationship between observable teacher characteristics and teacher effectiveness. Effectiveness is measured as a teacher's ability to improve student achievement on a standardized test. This analysis focuses on teachers of math and science at the elementary and middle school levels, as well…

The purpose of this research is to study the long-run impacts (i.e. on educational attainment) of a freshman math intervention called "double-dose algebra". The intervention was conducted in 2003 and 2004 within the Chicago Public Schools (CPS), a large, poor urban school district. In response to low passing rates in 9th grade algebra,…

This paper examines the Algebra II course and California Star Test (CST) proficiency levels in the San Francisco Bay Area and in the State of California. CST proficiency levels are examined by grade level for the State and nine counties of the San Francisco Bay Area region. Algebra II is shown to be one of the more complicated courses in the CSU…

A summer bridge program for incoming engineering and computer science freshmen has been used at the University of Wisconsin-Milwaukee from 2007 to 2010. The primary purpose of this program has been to improve the mathematics course placement for incoming students who initially place into a course below Calculus I on the math placement examination.…

In this article we examine gender differences in factors related to science, technology, engineering, mathematics, and medicine (STEMM) education and employment between the ages of 36 and 39. Using data from the Longitudinal Study of American Youth, we identified a STEMM high school talent pool. We found early gender differences in interest in…

Appropriate use of instructional technology can be an elusive quest for many faculty members. The iTouch is one of the latest technologies available to us, yet there is little literature on its use and effectiveness to support learners in their learning. Six new faculty members from various disciplines elected to integrate the device in their own…

This study researched a popularly used mathematics intervention, an extended time algebra class, and associated teacher professional development, to determine the effectiveness of this intervention on improving student mathematics performance. The study investigated whether providing additional time in class to struggling students along with…

The Carnegie Learning Cognitive Tutor curricula are based on cognitive models, which include a representation of the learner's thinking, strategies, and misconceptions. The Cognitive Tutor curricula typically speed up learning and yield greater learning as compared to traditional math curricula (Morgan & Ritter, 2002; Sarkis, 2004; Koedinger,…

2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mathematical Methods (CAS) Units 3 and 4. From 2006-2009 there was a common technology-free short answer examination that covered the same function, algebra, calculus and probability content for both studies with corresponding expectations for key…