Sfard and Kieran [Kieran, C., Educational Studies in Mathematics 46, 2001, 187-228; Sfard, A., Educational Studies in Mathematics 46, 2001, 13-57; Sfard, A. and Kieran, C., Mind, Culture, and Activity 8, 2001, 42-76] have developed a methodological framework, which aims at characterizing the students' mathematical discourses while they are working…

Many students struggle with college mathematics topics due to a lack of mastery of prerequisite knowledge. Set theory language is one such prerequisite for linear algebra courses. Many students' mistakes on linear algebra questions reveal a lack of mastery of set theory knowledge. This paper reports the findings of a qualitative analysis of a…

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

The Chinese used the idea of generating equivalent expressions for solving problems where the problems from a historical Chinese text are studied to understand the ways in which the ideas can lead into algebraic calculations and help students to learn algebra. The texts unify algebraic problem solving through complex algebraic thought and afford…

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,…

"Straight A's: Public Education Policy and Progress" is a biweekly newsletter that focuses on education news and events both in Washington, DC and around the country. The following articles are included in this issue: (1) "Setting the Stage for New High Schools": Alliance, National League of Cities Cohost Capitol Hill Briefing…

States are increasingly focusing the mission of their elementary and secondary education systems on preparing all students for success in postsecondary education and 21st century careers. As standards have increased, so too have graduation requirements. Today, 20 states and the District of Columbia have adopted such high school graduation…

Learning about mathematics begins in the early years. Through their everyday activities, young children build important foundational knowledge and understanding of mathematics, especially when adults provide specific opportunities to learn and practice concepts and skills. Young children develop early on an informal understanding of important…

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…