Online paths in mathematics teacher training: new resources and new skills for teacher educators

This paper considers the work carried out by online teacher educators and their professional development. We use the theoretical perspective of the documentational approach that focuses, in this case, on the interaction between teacher educators and the resources they use for their online training work. We thus study the following issues: (1) What kinds of resources do online teacher educators need, and how are such resources modified according to the educators?? specific skills and needs? (2) What specific skills are needed for setting up online training for mathematics teachers and how do these skills evolve as teacher education resources are used? We consider both questions simultaneously, while presenting results from a study within a specific teacher training programme in France that proposes ??training paths?? on a national platform. These ??paths?? are resources designed for teacher educators. We follow the appropriation of two training paths by two educator teams. The ways in which these educator teams were able to appropriate the paths give insights into the teacher educators?? skills and, as well, into the resources they need. By looking at their use of resources (as online mathematics teacher educators), we observe and analyse professional geneses, leading to the development of new skills.     

Being a mathematics teacher in times of reform

Within research on mathematics teachers and/or their professional development, the concept of identity emerges as a critique of views of how teaching practice is related to teachers’ ‘internal states’ of knowledge and beliefs. Identity relates teachers’ professional lives to teaching practices and to the contexts in which the teaching and/or professional development occurs. However, what might count as the context still needs in-depth discussion. In order to contribute to the development of a theoretical framework for understanding mathematics teachers’ professional lives, we will draw on one remarkable teacher’s identity as a primary mathematics teacher in relation to one political, sociocultural, and pedagogical context. We use this teacher’s experience to discuss how education policies that create what Ball (2003) called ‘terrors of performativity’ tend to impede the formation of a balanced teacher identity.     

Self‐Directed Teacher Learning in Collaborative Contexts

Two related case studies of secondary mathematics teachers examine the roles and conditions helpful in initiating, directing, and/or supporting teachers' own professional development. Using multiple data sources from school‐based and professional settings, we applied analytic induction to identify patterns of similarities and differences in teachers' experiences and developmental trajectories. Findings revealed how the teachers served as brokers in their own development process and how attitude, attention, and awareness played important roles in teacher learning. As the teachers initiated learning processes, they demonstrated awareness of broader educational contexts that support learning by identifying external policies and priorities that aligned with teachers' attitudes. They then used these external priorities as boundary objects to broker for teachers' learning, including other teachers' learning. They attended to learning needs in directing a plan for learning activities, rather than using externally mandated goals for changing practice (e.g., an external focus on improving students' tests scores). These cases suggest that in structuring professional learning, opportunities to self‐identify learning needs should be part of the process, and external supports can become more powerful when teachers play a brokering role in relating these supports to their immediate contexts. Further implications for professional development processes are explored.     

Ways of promoting the sustainability of mathematics teachers’ professional development

This paper deals with the sustainable effectiveness of professional development programmes. Based on a review of literature and research findings, the following questions are raised: What is regarded as an effective way of promoting mathematics teachers’ sustainable professional development? Which levels of impacts are aimed at? What are the factors promoting the effectiveness of professional development programmes? Regarding these questions, the article links theoretical considerations with research findings from a case study. A secondary mathematics teacher, taking part in a teacher professional development programme in 2002, was revisited in 2005 and 2010 to gather data regarding the sustainable impact of the programme. The case study’s results provide information about the teacher’s professional growth and lead to a discussion of implications for mathematics teachers’ professional development and teacher education in general.     

The wholes that are greater than the sum of their parts: employing cooperative learning in mathematics teachers’ education

This paper presents a study on employing different types of cooperative learning (CL) settings in mathematics teacher education based on multiple research data. The study analyzes mechanisms in which CL contributes to the development of teacher knowledge of three kinds: subject matter knowledge, pedagogical content knowledge, and curricular content knowledge. Additionally, it reflects on interactions between different kinds of teachers’ knowledge in the process of development. Two wholes, which are greater than the sum of their parts, are analyzed in this paper. The first is a course whose design combines different CL settings, hence enhances different mechanisms for teachers’ professional development. The second whole, teachers’ “collaborative mind,” is presented as an outcome of the first. To exemplify possible contributions of employing CL in teacher education, this paper first zooms in on the structure of one particular course for mathematics teachers and then focuses on one particular mathematical activity.     

Collective work with resources: an essential dimension for teacher documentation

In this paper we study the collective dimensions of teachers’ work in their ordinary daily practice. We argue that teachers’ ordinary work comprises many collaborative aspects, and that the interactions with colleagues, often through resources, are crucial for teacher professional development. Using a theoretical framework based on teacher documentation work, we focused on interactions between teachers and resources to study two teachers’ work: one teacher in France and one teacher in Norway. For both teachers we identified collective dimensions in their work with resources. Contrasting these two cases enabled us to identify particular features, but also possible invariants, of teachers’ work with resources. Our results indicate that collective dimensions are always present in teachers’ work, but that true communities of practice, which could be considered as an achievement of collective teachers’ work, are scarce. We discuss the conditions for the emergence of such communities.     

