Proceedings of the Fourteenth Annual Meeting of the Georgia Association of Mathematics Teacher Educators Front Matter

We report on an action research study conducted by two mathematics teacher educators in the United Kingdom and Hong Kong. The project consisted of three phases, the first two taking place in our respective teacher education courses and a final phase in which prospective mathematics teachers from both locations engaged in dialogue through a speculative fiction task. Our aim was to explore how our prospective mathematics teachers can be supported in becoming mathematics teachers for sustainable futures by innovating our own mathematics teacher education curricula. This study suggests that generative methods which support teachers in speculating on paths to potential futures as teachers of mathematics, can provide access to how prospective teachers negotiate issues in relation to the climate crisis and ways in which they conceive of related changes in their practices. By identifying the aspects of mathematics teaching that are viewed by the prospective teachers as contingent, and through offering tasks that support an expansion of this view, teacher educators are better placed to support the development of teaching practices needed for sustainable futures.

The social, political and educational policy changes in South Africa provide a backdrop to this paper. Its authors report recent (2000–2006) research into the education of science and mathematics teachers in this country. International research trends provide a frame for the survey. Findings suggest that most of the research in both science and mathematics teacher education consists of small scale qualitative studies, generally conducted in urban contexts and among teachers participating in formal in-service programmes. In science teacher education, research emphases appear to have shifted towards process skill development, nature of science (NOS) and indigenous knowledge systems (IKS) while still acknowledging the importance of content knowledge. In mathematics teacher education research, there is a strong emphasis on the specificity of mathematical knowledge for mathematics teaching and teacher learning, with curriculum reform recently in focus in both mathematics and science teacher education literature. Gaps in the research have also been identified, including the education of primary mathematics and science teachers, teacher education for life sciences and the education of teachers in and for rural contexts. The authors argue for further research into mathematics and science teacher education and conclude with a research agenda focused on an examination of teacher education practices, investigations into primary teacher education, studies into life sciences teacher education and empirical research across diverse schooling contexts, with particular attention being paid to rural education.

Preface. Section I: Perspectives on Teacher Education. Considering the Paradoxes, Perils, and Purposes of Conceptualizing Teacher Development T.J. Cooney. A Review of Research Perspectives on Mathematics Teacher Education S. Lerman. Section II: Making Sense of Mathematics. Investigating Mathematics and Learning to Teach Mathematics J.P. da Ponte. Using the Intuitive-Rules Theory as a Basis for Educating Teachers D. Tirosh, et al. The Use of New Technologies as a Vehicle for Restructuring Teachers' Mathematics C. Laborde. Section III: Making Sense of Teaching. Digitizing Real Teaching Practice for Teacher Education Programmes: The MILE Approach F. Goffree, W. Oonk. Thinking Teaching: Seeing Mathematics Teachers as Active Decision Makers P. Sullivan, J. Mousley. Mathematics Teaching, Teacher Education, and Educational Research: Developing 'Practical Theorising' in Initial Teacher Education K. Ruthven. Preparing Teachers for Handling Students' Mathematical Communication: Gathering Knowledge and Building Tools A. Sfard, C. Kieran. Section IV: Making Sense of the Context of Teaching. An Approach for Supporting Teachers' Learning in Social Context P. Cobb, K. McClain. Educating Student Teachers About Values in Mathematics Education A.J. Bishop. Pedagogical Values, Mathematics Teaching, and Teacher Education: Case Studies of Two Experienced Teachers C. Chin, et al. Section V: Making Sense of the Complexity of Teacher Education. Teachers' Growth is More Than the Growth of Individual Teachers: The Case of Gisela K. Krainer. Developing Mathematics Teaching: Teachers, Teacher Educators, and Researchers as Co-Learners B. Jaworski. Index.

Prospective teachers bring countless stories of success and failure from different mathematics classrooms to their post-field teacher education courses. These reflective stories often glorify school mathematics classrooms and dominant traditions within, instead of confronting the marginalization of diverse groups in school environments. Mathematics teacher educators have a significant role to play in teaching prospective teachers to reflect critically on their field experiences and, in doing so, create spaces for disruption and disruptive pedagogies. Drawing on critical and equity-based theories applied within the fields of mathematics education and teacher education research, we propose a disruptive pedagogy analytical framework that enables us to study the roles and practices of mathematics teacher educators as they conduct their work in these post-field contexts of teacher education. In this paper, we introduce our disruptive pedagogy framework and present the results that followed from using it to analyze data from a research study in which mathematics teacher educators from across Canada and Norway were interviewed. We claim that our analytical framework can be used to identify those disruptive and transformative practices initiated by mathematics teacher educators—practices that are necessary to bring about shifts in inequitable and unjust classroom practices of school mathematics and in becoming a teacher. Unfortunately, however, results reported here point to the need for further shifts and growth toward more explicitly disruptive practices initiated by mathematics teacher educators in the post-field context.

