The study, "Technology's Edge: The Educational Benefits of Computer-Aided Instruction," examined whether the "I CAN Learn"[R] computer-based curriculum is more effective than traditional classroom instruction at teaching pre-algebra and algebra concepts to middle- and high-school students. The study included about 1,600…

This paper draws on a one year study of three secondary school classrooms to examine the nature of student-student-technology interaction when working in partnership with computer algebra systems (CAS) on mathematical modelling tasks and the classroom affordances and constraints that influence such interaction. The analysis of these data indicates…

Recent state legislation in Michigan mandates that all graduating seniors successfully pass algebra I and II. Numerous initiatives have been enacted to help mathematics teachers meet this challenge, yet school principals have had little preparation for the necessary curricular and instructional changes. To address this unmet need, university-based…

This research compared the effectiveness, in terms of mathematical achievement, of online homework to textbook homework over an entire semester for 145 students enrolled in multiple sections of college algebra at a large community college. A quasi-experimental, posttest design was used to analyze the effect on mathematical achievement, as measured…

This project is one of four that were issued to first semester sophomore undergraduates at the United States Military Academy as part of an integrated learning experience at the end of their Calculus II course work. This project was used during a short, seven lesson block of instruction that was intended to capitalize on their recent academic…

Seventy secondary mathematics pre-service teachers from two universities were assessed on their content knowledge, vocabulary knowledge, and their perceived confidence in teaching the content addressed on the eleventh grade state assessment. The results indicate the pre-service teachers had significant content weakness in data analysis, algebra,…

Flexible knowledge, knowing multiple approaches for solving problems, is a hallmark of expertise in mathematics. Frequently, the author writes, students memorize only one method of solving a certain kind of problem, without understanding what they are doing, why a given strategy works, and whether there are alternative solution methods. Comparison…

The Maui Hawaii Educational consortium sought evidence for the effectiveness of the "Cognitive Tutor[R] (CT) program, published by Carnegie Learning, to help inform adoption decisions. The question being addressed specifically by the research in both years of previous studies was whether students in classes that use "CT" materials…

This article provides a survey of some basic results in algebraic number theory and applies this material to prove that the cyclotomic integers generated by a seventh root of unity are a unique factorization domain. Part of the proof uses the computer algebra system Maple to find and verify factorizations. The proofs use a combination of historic…

In this article, the author explores the "algebra for all" issue to raise awareness about the many facets of this dilemma facing educators at the middle and high school levels. She discusses both sides of this controversial issue, especially regarding its impact on students' futures relative to higher education and employment. The author concludes…

After experiencing a Developing Mathematical Ideas (DMI) class on the construction of algebraic concepts surrounding zero and negative numbers, the author conducted an interview with a first grader to determine the youngster's existing level of understanding about these topics. Uncovering young students' existing understanding can provide focus…

New methods of teaching linear algebra in the undergraduate curriculum have attracted much interest lately. Most of this work is focused on evaluating and discussing the integration of special computer software into the Linear Algebra curriculum. In this article, I discuss my approach on introducing the concept of eigenvectors and eigenvalues,…

Four proofs, designed for classroom use in varying levels of courses on abstract algebra, are given for the converse of the classical Chinese Remainder Theorem over the integers. In other words, it is proved that if m and n are integers greater than 1 such that the abelian groups [double-struck z][subscript m] [direct sum] [double-struck…

Exact closed-form solutions of the time-dependent Schrodinger equation are obtained, describing the propagation of wavepackets in the neighbourhood of a potential. Examples given include zero reflection, total reflection and partial reflection of the wavepacket, for the sech[superscript 2]x/a, 1/x[superscript 2] and delta(x) potentials,…

For their course, mathematics students at Bath Spa University were asked to choose a topic and explore the mathematics. As well as learning some mathematics, the author hoped that the assignment would shed light on the process of mathematical investigation itself. Their course leader had suggested that the topic of conic sections was rich, and…