This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS…

This article describes a technology-based approach for dealing with a misconception that some students hold concerning the equivalency of geometric transformations. Students can begin to conceptualize transformations in terms of the relationship between preimage and image figures rather than focus on the motion of a figure. (Contains 7 figures.)

This article discusses the importance of measurement in providing a foundation for mathematical study and how measurement can be integrated with other mathematical strands. (Contains 1 table.)

During the preliminary stages of classroom-based research, this author conducted a sequence of interviews with six seventh graders regarding their understanding of fractions, decimals, ratios, and proportions. The students represented a variety of ability levels and were all in their first semester of prealgebra. The interviews began with notions…

This article describes an investigation involving several designs of airplane wings in trial flight simulations based on a NASA CONNECT program. Students' experiences with data collection and interpretation are highlighted. (Contains 5 figures.)

This article showcases four Shel Silverstein works and how they can be used to launch mathematics investigations across the curriculum. Each selection focused on a different mathematical strand; for example, a poem titled "Where the Sidewalk Ends" demonstrates measurement and proportional reasoning, and another poem, "Falling Up," demonstrates…

Computer algebra systems are being used more and more frequently in mathematics courses of all levels. For instructors to use these systems effectively, they need to have an idea of how the systems work. To illuminate the mechanics, the implementation of a simple computer algebra system will be described. Further, if instructors understand the…

The Departments of Mathematics and Statistics at Grand Valley State University are engaged in a project to address the mathematical preparation of all its majors, including prospective elementary and secondary mathematics teachers. In this article, we describe how the mathematics and mathematics education faculty in our mathematics department…

This article advances a view of Computer Algebra Systems (CAS) as powerful inquiry-based learning tools. Through an in-depth exploration of the "Emptying the Bowl" activity, upper level mathematics students test their own mathematical hypotheses, thoughtfully analyse and manipulate computer-generated output, and answer questions…

In a previous paper, we showed the importance of using low-level commands of a CAS in order to enhance the students' conceptual insight into mathematics. In this paper, we wish to emphasise a different use of a CAS, which makes possible the exploration of new topics, when the necessary theoretical results have still not been acquired, and avoids…

Previous studies on individual differences in mathematical abilities have shown that working memory contributes to early arithmetic performance. In this study, we extended the investigation to algebraic word problem solving. A total of 151 10-year-olds were administered algebraic word problems and measures of working memory, intelligence quotient…

Hurricane Katrina made landfall near New Orleans, Louisiana, on August 29, 2005. The author discusses the efforts she and other Association for Childhood Education International (ACEI) colleagues made for the welfare of children who suffered from the storm. After her initial search for family, friends, and professional colleagues, she began trying…

It is argued that studies of early adolescent peer victimization and bullying should be longitudinal because of the dynamism of this developmental period. Traditional methods for analyzing longitudinal data are inadequate because of the strict data requirements and inflexibility of models. A better alternative is linear mixed models (LMMs) for…

Student success in solving physics problems is related to the representational format of the problem. We study student representational competence in two large-lecture algebra-based introductory university physics courses with approximately 600 participants total. We examined student performance on homework problems given in four different…

This article describes a calculus project that exposes students to the concept of retirement annuities in both the saving and withdrawal phases, via revenue streams represented by integrals. Students use modeling skills to solve several related problems as the assumptions of the original problem are changed, and the project requires them to use a…