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The networking of theories is an increasingly common and powerful approach to analyzing complex phenomena such as learning processes in classrooms. In this paper, we aim to advance the theoretical coordination of two approaches that we have previously combined to analyze individual, small group, and whole class mathematical progress. The theoretical advances we make are twofold. First, we identify and illuminate environmental and internal-theoretical commonalities across the two approaches, commonalities that contribute to the productivity of networking. Second, we propose an argumentative grammar for the networking, thus elevating the methodological logic and rationale of networking in this case and potentially in general. [ABSTRACT FROM AUTHOR]

This paper is part of a broader study that draws on Wenger's (Wenger, E.: 1998, Communities of Practice: Learning, Meaning, and Identity, Cambridge University Press, New Work) social practice perspective to investigate teacher learning. The study extends Wenger's complex model of interrelated components of leaning (as meaning, practice, identity and community) to describe and explain teacher learning that occurs within a mathematics senior-phase in-service program that was stimulated by curriculum change. The study uses qualitative ethnography in which the researcher performs the dual role of both coordinator and researcher of the in-service practice. In a longitudinal study the phenomenon of confidence emerged in teachers' descriptions and explanations of their learning. In this paper I explore this phenomenon both empirically and theoretically. The extension of Wenger's (1998) theory to include the overarching and interacting component of confidence is embedded in and derived from data analysis of 10 teachers' learning, over a 2-year period, during a time of radical curriculum change. Since it would be incoherent within this framework to draw on psychological explanations of confidence I set out to explore confidence from within a social practice frame in a way that is grounded in data of the teachers in this study. The paper offers a concept of confidence in relation to teacher learning as 'learning as mastery', and confidence as both a product and a process of learning. Teachers can at once state their confidence as mathematics teachers, and their confidence to admit to what they do not know and still need to learn. It is argued that this is a primary condition for ongoing learning in a profession like mathematics teaching. In addition, the paper provides a critique of the applicability of Wenger's work to the context of teacher education and in particular highlights the absence of the notion of confidence within his work. [ABSTRACT FROM AUTHOR]

This paper develops an understanding of the issues, interests and concerns within the mathematics education community related to the use of computers and other digital technologies in the teaching and learning of mathematics. It begins by arguing for the importance of understanding this landscape of interests and concerns, and then turns to the theoretical and methodological choices made in this study, explaining how it has drawn on the approach developed by the STELLAR European Network of Excellence. By analysing the titles and abstracts of a conference chosen to represent the mathematics education community, it maps out the landscape framed by three 'Grand Challenges', finding that an understanding of orchestrating learning is at the heart of the interests of the community, and that the community is interested in exploring new and different contexts for the teaching and learning of mathematics. However, there is currently less interest in investigating and exploiting the increasing connectedness of learners within this community. Further, while the 'Grand Challenges' framing is useful in mapping the landscape, it fails to take into account both the personal concerns of teachers and students, such as attitude and confidence, and issues related to doing research and understanding research concerns. [ABSTRACT FROM AUTHOR]

This case study deals with a solitary learner’s process of mathematical justification during her investigation of bifurcation points in dynamic systems. Her motivation to justify the bifurcation points drove the learning process. Methodologically, our analysis used the nested epistemic actions model for abstraction in context. In previous work, we have shown that the learner’s attempts at justification gave rise to several processes of knowledge construction, which develop in parallel and interact. In this paper, we analyze the interaction pattern of combining constructions and show that combining constructions indicate an enlightenment of the learner. This adds an analytic dimension to the nested epistemic actions model of abstraction in context. [ABSTRACT FROM AUTHOR]

This paper comments on the expanded repertoire of techniques, conceptual frameworks, and perspectives developed to study the phenomena of gesture, bodily action and other modalities as related to thinking, learning, acting, and speaking. Certain broad issues are considered, including (1) the distinction between “contextual” generalization of instances across context (of virtually any kind—numeric, situational, etc.) and the generalization of structured actions on symbols, (2) fundamental distinctions between the use of semiotic means to describe specific situations versus semiosis serving the process of generalization, and (3) the challenges of building generalizable research findings at such an early stage in infrastructure building. [ABSTRACT FROM AUTHOR]

This paper reports the outcomes of an empirical study undertaken to investigate the effect of students’ cognitive styles on achievement in measurement tasks in a dynamic geometry learning environment, and to explore the ability of dynamic geometry learning in accommodating different cognitive styles and enhancing students’ learning. A total of 49 6th grade students were tested using the VICS and the extended CSA-WA tests (Peterson, Verbal imagery cognitive styles and extended cognitive style analysis-wholistic analytic test—Administration guide. New Zealand: Peterson, ) for cognitive styles. The same students were also administered a pre-test and a post-test involving 20 measurement tasks. All students were taught a unit in measurement (area of triangles and parallelograms) with the use of dynamic geometry, after a pre-test. As expected, the dynamic geometry software seems to accommodate different cognitive styles and enhances students’ learning. However, contrary to expectations, verbalisers and wholist/verbalisers gained more in their measurement achievement in the environment of dynamic geometry than students who had a tendency towards other cognitive styles. The results are discussed in terms of the nature of the measurement tasks administered to the students. [ABSTRACT FROM AUTHOR]

As a first step of a project on learning difficulties in elementary set theory, we carried out a study aimed at identifying some of the difficulties encountered by a group of 21 mathematics majors taking a course on logic and set theory. In this paper, we shall discuss one of the difficulties that we observed, namely a difficulty in conceiving a set as an object distinct from its elements, i.e. failing to fully grant sets the status of objects. This difficulty may be related to the following three types of errors that we observed in the students' first assignment: (1) confusing belonging and inclusion, (2) confusing the union of sets A, B, C, ... with the set whose elements are A, B, C, ... and (3) adding or deleting curly brackets. We shall present excerpts from the students' work illustrating these three types of errors and explain how they may be related to a difficulty in conceiving a set as an object distinct from its elements. [ABSTRACT FROM AUTHOR]

The CAME1 project was inaugurated in 1993 as an intervention delivered in the context of mathematics with the intention of accelerating the cognitive development of students in the first two years of secondary education. This paper reports substantial post-test and long-term National examination effects of the intervention, yet, by discussing the methodology used, questions the assumptions implicit in the original intention. It is now suggested that a better view is to regard CAME as a constructive criticism of normal instructional teaching, with implications for the role of mathematics teachers and university staff in future professional development. [ABSTRACT FROM AUTHOR]

The paper is a reflective account of the design and implementation of mathematical tasks that evoke uncertainty for the learner. Three types of uncertainty associated with mathematical tasks are discussed and illustrated: competing claims, unknown path or questionable conclusion, and non-readily verifiable outcomes. One task is presented in depth, pointing to the dynamic nature of task design, and the added value stimulated by the uncertainty component entailed in the task in terms of mathematical and pedagogical musing. [ABSTRACT FROM AUTHOR]

My purpose in this paper is to present a didactic tool – a set of specially designed problems and questions for discussion – that can help making students better aware of the various aspects of the formal notion of limit of a sequence. The didactic tool will be justified using results from my own and other authors' research on students' naïve or erroneous conceptions of limit of a sequence. [ABSTRACT FROM AUTHOR]

Provides a commentary on the papers presented in the issue of 'Educational Studies in Mathematics.' Range of general theories underpinning the emerging social paradigm; Development in mathematical learning; Analyses of tool mediation.