In this paper we present a versatile technique to solve several types of solvable quintic equations. In the technique described here, the given quintic is first converted to a sextic equation by adding a root, and the resulting sextic equation is decomposed into two cubic polynomials as factors in a novel fashion. The resultant cubic equations are…

This paper introduces a class of matrices, the rows and columns of which add up to identical constants (generally speaking, different for rows and columns). Some properties of these matrices, which will be called "magic rectangles" are discussed.

This study illustrates how a diagnostic testing model can be used to make detailed comparisons between student populations participating in international assessments. The performance of Turkish students on the TIMSS-R mathematics test was reanalyzed with a diagnostic testing model called the Rule Space Model. First, mathematical and cognitive…

Secondary special educators are in desperate need of progress monitoring measures in mathematics that appropriately reflect their students' instructional content. As educators across the country respond to increasing standards for challenging curricula, growing numbers of students with disabilities are participating in more advanced mathematics…

This correlational study examined the relationship between gender and the students' attitude and prior knowledge of using one of the mathematical software programs (MATLAB). Participants were selected from one community college, one state university and one private college. Students were volunteers from three Calculus I classrooms (one class from…

This study investigates whether the functions linking number-correct scores to the College-Level Examination Program (CLEP) scaled scores remain invariant over gender groups, using test data on the 16 testlet-based forms of the CLEP College Algebra exam. To be consistent with the operational practice, linking of various test forms to a common…

This interview study takes place in the context of a single small district in the United States. In the algebra curriculum of this district, there was a shift in the conception of equation, from a statement about unknown numbers to a question about the comparison of two functions over the domain of the real numbers. Using two of Shulman's…

This study examined conceptions of algebra held by 30 preservice elementary teachers. In addition to exploring participants' general ''definitions'' of algebra, this study examined, in particular, their analyses of tasks designed to engage students in relational thinking or a deep understanding of the equal sign as well as student work on these…

The purpose of this study was to determine the effect of systematic instruction with a concrete representation on the acquisition of an algebra skill for students with moderate developmental disabilities. Three high school students with moderate developmental disabilities participated in this study. A multiple probe across participants research…

The concept of "revoicing" has recently received a substantial amount of attention within the mathematics education community. One of the primary purposes of revoicing is to promote a deeper conceptual understanding of mathematics by positioning students in relation to one another, thereby facilitating student debate and mathematical…

Algebra knowledge is a critical part of middle-school mathematics achievement, and success in algebra is necessary for taking higher level mathematics courses and leads to higher scores on standardized tests. The purpose of this study was to simultaneously examine relationships between mathematics beliefs, classroom instructional strategies, and…

Ensuring that students have a strong foundation in mathematics by the end of 7th grade is essential if they are to move successfully into an advanced math curriculum that begins with algebra. But student achievement at the end of 7th grade varies widely in California--and this has consequences. Some 7th graders are taking a full Algebra I course;…

The purposes of this study were to (1) investigate non-accelerated middle schools students' understanding of pre-algebraic concepts, in particular, addition and subtraction of integers and the notion of equality; (2) describe and analyze how non-accelerated middle school students interact with The Geometer's Sketchpad (GSP) applets depicting…

As a follow up to the National Council on Teacher Quality (NCTQ) national studies of how well elementary teachers are prepared to teach reading and mathematics, NCTQ looked at preparation in both subjects in all undergraduate teacher preparation programs in Utah. This study evaluated Utah's nine undergraduate elementary teacher preparation…

The implementation of a new mathematics syllabus in the elementary context is problematic, especially if it contains a new content area. A professional development model, Transformative Teaching in the Early Years Mathematics (TTEYM) was specifically developed to support the implementation of the new Patterns and Algebra strand. The model was…