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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 examines the interactions between teachers’ decisions, discourses and acts, and the intended students’ learning. The focus is theoretical and methodological as it attempts to exemplify theoretical perspectives in studying mathematics teaching in its complexity. It takes into account, together or separately, the overall setting : sociocultural and institutional and the epistemological point of view on mathematics and its teaching in class. For some of the authors, the study of teacher activity in relation to students’ mathematical activity, and affective and social needs has been the focus of their research for many years, using different theoretical constructs and empirical data. As for the others, their research in the same area was focused more on the presumed cognitive needs, in relation to the practices and the mathematics at stake. The article reveals that Activity Theory has been used differently by the two traditions (English and French) as a framework for analyzing and interpreting the relations and interactions between teacher and students’ mathematical activity in research studies of the authors. This article exemplifies these different ways of using AT and discusses issues the perspectives raise for interpretation and analysis. Ce texte est centré sur l’étude des relations entre les activités des enseignants et celles des élèves, les premières étant décrites en matière de décisions, de discours et d’actions. Il s’agit d’adopter un point de vue théorique et méthodologique, en lien avec les perspectives adoptées pour ces analyses complexes ; cela fait intervenir, sans qu’il y ait exclusion d’un des aspects, l’ensemble des déterminants socioculturels et institutionnels, les déroulements en classe et le point de vue épistémologique. Une partie des auteurs fait notamment intervenir dans l’étude des pratiques enseignantes les besoins affectifs et sociaux, l’autre insiste davantage sur les besoins cognitifs présumés et les mathématiques en jeu. Tous les auteurs se réclament de la théorie de l’activité comme cadre théorique pour analyser et interpréter les relations et interactions entre l’activité enseignante et les activités mathématiques des élèves. Nous illustrons chaque point de vue par un exemple en discutant des questions qui se posent à l’autre point de vue.

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 pandemic has demonstrated more than ever that citizens around the world need to understand how mathematics contributes to understanding global challenges and ways of overcoming them. People need to understand that predictions are based on models that make use of assumptions and the best inputs available. They also need to learn to critically evaluate reports based on the outcomes of models to make effective decisions and deal with the inherent uncertainty in an appropriate way. These capabilities make it clear that mathematical modelling is a key element of citizenship education. Given this fundamental role of modelling, we take a closer look at its definition, its history, its connection to other teaching approaches, as well as the competences students need to carry through modelling processes and the competences teachers need for teaching modelling.

The chapter focuses on the attempts of a group of mathematics teacher educators (MTEs) to support teachers in exploiting workplace situations in their mathematics teaching. We report on MTEs’ professional learning in the context of a European-funded project which brought together 18 partners from 13 countries. In Greece, 11 MTEs (academic researchers, teachers and mentors) with different research and teacher education experiences worked with 13 groups of practising teachers who collaborated to plan, enact and reflect on lessons aligned to the aims of the project. The project provided substantial opportunities for challenging MTEs’ professional knowledge and teacher education practice. The analysis of the discussions during a series of meetings, where design and reflection on professional development activities took place, allowed for identifying and describing MTEs’ concerns and emerging tensions. Using the construct of boundary crossing, we traced shifts in MTEs’ movements across different practices indicating an interplay of research, teacher education and mathematics teaching.

In this chapter, we study the transferring process of three apprentice engineering students (as illustrative cases) who were doing their internship in a telecommunication organization. We analyze students’ interpretations of four different authentic representations (table, professionals’ explanations, formula, and graph) of a functional relation hidden behind a workplace task concerning the selection of the proper type of copper wires in the local subscriber network. By conceptualizing transfer as a sociocultural, meaning-making process of objectification, we used the theory on developmental transfer by Engestrom's theory on developmental transfer and Radford’s objectification theory. Transfer in this way was conceptualized as the development of a shared object between the academic and workplace activity systems. The above theoretical constructs helped us to zoom in on the nature of the shared object and on how it was developed. In the latter case, we identified the role of elements of both activity systems in students’ transferring process.

