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.     

Researcher–teacher relationships and models for teaching development in mathematics education

This article offers theoretical and analytical approaches to investigating how researchers and teachers can work together to create knowledge in mathematics education. It argues that researchers and teachers are members of separate, but related, communities of practice, which create and value different types of knowledge. However, connections between communities can be established through discrete boundary encounters, longer term boundary practices, or peripheral participation by members of one community in the practices of another community. A framework for analyzing researcher–teacher relationships is presented and then used to compare ways in which I, as a university-based researcher, worked with teachers in three different types of research projects. The analysis indicates that successful research collaborations are characterized by mutuality of researcher and teacher motivations, roles, and purposes, and complementarity of their expertise and knowledge. Such collaborations build two-way connections between communities through practices that support mutual engagement across the boundaries that define them.     

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.     

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.     

Building teachers’ expertise in understanding, assessing and developing children’s mathematical thinking: the power of task-based, one-to-one assessment interviews

In this paper, we outline the benefits to teachers’ expertise of the use of research-based, one-to-one assessment interviews in mathematics. Drawing upon our research and professional development work with teachers and students in primary and middle years in Australia and the research of others, we argue that the use of the interviews builds teacher expertise through enhancing teachers’ knowledge of individual and group understanding of mathematics, and also provides an understanding of typical learning paths in various mathematical domains. The use of such interviews also provides a model for teachers’ interactions and discussions with children, building both their pedagogical content knowledge and their subject matter knowledge.     

Sociocultural perspectives in research on and with mathematics teachers: a zone theory approach

Sociocultural theories view teacher learning as changing participation in social practices that develop their professional identities rather than as acquisition of new knowledge or beliefs that are internal to the individual. Although sociocultural research on mathematics teacher education has tended to focus on understanding teachers’ learning, this article argues that sociocultural perspectives can also guide more interventionist research involving changing classroom practice. The approach illustrated here uses an adaptation of Valsiner’s zone theory to analyse teacher learning and development in two separate research studies. In one study the aim was to understand how teachers incorporated digital technologies into their practice, while the other study helped teachers implement an investigative approach to working mathematically consistent with a new syllabus. In both studies, productive tensions between teachers’ beliefs, contexts, and goals were a trigger for learning and development.     

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.     

Influence of mentoring and professional communities on the professional development of a cohort of early career secondary mathematics and science teachers

A challenge for public schools is to successfully support and professionally develop early career teachers (ECTs) and thereby prepare them for long and successful careers in education. The purpose of this qualitative research study was to describe how the professional practices of early career science and mathematics teachers, some of whom are career changers, were influenced by their interactions with mentors and professional communities. Topics examined included the contextual elements that influenced the ECTs’ interactions with mentors and professional communities, how teachers positioned themselves within multiple professional communities, and how they perceived these experiences had influenced the development of their teaching practice. An extensive semi-structured interview of the ECTs generated data that were analyzed to identify emergent themes and patterns. The findings of this study indicated that navigating professional communities and interacting with mentors had influenced the ECTs’ decisions to adopt important components of a learner-centered approach to teaching that included engaging students in active learning processes, utilizing formative assessment, and responding to students' individual needs. These findings have implications for school policies and approaches related to supporting and professionally developing unique cohorts of ECTs.     

Knowledge and confidence of pre-service mathematics teachers: the case of fraction division

To make teacher preparation and professional development effective, it is important to find out possible deficiencies in teachers’ knowledge as well as teachers’ own perceptions about their needs. By focusing on pre-service teachers’ knowledge of fraction division in this article, we conceptualize the notion of pre-service teachers’ knowledge in mathematics and pedagogy for teaching as containing both teachers’ perceptions of their preparation and their mathematics knowledge needed for teaching. With specific assessment instruments developed for pre-service middle school teachers, we focus on both pre-service teachers’ own perceptions about their knowledge preparation and the extent of their mathematics knowledge on the topic of fraction division. The results reveal a wide gap between sampled pre-service middle school teachers’ general perceptions/confidence and their limited mathematics knowledge needed for teaching fraction division conceptually. The results suggest that these pre-service teachers need to develop a sound and deep understanding of mathematics knowledge for teaching in order to build their confidence for classroom instruction. The study’s findings indicate the feasibility and importance of conceptualizing the notion of teachers’ knowledge in mathematics and pedagogy for teaching to include teachers’ perceptions. The applicability and implications of this expanded notion of teachers’ knowledge is then discussed.     

Mathematics teacher educators’/researchers’ collaboration with teachers as a context for professional learning

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.     

Professional Development Strategically Connecting Mathematics and Science: The Impact on Teachers' Confidence and Practice

The press to integrate mathematics and science comes from researchers, business leaders, and educators, yet research that examines ways to support teachers in relating these disciplines is scant. Using research on science and mathematics professional development, we designed a professional development project to help elementary teachers improve their teaching of mathematics and science by strategically connecting these disciplines. The purposes of this study are: (a) to identify changes in teachers' confidence and practice after participating in the professional development and (b) to identify different ways to connect mathematics and science during the professional development. We use a Likert‐scale survey to assess changes in teachers' confidence related to teaching mathematics and science. In addition, we report on a thematic analysis of teachers' written responses to open‐ended questions that probed teachers' perceived changes in practice. We analyze field notes from observations of project workshops to document different types of opportunities for connecting mathematics and science. We conclude with implications for future professional development that connects mathematics and science in meaningful ways, as well as suggestions for future research.     

