In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

All advocates of curriculum reform talk about an increased emphasis on conceptual understanding in mathematics. In this article, the authors use many examples to address the following issues: What does conceptual understanding mean, especially in introductory courses such as college algebra, precalculus, or calculus? How do we recognize its…

College students' strategies to discriminate relevant from irrelevant information in algebra story problems were identified and compared to strategies used by younger students in previous studies. College students identified numbers relevant for solution (Experiment 1) or provided verbal reports as they computed answers (Experiment 2). Type of…

English language learners (ELLs)--one of the lowest-achieving and fastest growing middle-school subpopulations--are challenged in the classroom by language components which could potentially jumpstart real mathematical growth for these and, eventually, all other students as well. Going beyond traditional word problems, this study documented and…

A heuristic description is given of the rediscovery with "Sketchpad" of a less-well-known, but beautiful, generalization of the nine-point circle to a nine-point conic, as well as an associated generalization of the Euler line. The author's initial analytic geometry proofs, which made use of the symbolic algebra facility of the TI-92 calculator,…

The New Zealand Ministry of Education has introduced a Numeracy Project for students aged 5-14 years in selected schools. The project encourages the adoption of flexible strategies for solving numerical problems, and discourages reliance on standard computational algorithms. One potential benefit of the project is that the methods students acquire…

This paper is concerned with the use of spreadsheets within mathematical investigational tasks. Considering the learning of both children and pre-service teaching students, it examines how mathematical phenomena can be seen as a function of the pedagogical media through which they are encountered. In particular, it shows how pedagogical apparatus…

This paper is inscribed within the research effort to produce evidence regarding primary school students' learning of algebra. Given the results obtained so far in the research community, we are convinced that young elementary school students can successfully learn algebra. Moreover, children this young can make use of different representational…

Differing perspectives have been offered about student use of recursive and explicit rules. These include: (a) promoting the use of explicit rules over the use of recursive rules, and (b) encouraging student use of both recursive and explicit rules. This study sought to explore students' use of recursive and explicit rules by examining the…

The article presents an integrated exposition of aspects of secondary school mathematics and a medical science specialty together with related classroom activities. Clinical medical practice and theoretical and empirical literature in mathematics education and radiology were reviewed to develop and pilot model integrative classroom topics and…

The use of the computer, and specifically the mathematics software package Maple, has played a central role in the authors' abstract algebra course because it provides their students with a way to see realistic examples of the topics they discuss without having to struggle with extensive computations. However, Maple does not provide the computer…

This paper addresses the dialectical relation between theoretical thinking and technique, as they co-emerge in a combined computer algebra (CAS) and paper-and-pencil environment. The theoretical framework in this ongoing study consists of the instrumental approach to tool use and an adaptation of Chevallard's anthropological theory. The main aim…

The "Connected Mathematics Project" is a problem-centered mathematics curriculum designed to help students in grades 6 to 8 develop mathematical knowledge, understanding, and skills. It contains eight student units for each grade level and covers five content strands: number and operations, geometry, measurement, data analysis and…

I Can Learn Algebra (ICL) is a standards-based math curriculum for use in grades 7 through 10 that was developed by New Orleans-based JRL Enterprises. ICL provides self-paced, interactive, computerized lessons and frequent assessments to track student progress. This Brief WWC Study Report reviews a study of the effects of ICL students' achievement…

This appendix focuses on the descriptive statistics of the middle study schools that participated in the "Gaining Ground in the Middle Grades: Why Some Schools Do Better. A Large-Scale Study of Middle Grades Practices and Student Outcomes. Initial Research." This appendix contains the following figures: (1) Student…