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 οn 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.

This chapter has the aim of supporting early career researchers who want to publish a paper in the Journal of Mathematics Teacher Education (JMTE) by providing them with information about the scope of the journal, its impact on the field, the papers published, the reviewing process and the required quality. It ends by providing some advice on issues that an early career researcher needs to consider if he or she decides to submit a paper to JMTE.

In this article, we elaborate methodologies to study the argumentation speech of a teacher involved in argumentative activities. The standard tool of analysis of teachers’ argumentation concerning pedagogical matters is Toulmin’s model. The theory of argumentation schemes offers an alternative perspective on the analysis of arguments. We propose an integrated way of analysis employing Toulmin’s model and argumentation scheme, based on Walton’s taxonomy. We examine the change of pedagogical argumentation of a teacher that participated in a graduate course that was based on the analysis of hypothetical classroom scenarios on the teaching of calculus in high school. By exhibiting our methodological analysis in a particular case, we show that by adopting two different analytical perspectives, we gain a deeper understanding of the structure and quality of teachers’ argumentation on pedagogical matters. The integration of the two qualitative methodologies could help identify several aspects of possible construction of knowledge in argumentative activities.

In the context of a community of practice (CoP), eleven secondary mathematics teachers collaborated in exploring various resources that aim to support teaching statistics that fosters learners in developing statistical thinking and reasoning (DSTR). The tracking of a certain material resource, namely the dynamic software tools for statistics instruction (STSI), revealed three phases in the process of the resource’s integration in the community’s shared repertoire. A qualitative analysis illuminates the characteristics and particularities of each phase in terms of the negotiation of meaning with respect to the practice of the community. We also consider and discuss aspects that seem to frame the transition among the various phases of this process and implications for the re-sourcing process of the DSTR practice.

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This paper aims to analyze the structure and quality of prospective mathematics teachers’ (PMTs)’ argumentation when identifying and interpreting critical incidents from their initial field experiences. We use Toulmin’s model and recent elaborations of it to analyze the discussions that took place at the university where PMTs reflected on their recent classroom experiences. Our aim is to identify the structure of the argumentation and characterize the emerging warrants, backings, and rebuttals. Results indicate different argumentation structures and types of warrants, backings, and rebuttals in the process of PMTs’ interpretations of students’ mathematical activity. We discuss these findings from the perspective of noticing to identify shifts at the level of PMTs’ interpretations.

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.

This study examines children’s thinking about geometrical solids through an investigation of dynamic transformations employed by young children making mental transformations of an orthogonal parallelepiped. The focus of the study is on the investigation of the role that a dynamic environment could play in the development of children’s geometrical thinking concerning geometrical solids and their properties. Twenty 6th grade children, who had previously worked with dynamic transformations of physical models of geometrical solids in their classroom, were interviewed. Analysis of the data resulted in a categorization of children’s thinking, and indicated a development from a perceptual to a geometrical consideration of the solid. Although not all the children reached an advanced level of thinking, the context of dynamic transformations promoted the development of most children’s geometrical thinking. There is also an indication that children’s experience with dynamic transformations of physical models in a mathematics classroom environment can act to allow children to transfer experience to the context of mental transformations.

This chapter describes how novice and experienced mathematics teachers integrate authentic workplace contexts into mathematics teaching. This goal was inspired by the European MaSciL project and introduced to the teachers in the context of a masters programme in mathematics education. Under an Activity Theory perspective, we use the notions of activity system and boundary crossing to study the process of teachers’ professional learning. In particular, we analyse teachers’ boundary crossings between two activity systems: mathematics teaching and workplace. Results indicate that collaborative task design and reflection made teachers combine elements from the workplace into mathematics teaching. Different ways of linking reality and mathematics teaching were identified in the modelling process in which the students were asked to be engaged.

