The analysis presented in this article tries to obtain a global view of the field of interactive learning environments (ILE) dedicated to arithmetic and algebra. As preliminaries, a brief overview of evaluation methods focusing on educational software is given and a short description of ten ILEs concerned by the study is provided as a kind of a…

The use of Computer Algebra Systems (CAS) is becoming increasingly important and widespread in mathematics research and teaching. In this paper, I will report on a questionnaire study enquiring about mathematicians' use of CAS in mathematics teaching in three countries; the United States, the United Kingdom, and Hungary. Based on the responses…

In this important resource, Dr. Fleming (a noted expert in the field of minority retention) draws on educational evaluations she has developed in the course of her distinguished career. This book analyzes the common factors and the role institutional characteristics play in minority student retention to show what really works in increasing…

In this era of high-stakes testing and accountability, curricula are viewed as catalysts to improve high school students' mathematics performances and a critical question is whether single subject or integrated curricula produce stronger student outcomes. This study was designed to investigate the effects of an integrated reform-based curriculum,…

The purpose of this quantitative quasi-experimental study was to analyze the effect of one type of professional development, Japanese lesson study, on student achievement at the high school level. The study examined the effect by comparing student achievement of students with non-lesson study teachers (control group) and those using the lesson…

Research investigating algebra students' abilities to generalize and justify suggests that they experience difficulty in creating and using appropriate generalizations and proofs. Although the field has documented students' errors, less is known about what students do understand to be general and convincing. This study examines the ways in which…

Newton's proof of the connection between elliptical orbits and inverse-square forces ranks among the "top ten" calculations in the history of science. This time-honored calculation is a highlight in an upper-level mechanics course. It would be worthwhile if students in introductory physics could prove the relation "elliptical orbit" [arrow right]…

In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year…

PreCalculus students can use the Completing the Square Method to solve quadratic equations without the need to memorize the quadratic formula since this method naturally leads them to that formula. Calculus students, when studying integration, use various standard methods to compute integrals depending on the type of function to be integrated.…

Reactions to John Monaghan's "Computer Algebra, Instrumentation and the Anthropological Approach" focus on a variety of issues related to the ergonomic approach (instrumentation) and anthropological approach to mathematical activity and practice. These include uses of the term technique; several possibilities for integration of the two approaches;…

The authors of this paper examine the use of formative assessment as a tool to assist teachers of mathematics to become more mindful developers of curricula. They focus on instructional design that is based on careful examination of student answers to questions. Empirical studies have shown the effectiveness of formative assessment for students,…

Student enrollment in K-12 online learning programs showed a tenfold expansion in the years between 2002 and 2005. Despite increased implementation to fulfill critical local needs, there is very little evidence-based research available to inform education leaders' decisions relating to these initiatives. To address the important question of…

A k-dimensional integer point is called visible if the line segment joining the point and the origin contains no proper integer points. This note proposes an explicit formula that represents the number of visible points on the two-dimensional [1,N]x[1,N] integer domain. Simulations and theoretical work are presented. (Contains 5 figures and 2…

The author introduces some basic dynamic programming techniques, using examples, with the help of the computer algebra system "Maple". The emphasis is on building confidence and intuition for the solution of dynamic problems in economics. To integrate the material better, the same examples are used to introduce different techniques. One covers the…

Geometric pattern tasks can be a useful tool for developing students' capacities to reason algebraically and in helping establish classroom norms and practices at the beginning of the school year. In this article, the authors consider the mathematical and social purposes that pattern tasks can serve by examining one middle school's…