This new volume of the Association of Mathematics Teacher Educators (AMTE) Professional Book Series provides mathematics teacher educators practical ideas of how to build community to center conversations and action on equity and justice in mathematics teacher education. This 24-case collection of experiences from mathematics teacher educators (MTEs) expresses how they build community in the following kinds of settings in order to provide examples of how this work can be done in a variety of MTE contexts: Cases to Build Community with Prospective Teachers; Cases to Build Community in Professional Development with Practicing Teachers; and Cases to Build Community with Graduate Students and Fellow Mathematics (Teacher) Educators. This book is written from and with a critical, practitioner stance and provides a variety of research-based cases (e.g., scenarios, tasks, modules, activities) to support MTEs to build community in mathematics teacher education courses and professional development collaborations. Creating learning communities that center on the joy, beauty, resiliency and variety of experiences and ways of knowing community members, particularly marginalized communities, is critical to promote agency and action that can support critical conversations that disrupt oppression in mathematics and mathematics teacher education.

In the past four decades, attention in research in teaching has turned from the content of teaching and learning to the context in which they occur. Many researchers now view learning as active construction rather than passive absorption, and teaching as facilitation rather than transmission. A similar shift has occurred in the view of the school curriculum, now less a collection of topics than a set of experiences. In mathematics, the National Council of Teachers of Mathematics publication The Agenda for Action (1980) opened a new dimension to how many educators view teaching. The recommendations in the Agenda emphasized problem solving and applications; a reexamination of basic skills; incorporation of calculators, computers, and other technology into the mathematics curriculum; and more mathematics for all students. As a response to the Agenda, in 1986, the Board of Directors of the National Council of Teachers of Mathematics NCTM) established the Commission on Standards for School Mathematics to help improve the quality of school mathematics (NCTM, 1989). Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), which established a framework to guide reform in school mathematics, is the product of the Commission. This document, along with the Professional Teaching Standards (NCTM, 1991) and the Assessment Standards for Teaching Mathematics (NCTM, 1995), set forth a vision of school mathematics curriculum and teaching and a view of evaluation different from what most teachers experienced in their mathematical education and what they found in most textbooks. If the mathematics curriculum changes as proposed, the need for competent teachers will become more acute. Teachers will need more and better preparation, for teaching for better mathematics (Begle, 1972) demands better teaching of mathematics. The recommendations of the current reform for school mathematics focus attention on teaching. They require that teacher education programs play an integral role in familiarizing teachers with current recommendations and preparing them with the professional knowledge base for realizing those visions. Research on mathematics teachers and teacher education indicate that this process is neither straightforward nor simple. The National Council of Teachers of Mathematics standards for content, pedagogy, and evaluation provide the direction, but not the mechanism, for reform in school mathematics. A mechanism for reform must be developed; without it even current guidance will not affect the teaching of mathematics. This mechanism must take into account the challenges of preparing teachers to teach in accord with the proposed visions and provide a perspective on how to deal with the complexities of teacher change. This mechanism must serve as the vehicle for improving teaching as well as teacher education. The mathematics teacher education community has recognized this need for some time. Bruner (1966) indicated that a theory of instruction must specify how a body of knowledge should be structured so that learners can most readily grasped it. A theory of instruction should identify the most effective ways in to facilitate learning. Cooney and Brown (1985) argue that a theory or theories in mathematics education must ultimately provide a basis for improving the teaching and learning of mathematics. Recent researchers on mathematics teacher education have examined four reform areas in educating mathematics teachers: teacher beliefs, content knowledge, pedagogical content knowledge, and pedagogical reasoning. In this article, I synthesize research on these areas and provide several recommendations for the reform in teacher education. Beliefs I believe teachers make decisions about students and curriculum in rational ways according to conceptions they hold. To design teacher education programs without understanding those conceptions and their role creates a context where teacher educators believe that their insights into the teaching/learning cycle are synonymous or even consistent with those of the teachers they teach (Cooney, 1994, p. …

The interrogation of often unintended practices of marginalisation has gained focus in research on mathematics teaching and mathematics teacher education throughout the last decades. In this introductory survey paper, work against marginalisation in these contexts of mathematics education is viewed in terms of work towards equity, diversity and inclusion. Based on this interpretation, we present a framework on awareness and practice of equity, diversity and inclusion in mathematics teaching and mathematics teacher education research. We then use this framework and a survey method of mapping review to identify and comment on a selection of studies. As a result, we illustrate three research moves towards equity, diversity and inclusion, in the form of interconnected themes: (1) Widening the understanding of the mathematics and the mathematics education curricula (2) Improving the practice and discussion of mathematics teaching (3) Unpacking ideologies in mathematics teaching and mathematics teacher education. We finally examine the themes and the special issue papers together to foreground commonalities regarding awareness of discriminatory discourses and practices of creating and distributing opportunities for all groups, including those historically and currently marginalised. Despite the important increase of equity-driven principles of awareness, we conclude that mathematics education research on teaching and on teacher education needs more examples of practices whose development has been proved to challenge marginalisation.