The process of becoming a mathematician is related to a number of ontological questions such as: what does it mean to be a mathematician; what is the nature of mathematics; and what is the process ...

This paper describes our joint activity as mathematics teacher educators and academic researchers in collaborating with both experienced and novice teachers in two contexts: an emergent community of inquiry into mathematics teaching and its development; and a research methods course, offered as part of a mathematics education Master’s program, aspiring to initiate participating teachers into research practice through inquiry. Adopting an Activity Theory (AT) perspective, we analyse our activity, identifying its nature and transformations that frame our professional learning. The results indicate that our professional learning is the outcome of a continuous process of becoming aware of our own activity and its transformation in relation to that of the teachers.

This paper describes certain interactions between the activity of "teaching" and the activity of "researching" in which the teachers participate in a 52-h professional development course aiming to introduce them to research in mathematics education as a tool for inquiry in their teaching. The teachers are involved in different research tasks such as: reading and presenting research papers; analyzing classroom dialogues and tasks; and designing, implementing, and evaluating collaboratively a classroom teaching intervention. From an activity theory (AT) perspective, and in particular Engeström's (2001) third generation AT, distinguish two activity systems, the activity system of research and the activity system of teaching, to identify links that the participating teachers make. These links indicate the development of an inquiring stance to mathematics teaching and learning as a means of professional learning. © 2013 FIZ Karlsruhe.

This chapter focuses on research on pre-service secondary school mathematics teachers’ (PSMT) knowledge. Fifty-nine papers were reviewed and each paper was coded according to its research focus, theoretical and methodological framework, main findings and the contribution of the study. We identified three main thematic areas to frame the discussion of the papers: the exploration of knowledge, the impact of teacher education on its development, and the process that this knowledge develops. The review shows that: both small-scale and large-scale studies continue to recognize different aspects of teacher knowledge and indicate certain difficulties of PSMTs; a large number of teacher education practices have a positive impact on PSMTs’ knowledge; research has started to focus on the process of how PSMTs’ knowledge develops either in mathematical or in teaching discourses.

Coping with the complexity of mathematics teaching and learning in the practice ofteaching is an everyday task for a mathematics teacher, teacher educator, and researcher.Krainer (2003) considers that the field of mathematics education has moved toward a betterunderstanding of this complexity: ‘‘The growth of mathematics education as a scientificfield can be regarded as a continuous process of having a deeper and deeper understandingof the complexity of learning and teaching’’ (p. 93). In mathematics teacher educationresearch, as reported in a number of articles of the Journal of Mathematics TeacherEducation (JMTE), this complexity is tackled in different ways and contexts. Some studiesare exploratory with a focus on how teachers cope with the classroom complexity. Othersare developmental in the sense of creating contexts for teachers, which would promotetheir awareness of the complexity of teaching and learning mathematics and support themto cope with this in the classroom.At the exploratory level, the complexity lies in the classroom interactions and the waysthat the teacher is balancing mathematical goals, students’ reasoning and thinking, andclassroom management. As Wood (2002) argues, the alternate forms of teaching and theresearch on them have brought under consideration situations such as classroom norms,patterns of interaction, supporting students’ mathematical thinking, and reasoning asimportant issues in mathematics teaching that pose new challenges for the teacher, theteacher educator, and the researcher. Moving beyond this micro level of the mathematicsclassroom and addressing wider social factors that frame mathematics learning andteaching, Valero (2010) addresses another layer of complexity involving a network ofdifferent practices that seem to frame the didactical triangle and emphasizes the need formathematics education research to consider the connections between these differentpractices and mathematics teaching and learning. Sullivan (2006), in his editorial, alsooffers specific examples to indicate that ambiguities that exist in curriculum goals and inresearch findings create dilemmas to teachers and teacher educators who try to balancedifferent and often dichotomous goals of mathematics teaching. These complexities raised

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 the 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.