Search

In this paper, we draw on our recent research to inspect again some of the theoretical perspectives we have been using to analyze data and to characterize teaching-learning in university settings. We focus particularly, within a sociocultural perspective on Activity Theory and the construct the "Teaching Triad," seeking to embed the Triad within an Activity Theory perspective. To achieve this, we relate the Teaching Triad with aspects of the sociocultural setting both in and beyond direct interactions in face-to-face teaching. While this is mainly a theoretical paper, an example is taken from observations of teaching in university lectures in a Greek university to show how these theoretical perspectives have provided insights to the institutional and cultural complexities involved and in what ways the Triad construct has evolved.

The paper reports on updating and integrating two reformed curricula designed in an era of national crises in Greece. In particular, the curriculum design activity of the Leading Coordinators (LCs) is studied under the lenses of Activity Theory and Positioning Theory. Sixteen transcribed videotaped meetings over a period of ten months are analysed to examine LCs' positionings enacted within the design activity as well as the interaction of the latter with other activity systems in situ. LCs' discourse brought to the fore convergent and divergent positionings mainly related to their research identity, occasionally revealing tensions. Research was the dominant activity system that interacted with that of the curriculum design activity, giving rise to contradictions. These were intensified by socio-political implications of the crises and were mainly related to the formation of a shared object for the design activity, its course of development and the activity of other stakeholders.

This paper addresses implementation with respect to the professional development (PD) of teachers of mathematics and the educators/didacticians who work with them, through an "inquiry-based" developmental model. In contrast with a PD model in which educators show, guide or instruct teachers in classroom approaches and mathematical tasks, we present a developmental model in which teachers and educators collaborate to inquire into and develop their own teaching practice. The project, "Learning Communities in Mathematics" (LCM: e.g., Goodchild, Fuglestad and Jaworski, 2013) exemplifies this developmental model. Here we focus on a project "Teaching Better Mathematics" (TBM) which extends LCM and implements its developmental model at larger scale. We trace the implementation process through analysis of data gathered during and after the extended project, including written reflections of key didacticians, minutes from leadership meetings and two versions of the project proposal. Particularly, we trace learning and development through an activity theory analysis of the issues, tensions and contradictions experienced by participation in TBM.

This study explores teacher educators' (TEs') activity as they support mathematics and science teacher collaboration in co-designing and jointly implementing tasks. We view TEs' activity through the lens of Activity Theory and expansive learning and draw evidence from data generated within the mascil project that linked mathematics and science teaching with workplace situations through inquiry-based teaching. We focus on five TEs' actions and goals, use data from their professional development sessions with teachers and from the TEs' interactions during their own meetings, and highlight the illuminating case of one teacher educator. We trace evidence indicating paths of actions followed by each Teacher Educator and look for indications of their professional learning. Our analysis reveals generic and content-focused actions. All TEs faced different kinds of contradictions and had difficulties handling them. In terms of professional learning, all TEs adapted their prior teacher education practices and appreciated the critical role of epistemological differences between the two disciplines.

This paper investigates mathematics teaching to first year students of two mathematics departments in the context of large-group lectures. It goes beyond what may be seen as implicit in this context by focussing on the links between two lecturers' thinking about students' learning of advanced mathematics and their practice. Data includes lecture observations and reflective discussions with the lecturers. Three layers of data analysis are drawn on Activity Theory, the Teaching Triad, and, grounded analytical approaches. Findings suggest that the formation of teaching goals is motivated by aspects of sensitivity to student's participation and that the complementarities among these aspects are important qualitative characteristics of teaching in this context.

The reported study is situated within the process of developing a reform-oriented national mathematics curriculum for compulsory education in Greece by a design team that involved teachers, academic researchers, and policy-makers. From an activity theory perspective, we identify the activity systems of mathematics teaching, research in mathematics education, and educational policy interacting in the design process. We focus on the contradictions between the three activity systems and how these were dealt with. We based our analysis on email exchanges during the curriculum design, field notes from whole-team sessions, and interviews with key persons. Our results highlight that the emerging contradictions primarily concerned the teaching and research activity systems. Members of the team who acted as brokers between the different activity systems and facilitated their interaction played an important role in overcoming the contradictions.

The study reported in this paper concerns the tensions and conflicts that teachers experience while they enact a new set of reform-oriented curricular materials into their classrooms. Our focus is ?n the interactions developed in two groups of teachers in two schools for a period of a school year. We use Activity Theory to study emerging contradictions and we elaborate on the construct of dialectical opposition to understand the nature of these contradictions and their potential for teacher learning. We provide evidence that discussions about contradictions and their dialectical character in the two groups support teachers to engage differently in mathematics teaching and learning and carry potentials for shifts in the practices that evolve in their classrooms. Our study addresses empirically in the context of mathematics teaching the philosophical claim about the role of contradictions as a driving force for any dynamic system.

The present study explores reasoning and argumentation in Greek mathematics and physics texts in specific topics related to the notion of periodicity. In our study, argumentation is taken as the sequence of the modes of reasoning (MsoR) that an author develops in a text when organizing and presenting new knowledge. Inductive content analysis was applied on 71 thematic units taken from 4 mathematics and 4 physics textbooks, and a coding system of categories and subcategories of MsoR was produced. Our analysis discerned 4 main categories of MsoR: empirical, logical-empirical, nomological, and mathematical; we argue that each mode of reasoning (MoR) plays a different role in conceptualizing aspects of periodicity. Analysis of the sequence of MsoR in two thematic units raised pragmatic considerations on the text understanding in relation to the scientific argumentation discourse and highlights ontological differences in the two subjects when ascending from observations to generalizations. Educational implications of the findings are discussed.