Examining Secondary Mathematics Teachers' Opportunities to Develop Mathematically in Professional Learning Communities

To make progress toward ambitious and equitable goals for students’ mathematical development, teachers need opportunities to develop specialized ways of knowing mathematics such as mathematical knowledge for teaching (MKT) for their work with students in the classroom. Professional learning communities (PLCs) are a common model used to support focused teacher collaboration and, in turn, foster teacher development, instructional improvement, and student outcomes. However, there is a lack of specificity in what is known about teachers’ work in PLCs and what teachers can gain from those experiences, despite broad claims of their benefit. We discuss an investigation of the work of secondary mathematics teachers in PLCs at two high schools to describe and explicate possible opportunities for teachers to develop the mathematical knowledge needed for the work of teaching and the ways in which these opportunities may be pursued or hindered. The findings show that, without pointed focus on mathematical content, opportunities to develop MKT can be rare, even among mathematics teachers. Two detailed images of teacher discussion are shared to highlight these claims. This article contributes to the ongoing discussion about the affordances and limitations of PLCs for mathematics teachers, considerations for their use, and how they can be supported.     

Chinese elementary mathematics teachers’ knowledge in mathematics and pedagogy for teaching: the case of fraction division

In this study, we investigated the extent of knowledge in mathematics and pedagogy that Chinese practicing elementary mathematics teachers have and what changes teaching experience may bring to their knowledge. With a sample of 18 mathematics teachers from two elementary schools, we focused on both practicing teachers’ beliefs and perceptions about their own knowledge in mathematics and pedagogy and the extent of their knowledge on the topic of fraction division. The results revealed a gap between these teachers’ limited knowledge about the curriculum they teach and their solid mathematics knowledge for teaching, as an example, fraction division. Moreover, senior teachers used more diverse strategies that are concrete in nature than junior teachers in providing procedural justifications. The results suggested that Chinese practicing teachers benefit from teaching and in-service professional development for the improvement of their mathematics knowledge for teaching but not their knowledge about mathematics curriculum.     

Relationship Between Professional Development,Teachers' Instructional Practices,and the Achievement of Students in Science and Mathematics

The purpose of this study was to examine the relationship between different types of professional development, teachers' instructional practices, and the achievement of students in science and mathematics. The types of professional development studied included immersion, examining practice, curriculum implementation, curriculum development, and collaborative work. Data regarding teachers' instructional practices and the amount of professional development were collected using teacher surveys. Ninety‐four middle school science teachers and 104 middle school mathematics teachers participated in the study. Student achievement was measured using eighth grade state science and mathematics achievement test data. Regression analyses suggested that for both science and mathematics teachers, examining practice and curriculum development were significantly related to the use of standards‐based instructional practices. Only curriculum development for mathematics teachers was significantly related to student achievement. Implications of results for the professional development of science and mathematics teachers are discussed.     

Including Curriculum Focus in Mathematics Professional Development for Middle‐School Mathematics Teachers

This paper examines professional development workshops focused on Connected Math, a particular curriculum utilized or being considered by the middle‐school mathematics teachers involved in the study. The hope was that as teachers better understood the curriculum used in their classrooms, i.e., Connected Math, they would simultaneously deepen their own understanding of the corresponding mathematics content. By focusing on the curriculum materials and the student thought process, teachers would be better able to recognize and examine common student misunderstandings of mathematical content and develop pedagogically sound practices, thus improving their own pedagogical content knowledge. Pre‐ and post‐mathematics content knowledge assessments indicated that engaging middle‐school teachers in the curriculum materials using pedagogy that can be used with their middle‐school students not only solidified teachers' familiarity with such strategies, but also contributed to their understanding of the mathematics content.     

Developing teachers’ and teaching researchers’ professional competence in mathematics through Chinese Lesson Study

This study examines co-learning of mathematics practicing teachers and mathematics teaching researchers through parallel lesson study in China. Two cases are illustrated and compared to highlight what practicing teachers and teaching researchers learned. The practicing teachers developed their competence in identifying instructional objectives, improving instructional process, selecting and sequencing mathematical tasks, and developing professional vision. The mathematics teaching researchers developed their professional competence in effectively carrying out teaching research activities, effectively mentoring teachers, and deepening the understanding of teaching.     

Building on mathematical events in the classroom

Mathematical events from classrooms were used as stimuli to encourage mathematical discussion in two groups of mathematics teachers at the secondary level. Each event was accompanied by an analysis of mathematics that would be useful to the teacher in such a situation. The Situations, mathematical events and analyses, were used originally to create a framework describing the Mathematical Proficiency for Teaching at the Secondary Level, and then they were used with both Prospective and Practicing teachers to validate the framework. Teachers involved in the validation research claimed that the process was instructional. The process is explained, and teachers’ quotes provide evidence that the experience provoked changes in teachers’ understanding of mathematics. This process, which builds on mathematical events from the classroom, holds potential as a professional development experience that helps teachers expand their expertise in teaching mathematics.     

Boundary crossing through in-service online mathematics teacher education: the case of scenarios and half-baked microworlds

We address online mathematics teacher education as a means of immersing teachers into new kinds of collectives where professional development may be enhanced by crossing the boundaries of their habitual communities and the norms within these. We analyse the ways in which newly trained teacher educators interacted around their designs and productions for in-service courses they were giving to colleagues. We focus on their uses of scenarios and half-baked microworlds as two kinds of artefacts we had designed to play the role of improvable boundary objects. We consider these interactions as a forum for challenge and for professional development through frequent and relevant boundary crossing.     

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.