Examines possibilities for learning offered by a piece of software, Fonctuse, likely to encourage the linking of algebraic and graphical representations of functions. Studied the influence of prior algebraic knowledge on the cognitive processes and constructions of knowledge at play in this environment. (Author/MKR)

Four human judges agreed highly among themselves about the presence of errors committed by 60 adults solving algebra word problems, but were in less agreement about categorizing faults. An expert system agreed with judges about correctness of answers, but was in even less agreement about categorizing the faults. (SLD)

Reports on a case study of one student's pattern of engagement in an 8th grade algebra class. Argues both empirically and theoretically that none of the current theories of engagement and motivation serve to characterize the core of this student's decision about engagement: his affective assessment of mathematics. (Author/MM)

The expertise reversal effect occurs when a learning procedure that is effective for novices becomes ineffective for more knowledgeable learners. The authors consider how to match instructional presentations to levels of learner knowledge. Experiments 1-2 were designed to develop a schema-based rapid method of measuring learners' knowledge in a…

The purpose of this study was to examine how various opportunity to learn (OTL) variables impact student outcomes and whether these effects are consistent across different subject areas. In this study, we examined the impact of OTL variables on student performance on English and algebra assessments. Despite the differences in the subject areas, 3…

This article describes ways in which students develop schemas as they generalize and formalize patterns when solving related algebraic problems that involve size, shape, growth, and change. (Contains 7 figures and 3 tables.)

In this article, Laura Grandau traces a self-study research project focused on teaching algebra to fourth-grade students. Facing a new curriculum and a new grade level, Grandau considers what good instruction and "good habits of practice" may be. Through journaling, videos, observations, analysis of students' verbal and written responses, and…

The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…

Three issues about students' reasoning, proving and understanding proof in number patterns are investigated in this paper. The first is to elaborate the features of junior high students' reasoning on linear and quadratic number patterns. The second is to study the relationships between 9th graders' justification of mathematical statements about…

The purpose of this paper is to provide researchers with a shared framework, terminology and tool to improve the coherence of research into learning mathematics with CAS and to assist its findings to accumulate into a significant body of knowledge. Experience with calculators in arithmetic led to a framework for number sense. There is an obvious…

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…

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…

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…

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…