In this study, we investigate the meaning students attribute to the structure of mathematical induction (MI) and the process of proof construction using mathematical induction in the context of a geometric recursion problem. Two hundred and thirteen 17-year-old students of an upper secondary school in Greece participated in the study. Students' responses in 3 written tasks and the interviews with 18 of them are analyzed. Though MI is treated operationally in school, the students, when challenged, started to recognize the structural characteristics of MI. In the case of proof construction, we identified 2 types of transition from argumentation to proof, interwoven in the structure of the geometrical pattern. In the first type, MI was applied to the algebraic statement that derived from the direct translation of the geometrical situation. In the second type, MI was embedded functionally in the geometrical structure of the pattern.

The study reported here concerns 4 years of collaboration between secondary school teachers and academic researchers, constituting an emerging community of inquiry into mathematics teaching. In the article, the process of forming of this community is discussed, focusing on the reflective activity developed by its members as well as the tensions and conflicts that emerged in the shaping of an inquiry identity by them. Furthermore, shifts in the mode of participation in the community and thus learning gains of all members are identified, with the teachers gradually developing an awareness of teaching practice in general, and the researchers becoming progressively acquainted with the reflexive relationship between inquiring into teaching practice and teachers' professional development.

This study investigates teachers' argumentation aiming to convince students about the invalidity of their mathematical claims in the context of calculus. 18 secondary school mathematics teachers were given three hypothetical scenarios of a student's proof that included an invalid algebraic claim. The teachers were asked to identify possible mistakes and explain how they would refute the student's invalid claims. Two of them were also interviewed. The data were analysed in terms of the content and structure of argumentation and the types of counterexamples the teachers generated. The findings show that teachers used two main approaches to refute students' invalid claims, the use of theory and the use of counterexamples. The role of these approaches in the argumentation process was analysed by Toulmin's model and three types of reasoning emerged that indicate the structure of argumentation in the case of refutation. Concerning the counterexamples, the study shows that few teachers use them in their argumentation and in general they underestimate their value as a proof method. (Contains 1 table and 3 figures.)

This paper investigates the role of tools in the formation of mathematical practices and the construction of mathematical meanings in the setting of a telecommunication organization through the actions undertaken by a group of technicians in their working activity. The theoretical and analytical framework is guided by the first-generation activity theory model and Leont'ev's work on the three-tiered explanation of activity. Having conducted a 1-year ethnographic research study, we identified, classified, and correlated the tools that mediated the technicians' activity, and we studied the mathematical meanings that emerged. A systemic network was generated, presenting the categories of tools such as mathematical (communicative, processes, and concepts) and non-mathematical (physical and written texts). This classification was grounded on data from three central actions of the technicians' activity, while the constant interrelation and association of these tools during the working process addressed the mathematical practices and supported the construction of mathematical meanings that this group developed from the researchers' perspective. Technicians' emerging mathematical meanings referred to place value, spatial, and algebraic relations and were expressed through personal algorithms and metaphorical and metonymic reasoning. Finally, the educational implications of the findings are discussed.

This paper is methodologically based, addressing the study of mathematics teaching by linking micro- and macro-perspectives. Considering "teaching as activity", it uses "Activity Theory" and, in particular, the "Expanded Mediational Triangle" (EMT) to consider the role of the broader social frame in which classroom teaching is situated. Theoretical and methodological approaches are illustrated through episodes from a study of the mathematics teaching and learning in a Year-10 class in a UK secondary school where students were considered as "lower achievers" in their year group. We show how a number of questions about mathematics teaching and learning emerging from microanalysis were investigated by the use of the EMT. This framework provided a way to address complexity in the activity of teaching and its development based on recognition of central social factors in mathematics teaching-learning.

This article refers to a longitudinal case study of a primary school teacher over a period of 4 years. The focus is on the development of the teacher's beliefs regarding mathematics teaching and learning from the last year of her university studies up to the third year of teaching mathematics in school. This development has been investigated within three different contexts, which have been distinguished in terms of the kind of support provided to this teacher. Two dominant beliefs emerged which have been traced through the period of the study from both the teacher's reflections and actions. The first belief drew on the idea that what was considered an easy mathematical task by an adult could also be easily understood by children, while the second was that children learn mathematics through their actual involvement in a variety of teaching activities. The results indicate the way that teacher's experiences from her university studies, actual classroom practice and inservice education interact and influence her beliefs and professional development.

Focuses on the role of tools provided by a computer microworld (C.AR.ME) on the strategies developed by 14-year-old students for the area measurement of a non-convex polygon. Interprets and classifies student strategies on a transformation and comparison task into categories in terms of the tools used for their development. (Author/MM)

Attempts to make sense of the complexity of mathematics teaching and its development at secondary school level. Conducts a partnership between teachers and researchers in U.K. schools and analyzes interactions between the teacher and students at whole class and small group level. Uses the teaching triad as an analytical device and reflective agent for teaching development. Discusses the advantages of the triad for teaching development. (Author/KHR)

Focuses on two main issues concerning the mathematics education of prospective primary school teachers in Greece: the integration of mathematics and pedagogy, and the relationship of theory to practice. Discusses specific teaching approaches concerning the problem of integration both in mathematics and in mathematics education courses. (Contains 11 references.) (Author/ASK)

Explores the arguments used by 14-year-old students in making decisions about the design of a road in their area. Describes the general perspective of such an approach and the process of argumentation, then analyzes the nature of the students' arguments which are discussed on the basis of a specifically-constructed network. Contains 20 references. (Author/WRM)

Describes a computer microworld for learning the concept of conservation of area and its measurement; analyzes its main features (drawing segments and polygons, manipulation of areas using simulations of children's sensory-motor actions, measuring areas, transforming areas into equivalent ones, and measuring lengths and angles); and presents the results of a pilot study evaluating the microworld. (Author/PEN)