Rural teacher leadership in science and mathematics

This study adds to our understanding of science and mathematics teacher leadership in rural schools. Through In Vivo and Concept coding of teacher interviews, we investigated 20 secondary science and mathematics teachers' perceptions of rural teacher leadership during their participation in a three-year professional development program. As the teachers developed as teacher leaders, they broadened their focus from improving their own students' learning to sharing new knowledge learned through the program with other teachers both informally and formally. We compared our program components to the Teacher Leader Model Standards and added an emphasis on the importance of disciplinary content knowledge. We also identified patterns in science and mathematics teacher leadership that are contextually connected to teachers' instruction in rural high poverty schools. Rural teacher leadership included the importance of building strong teacher–student relationships, providing new academic opportunities for students, encouraging students' success, and building community connections.     

Science Conference Presenters’ Images of Inquiry

Inquiry‐focused professional development and conceptions of inquiry held by eight professional development leaders were investigated within the context of a state science teacher conference. The prominent session format involved session leaders modeling classroom experiences. In all sessions, classroom inquiry was portrayed as a teacher‐guided activity with the primary goal being to increase motivation for engaging students in classroom inquiry. The leaders’ conceptualized inquiry primarily as a teaching approach with various goals, characteristics, and potential barriers. The findings of this study provide evidence of how inquiry, a prominent feature of science education reform, was portrayed in sessions at a conference sponsored by a state affiliate of the National Science Teachers Association and thought about by persons who led these sessions. The findings have implications for teacher learning from conference‐based professional development and its potential influence on science teacher thinking and practice.     

Classroom video in teacher professional development program: community documentational genesis perspective

We examine classroom video recordings as a means of supporting the learning of teacher communities. Drawing on a longitudinal professional development program for middle years mathematics teachers in the USA, we first outline two contrasting episodes in which the teachers analyzed same segments of classroom video in two different points in the program, 2 years apart. We document that the teachers considered dramatically different aspects of video-recorded instruction as relevant to their professional interests and learning in the two episodes. We then analyze the episodes, and the intervening developments, from point of view of the community documentational genesis. In doing so, we highlight the teacher community’s creation of shared repertoire of ways of reasoning.     

Re-sourcing teachers’ work and interactions: a collective perspective on resources, their use and transformation

This paper reviews the literature on the theme of mathematics teachers’ work and interactions with resources, taking a particular perspective, the so-called ‘collective perspective’ on resources, their use and transformation. The review is presented under three headings: (1) theoretical frameworks commonly used in this area of research; (2) teachers’ interactions with resources in terms of their design and use; and (3) teachers’ interactions with resources in terms of teacher learning and professional development. From the literature, and the collection of papers in this issue, we argue that the collective dimensions play an important role in mathematics teachers’ work with resources and in their professional learning/development. Further empirical investigations are likely to be needed on: how teachers may work in collectives and with resources, and in which ways ‘productive’ collectives may form and work together; which roles particular resources can play in these delicate constellations and how particular resources may support teachers in their work and learning; and which kinds of resources offer opportunities for community building.     

Mathematics teacher education advanced methods: an example in dynamic geometry

We present a research work about an innovative national teacher training program in France: the Pairform@nce program, designed to sustain ICT integration. We study here training for secondary school teachers, whose objective is to foster the development of an inquiry-based approach in the teaching of mathematics, using investigative potentialities of dynamic geometry environments. We adopt the theoretical background of the documentational approach to didactics. We focus on the interactions between teachers and resources: teachers’ professional knowledge influences these interactions, which at the same time yield knowledge evolutions, a twofold process that we conceptualise as a documentational genesis. We followed in particular the work of a team of trainees; drawing on the data collected, we analyse their professional development, related with the training. We observe intertwined evolutions and stabilities, consistent with ongoing geneses.     

Mathematics professional development as design for boundary encounters

This theoretical paper examines a process for researchers and teachers to exchange knowledge. We use the concepts of communities of practice, boundary encounters, and boundary objects to conceptualize this process within mathematics professional development (MPD). We also use the ideas from design research to discuss how mathematics professional development researchers can make professional development the focus of their research. In particular, we examine the question: How can MPD be conceptualized and designed around research-based knowledge in ways that promote knowledge exchange about students’ mathematics and mathematics learning among researchers and teachers to improve the practices of both the research and the teaching communities? We propose that MPD is a premier space for researchers and teachers to exchange knowledge from their communities, impacting both researchers’ and teachers’ practices without reducing the importance of either.     

