Painting the Cube is commonly used in middle and high school mathematical courses as a mathematically rich problem, wherein the exposed faces of the large cubes are painted after being assembled from small unit cubes. The problem perfectly combines algebraic as well as geometrical aspects and helps students to study and understand various linear,…

In this article I discuss the factors that led me to implement study groups in the teaching of mathematics. An important influence in this decision began with an experimental study conducted with two College Algebra classes in which students were randomly assigned to treatment groups. While there was no statistical difference between the study…

Although the WebQuest has been around for several years, it appears that not many educators are aware of it, or know how to use it. Thus, it is important to not only expose developmental educators to the use of this strategy, but also to help them realize how they can easily implement it into their curriculum. The use of a Webquest integrates…

This study investigated factors promoting the use of self-constructed diagrams by examining students' perceptions and daily class activities, and comparing Japanese (n = 291) and New Zealand (n = 323) students. Algebra word problems and a questionnaire were administered. The results revealed that the New Zealand students used diagrams more often…

Middle school teachers realize the value of students playing games in mathematics classes if those games emphasize problem-solving strategies, algebraic reasoning, or spatial sense. This article describes various versions of the traditional game of nim and shows how working backward can be used to find a winning strategy. The link is then made…

Computer Algebra Systems (CAS) are increasing components of university-level mathematics education. However, little is known about the extent of CAS use and the factors influencing its integration into university curricula. Pre-university level studies suggest that beyond the availability of technology, teachers' conceptions and cultural elements…

The majority of new jobs in the 21st century will require some postsecondary education. Yet more than one third of those entering college are underprepared and needful of remediation. In this essay the author shares with the reader his first experience of teaching the lowest level prealgebra course at an urban community college. This is a story of…

This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview…

This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…

Both virtual and physical manipulatives are reported as effective learning tools when used with different groups of students in a variety of contexts to learn mathematical content. The use of multiple representations and the flexibility to translate among those representational forms facilitates students' learning and has the potential to deepen…

This brochure is part of NAEPFACTS, a new series that briefly summarizes findings from the National Assessment of Educational Progress (NAEP). Course-taking is generally a powerful indicator of mathematics achievement. This occurs partially because students who are more proficient tend to take more mathematics classes and, at the eighth grade, the…

This book takes the position that the teaching of elementary linear algebra can be made more effective by emphasizing applications, exposition, and pedagogy. It includes the recommendations of the Linear Algebra Curriculum Study Group with their core syllabus for the first course, and the thoughts of mathematics faculty who have taught linear…

This article reports the results of a questionnaire applied to secondary school students (n=35) to explore efficiency in the resolution of equations in the domain of whole numbers and the spontaneous responses to problems leading to negative solutions. The most significant results obtained with the questionnaire are the lack of knowledge of the…

This book aims to present helpful, practical ideas and suggestions for mathematics teaching. Focus is on how teaching can be developed in a Rudolf Steiner (Waldorf) School and includes treatment of mathematical topics applicable to the 7-14 age group. Suggestions for curriculum and examples for children to work on are presented with a very wide…

Research indicates that students have great difficulty solving algebra word problems and that few high school seniors have mastered the fundamentals of algebra, let alone algebra problem-solving skills. Improving students' algebra problem solving skills is considered to be critically important by those who have worked on reforming mathematics…