Argues that students should be given mathematics credits for completing accounting classes. Demonstrates that, although the terminology is different, the mathematical concepts are the same as those used in an introductory algebra class. (JOW)

Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

Reports on a study of the nature of abstract algebra students' understanding of permutations and symmetries. Examines the epistemology of permutations in a finite set of symmetries of a regular polygon. Concludes that the initial genetic decompositions of both concepts are relatively consistent with the data, although a few refinements of these…

Discusses the usefulness of Kuhn's concept of paradigm in describing major developments in mathematics and education. Presents the pre-Al-Khawarizmi paradigm in algebra and Al-Khawarizmi's algebra. Analyzes Al-Khawarizmi's algebra as a paradigm and discusses some pedagogical implications. Contains 11 references. (ASK)

In this paper, using the Lambert series and other known results, the authors consider the computation of a class of series involving the powers of generalized Fibonacci and Lucas numbers, and obtain their approximate values.

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…

In the year 1837 mathematical proof was set forth authoritatively stating that it is impossible to trisect an arbitrary angle with a compass and an unmarked straightedge in the classical sense. The famous proof depends on an incompatible cubic equation having the cosine of an angle of 60 and the cube of the cosine of one-third of an angle of 60 as…

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…