Search

This paper documents how the limit concept is treated in high school, at a university and in teacher education in England, France and Sweden. To this end we make use of vignettes, data-grounded accounts of the situation at the three levels in the three countries. These are analysed using the Anthropological Theory of the Didactic (ATD). While university praxeologies are relatively similar across the three countries, greater differences manifest themselves in high school and teacher education. For instance, at the high school level, in France a local praxeology on the limits of sequences is taught, which is not the case in England or Sweden. Results from the analysis of limits are extrapolated to comment on implications for the teaching of calculus, and for teacher education, in the three countries. The paper also raises methodological issues in our approach.

This paper takes a 'networking of theories' approach to understand the complexity of the phenomenon of agency. We examine an episode, where a kindergarten teacher and nine children work on an addition problem, from three different perspectives: Valsiner's zone theory; Radford's theory of objectification; and Pickering's dance of agency. Our networking of these approaches offers a way of thinking about agency as 'forces' that emerge through activity and operate on human actions. We end the paper by indicating that ethics, as a human relation, may be a catalyst for bringing out the potential that lies in the other agentic forces.

This paper examines a didactic phenomenon, a perception that the elements of sets have a common property, e.g. that {1, 2, 3} and {a, b, c} are sets but {1, 2, 3, a, b, c} is not a set. The paper reports manifestations of this phenomenon in one country: across a range of school students in textbooks and in curricula and across pre-service and in-service teachers. The paper considers interpretations of the results under various theoretical frameworks and argues that these interpretations can be synthesized around the anthropological theory of the didactic. The paper ends with implications for what is taught under the name 'mathematics'.

This paper reports on themes that arose in an investigation of university lecturers' views on the teaching of linear algebra. This focus on themes was the initial part of a study concentrating on four areas: What is important to teach in a first course in linear algebra? Are there teaching methods which are particularly suited for such a course? Are there tools that should/should not be used; and do the answers to these questions vary according to the degree (Engineering or Mathematics) the students follow? Questionnaire data was coded using thematic analysis which generated 11 themes related to the four questions above. The Results section presents the themes. The Discussion section considers the themes as a whole; splits -- dualities -- in teaching linear algebra; students' challenges with abstraction; aspects of doing mathematics; and pedagogical issues.

This paper presents 'expert opinions' on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors--called 'experts' in this study--addressed the following questions: What should be on a first-year linear algebra undergraduate course for engineering and/or mathematics students? How could such courses be taught? What tools (if any) are essential to these two groups of students? The results of the investigation, these experts' opinions, mainly concern what should be in a linear algebra course (e.g. problem-solving and applications) and what students should be able to do. The experts also emphasized that certain theoretical aspects (e.g. proofs, abstract structures, definitions and relationships) were more important to mathematics students. There was no real consensus among the experts on teaching methods or the use of digital tools, but this lack of consensus is interesting in itself. The results are discussed in relation to extant research.

This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in context. This model constitutes the basis of the second section where we describe an empirical study designed to investigate mathematical abstraction in socially rich (e.g., peer-interacted and tutor-assisted) environments. We then present data on two students working with the help of a tutor on tasks concerned with graphs of absolute value functions. On the basis of these data, we discuss four particular themes which are relevant to the purpose of this special issue and are important in the discussion of mathematical abstraction: human and artefact mediation, tutor interventions in assisting the formation of mathematical abstractions, implications of a dialectical view on student development, and the things that are abstracted. (Contains 1 footnote and 2 figures.)

This report explores first year undergraduate mechanical engineering and mathematics students' conceptions of the derivative and the contribution that membership of different departments may have on these conceptions. Quantitative results suggest that mechanical engineering students develop a proclivity for rate of change aspects of the derivative whilst mathematics students develop a proclivity for tangent-oriented aspects. The analysis of qualitative results further suggests that students' conceptual development of the derivative and their emerging identities are closely related and co-evolve in accordance with the departmental practices in which learning and teaching occur. (Contains 5 tables.) [For complete proceedings, see ED489632.]

This paper reports on classroom observations of senior high school mathematics lessons with a focus on the use of digital technology. The observations were of teachers enrolled in an in-service course, Teaching Advanced Mathematics. The paper reports selected results and comments on: software that was observed to have been used; the use (or not) of software for specific topics; who used the software and for what purpose; and implications for teacher development programmes.

This paper focuses on kindergarten teachers' interactions with young children during mathematical learning activities involving the use of digital tools. We aim to characterise the teachers' roles and actions in these activities and extend considerations of teachers' orchestrations current in the research literature with regard to agency and mediation. Our analysis of teacher-children-digital tool interaction reveals that the kindergarten teachers took three roles in their work with young children, which we call Assistant, Mediator and Teacher roles. These roles were used interchangeably and purposefully by the kindergarten teachers. With regard to agency and mediation, we argue that agency is distributed over the human and non-human agents in the activity and that agency and mediation are interrelated.