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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 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 applies and extends Valsiner's "zone theory" (zones of free movement and promoted actions) through an examination of an intervention to establish inquiry communities in primary mathematics classrooms. Valsiner's zone theory, in a classroom setting, views students' freedom of choice of action and thought as mediated by the teacher. The extension of this theory adds that teachers' freedom of choice of action and thought is mediated by "significant others" and also by the actions of students with new freedoms. The paper presents necessary theoretical constructs and provides extracts from lessons and from teacher-teacher collaboration to illustrate the theoretical extension.

In TMA, Oldknow (2009, "TEAMAT", 28, 180-195) called for ways to unlock students' skills so that they increase learning about the world of mathematics and the objects in the world around them. This article examines one way in which we may unlock the student skills. We are currently exploring the potential for students to "see" mathematics in the real world through "marking" mathematical features of digital images using a dynamic geometry system (GeoGebra). In this article we present, as a partial response to Oldknow, preliminary results. (Contains 4 figures.)

Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on concept image and concept definition, is considered before outlining the research study, the calculus courses and results which inform considerations of concept image. Section 6 addresses three themes: students' developing concept images of the derivative; the relationship between teaching and students' developing concept images; students' developing concept images and their departmental affiliation. The conclusion states that studies of undergraduates' concept images should not ignore their departmental affiliations.

This article considers research and scholarship on the use of computer algebra in mathematics education following the instrumentation and the anthropological approaches. It outlines what these approaches are, positions them with regard to other approaches, examines tensions between the two approaches and makes suggestions for how work in this area can be extended.

The framework for this paper is a recently developed theory of abstraction in context. The paper reports on data collected from one student working on tasks concerned with absolute value functions. It examines the relationship between mathematical constructions and abstractions. It argues that an abstraction is a consolidated construction that can be used to create new constructions. Newly formed constructions are fragile entities. In the course of consolidating a construction this student creates connections between the new construction and already established mathematical knowledge and develops a language to describe and guide mathematical actions related to the construction. The resulting abstraction is a more resilient form of the construction and the student is able to justify his assertions. The paper also examines issues in designing tasks to consolidate a construction.

Examines the use of mathematics in a computer-aided design and manufacturing setting, whether this mathematics is related to school mathematics, how technicians understand this mathematics, and the role of technology in the technicians' mathematics-related problem solving activities. Focuses on technician's calculations of the interval volume of moulds they produce for glass factories. (Author/KHR)

Considers young peoples' views of infinity prior to instruction in the methods mathematicians use in addressing the subject of infinity. Presents a partially historical account of studies examining young peoples' ideas of infinity. Four sections address potential pitfalls for research in this area and the work of Piaget, issues concerning the contradictory nature of infinity and infinity as a process and as an object, infinite numbers, and contexts and tasks. (Author/MM)

Algebraic calculators with symbolic manipulation capabilities are tools in some classrooms for 14-19 year olds, and their use in learning and teaching mathematics is likely to increase over time. Explains the reports of government-initiated working groups that consider the implications of their use in academic mathematics examinations for 18-year-old students. (Author/ASK)

Presents the portion of a larger study of A-level British students understandings of calculus that deals with ambiguities inherent in the phrases "tends to,""approaches,""converges," and "limit." Responses to two questionnaires indicate that the four phrases generate everyday connotations that are at odds with the mathematical meanings. (MDH)

Reacts to an article published in a previous issue of this journal on the effects of graphing calculators and computer algebra systems (CAS) on students' manual calculation and algebraic manipulation skills. Considers the contribution made by Jean-Baptiste Lagrange to thinking about the role of CAS in teaching algebra. (ASK)

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. [ABSTRACT FROM AUTHOR]

This paper looks at the practices (or praxeologies) of mathematics education doctoral students and their supervisors from the perspectives of activity theory and the anthropological theory of the didactic. The paper examines three ways to view mathematics education research before discussing: research methods and methodologies ; the debate on qualitative and quantitative research ; and implications for the supervision of doctoral students. [ABSTRACT FROM AUTHOR]

This article addresses university students’ problem posing with a particular focus on importing photographs (of nature and of human constructions) into mathematical software to pose problems about mathematical properties of the object in the photograph. Student work is presented which leads to a discussion on the potential of the mathematical software GeoGebra to aid student mathematicizing and problem posing from visual images. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper reports on two students' work on geometry tasks in a dynamic geometry system. It augments prior work on students ' instrumental geneses via a consideration of emergent goals that arise in students' work. It offers a way to interpret students ' (working with new software) awareness of what software can and cannot do and students' developing sense of mathematical relationships in mathematical software. [ABSTRACT FROM AUTHOR]

This paper offers a framework, an extension of Valsiner's 'zone theory', for the analysis of joint student-teacher development over a series of technology-based mathematics lessons. The framework is suitable for developing research studies over a moderately long period of time and considers interrelated student-teacher development as well as the influence of 'significant others' on teacher development. After a short introduction, the paper sketches the need for a framework that can capture student and teacher development over technology-based mathematics lessons. It then outlines Valsiner's zone theory and the extension of this theory. The paper ends with a consideration of theoretical, methodological and practical issues in researching innovative mathematics classroom work with technology. [ABSTRACT FROM AUTHOR]

An introduction to the journal is presented in which the editors discuss various reports within the issue on topics including interactions of teachers and students using electronic-exercise-bases (EEB), technology-based lesson and activity theoretical framework for learning process.

In TMA, Oldknow (2009, TEAMAT, 28, 180–195) called for ways to unlock students’ skills so that they increase learning about the world of mathematics and the objects in the world around them. This article examines one way in which we may unlock the student skills. We are currently exploring the potential for students to ‘see’ mathematics in the real world through ‘marking’ mathematical features of digital images using a dynamic geometry system (GeoGebra). In this article we present, as a partial response to Oldknow, preliminary results. [ABSTRACT FROM AUTHOR]

This article considers research and scholarship on the use of computer algebra in mathematics education following the instrumentation and the anthropological approaches. It outlines what these approaches are, positions them with regard to other approaches, examines tensions between the two approaches and makes suggestions for how work in this area can be extended. [ABSTRACT FROM AUTHOR]

An introduction is presented which discusses various reports within the issue on topics including the construct cultural affordance in the software Alnuset, the activity theory, and the connection of reciprocal shaping between the tool and the learner.

Information about several papers discussed at the Seventh Congress of the European Society for Research in Mathematics Education (CERME 7) held February 9-13, 2011 in Poland on the theoretical approaches in research in mathematics education is presented. Topics include the onto-semiotic approach (OSA), the social dimensions of mathematics, and classroom activities from institutional and participant perspectives. The essential issue of the functionality of theoretical frameworks is also tackled.