Examining the design features of a communication-rich,problem-centred mathematics professional development

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The professional development was grounded in a set of mathematical tasks that each had one right answer, but multiple solution paths. The facilitator engaged participants in problem solving and encouraged participants to work collaboratively to explore different solution paths. Through analysis of this collaborative learning environment, we identified five design features for supporting teacher learning of important mathematics and pedagogy in a problem-solving setting. We discuss these design features in depth and illustrate them by presenting an elaborated example from the professional development. This study extends the existing guidance for the design of professional development by examining and operationalizing the relationships among research-based features of effective professional development and the enacted features of a particular design.     

Students’ ratings of teacher practices

In this paper, we explore a novel approach for assessing the impact of a professional development programme on classroom practice of in-service middle school mathematics teachers. The particular focus of this study is the assessment of the impact on teachers’ employment of strategies used in the classroom to foster the mathematical habits of mind and mathematical self-efficacy of their students. We describe the creation and testing of a student survey designed to assess teacher classroom practice based primarily on students’ ratings of teacher practices.     

Online education for in-service secondary teachers and the incorporation of mathematics technology in the classroom

This paper reviews existing research on how in-service high school teachers have learned about, worked on or thought about the incorporation of mathematics technology into their teaching practices. The paper reviews different scenarios of instruction issuing from important research related to teacher professional development. Specifically, we will deal with contributions to online in-service mathematics teacher education that refer to the use of digital technologies in classroom teaching practices. The different articles reviewed belong to a range of teams of researchers from several universities and countries, and who have implemented distinct online education approaches. That work has allowed the gaining of knowledge on the specificities of using Web 2.0 tools for mathematics professional development (MPD), the function that online teacher interaction has in teacher learning, and the actual classroom conditions in which mathematics technology is incorporated into instructional practice. This paper describes and discusses the design features of those approaches emphasizing the main concepts and their underpinning theoretical frames, noting important design elements, and specific results. Finally, the paper discusses how some of these research findings are connected with emergent issues in the field of MPD.     

Using Emerging Technologies to Help Bridge the Gap Between University Theory and Classroom Practice: Challenges and Successes

This article describes and illuminates the challenges that the authors faced as we integrated a web‐supported professional development system into elementary science methods courses housed at three different universities. Using a design experiment framework, the challenges and difficulties encountered while attempting to develop and sustain effective discussions about inquiry‐based teaching are discussed. Three main issues were identified through this analysis: (a) creating meaningful interactions for preservice teachers, (b) supporting preservice teacher reflection and articulation of their belief systems, and (c) technical, social, and institutional challenges of using a World Wide Web based professional development system. The article closes with recommendations concerning the implementation of a web‐based professional development system into elementary methods science courses and describes what appear to be successful strategies for fostering a collaborative atmosphere between teacher educators, preservice teachers, and in‐service teachers.     

Multi‐Year Professional Development Grounded in Educative Curriculum Focused on Integrating Technology With Reformed Science Teaching Principles

Visions of science teaching and learning in the newest U.S. standards documents are dramatically different than those found in most classrooms. This research addresses these differences through closely examining one professional development (PD) project that connects teacher learning and teacher practice with student learning/achievement. This study examines the effects on eighth grade science teachers and their students in the context of a PD focused on the integration of information communication technologies and reformed science teaching practices. Findings from this investigation suggest that teachers who participated in PD for two years learned more about technology, improved their practice, and their students’ achievement was significantly higher compared to teachers who participated in one year of the PD or non‐participating peers. Science educators face multiple challenges as they attempt to deliver instruction in fundamentally different ways than what they experienced as learners. The delivery of this professional learning suggest that PD for science teachers should include educative learning experiences if understandings of reforms supported by research are to be realized.     

First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes

We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original boundary by a different one. In doing so we establish the existence of the first-passage time density and provide an upper bound for this function. In the case of processes with diffusion interval equal to ℝ this is extended to a lower bound, as well as bounds for the first crossing time of a lower boundary. An extension to some time-inhomogeneous diffusions is given. These results are illustrated by numerical examples.      

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM—The International Journal on Mathematics Education—by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers’ and didacticians’ engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice.     

Using video as a tool for promoting inquiry among preschool teachers and didacticians of mathematics

This paper explores the use of video as a tool for promoting inquiry among preschool teachers and didacticians. In this case, the didacticians are teacher educators who are also mathematics education researchers. Preschool teachers recorded themselves with video implementing number and geometry tasks with children and shared these recordings with other teachers and didacticians. The session where the teachers and didacticians viewed and discussed these recordings was recorded and viewed later by a group of didacticians. The multiple uses of video led to inquiry on several levels. Teachers inquired into the practice of implementing tasks with children, evaluating children’s knowledge, and the practice of using video as a tool. Didacticians inquired into their practice of research with children, their practice as teacher educators, the use of video as a tool in professional development, and the use of video in their inquiry process. Teachers’ and didacticians’ inquiries led to increased appreciation for the practice of inquiry, belonging to a community of practice, and its role in promoting both teachers’ and didacticians’ knowledge for teaching.