Mathematics teacher educators (MTEs) within mathematics education systems have unearned assets that present strengths and challenges to the process of developing relationships with mathematics teachers (MTs), students, and their communities. Aware of such issues, we discuss in this chapter the concept and potential applications of allywork for the promotion of equitable systems in mathematics education. With this goal, we draw on literature from within and outside of mathematics education to (1) understand sociohistorical reasons for why MTEs should consider an ally stance in their work with MTs, (2) to consider who an ally is (and is not), and (3) to detail what allywork entails. An analysis of the coercive and hierarchical relations that the mathematics education field has inherited through the systemic feminization of education in the classroom and the masculinization of research and teacher education and the current diverse demographics of the US mathematics educational system frames the need and relevance of allywork. Allywork is understood as MTEs and MTs (as well as students and their community) working with each other in self, others, and systems (SOS) spaces. Description of an interior as well as exterior negotiation and disruption of issues of privilege and oppression highlight the personal and yet systemic dimensions required in MTEs’ work and identities as allies. This chapter further contrasts allywork with other stances, links these ideas to mathematics education, and raises questions on how MTEs’ work and identities critically address and intersect with the goals, needs, and actions of others in SOS spaces.

The topic study group on pre-service mathematical education of teachers is dedicated to sharing and discussing of significant new trends and development in research and practice about the various kinds of education of pre-service mathematics teachers and of pre-service primary teachers who teach mathematics and are trained as generalists. It aimed to provide both an overview of the current state-of-the-art as well as outstanding recent research reports from an international perspective. The group discussed research experiences with different practices of pre-service mathematical education of (mathematics) teachers throughout the world, i.e. similarities and differences concerning the formal mathematical education of teachers, types and routes of teacher education, curricula of (mathematics) teacher education, facets of knowledge and differences in their achievements and beliefs about the nature of their training, and a variety of factors that influence these differences.

A challenge of teacher education is to produce graduate primary school teachers who are confident and competent teachers of mathematics. Various approaches to primary school teacher education in mathematics have been investigated, but primary teacher education graduates still tend to be diffident in their teaching of mathematics. In an age where personal use of mobile technologies is becoming ubiquitous, such technologies could provide a conduit into making mathematics teaching and learning more accessible to primary teacher education students. This paper introduces the use of a pedagogical framework which can scaffold mobile learning in mathematics teacher education programs. The paper discusses ways in which this framework, the Mobile Pedagogical Framework, can contribute to enhanced primary teacher education in mathematics, using mobile technologies. The Framework has three major dimensions: authenticity, collaboration and personalisation. Each of these will be discussed in terms of their alignment with current ideas about quality teaching in mathematics.

This chapter focuses on the awareness and the practices of mathematics teacher educators in linguistically diverse classrooms across three countries—South Africa, Malawi, and Catalonia-Spain. We explore whether and how mathematics teacher educators’ awareness in three mathematics classrooms (one from each country) impact on classroom practice and whether these practices were anchored in becoming teachers of mathematics, becoming teachers of mathematics in multilingual classrooms, becoming learners of mathematics content or becoming proficient English users. The findings reveal that the mathematics teacher educators were generally aware of the context of their practice: that they were teaching linguistically diverse mathematics student teachers who would most likely teach mathematics in a similar linguistic context. However, the practices that were used by these teacher educators were anchored in and position mathematics student teachers as becoming teachers of mathematics and becoming learners of mathematics content. Little attention was paid to becoming teachers of mathematics in multilingual contexts.

Teaching is a complex process, which, in addition to an exceptional knowledge of the teaching process by the teacher, requires and implies a number of correlative relationships and factors that affect student achievement. The subject of this paper is the analysis of a broader network of potential contextual factors of action on student achievement in mathematics. Accordingly, the aim of the paper is focus on insight of resources of the educational system and the particular circumstances that influence the quality of achievement of students in mathematics. Three sections are considered by theoretical analysis: the impact of mathematics teachers 'professional education on the quality of student achievement, teachers and teaching strategies as a basis for building mathematical anxiety or student resilience, and the role of the school context and analysis of students' specific difficulties in mathematics. Vocational teacher education is one of the initial segments of developing quality in a teacher's vocation, while later professional development is an opportunity to influence not only teacher competences but also the outcomes of student learning. There is a tendency that the education of mathematics teachers and the education of teachers, also future teachers of mathematics, does not give sufficient support to all competencies required for practical work. Significant focuses are on construction and knowledge, while there is less focus on developing teaching competencies. For these reasons, a number of recommendations emerge to include the development of teaching skills in the initial education and training of mathematics teachers, with the aim of improving mathematics in practice and improving student outcomes. Teachers and teaching strategies are the factors that underpin mathematical resilience or anxiety in students, and thus represent variables with a direct impact on mathematics achievement. Mathematical failure can have a strong negative effect on the later life and work of individuals, while the teacher can influence the onset of mathematical anxiety, or through good programs and thoughtful activities can build mathematical resilience and enhance students' achievement in mathematics. The school context and the specific difficulties of the students in mathematics are part of the factors on which the success of the students in this subject depends, because an effectively organized school system causes the development of the maximum potential of students. The paper confirms the opinions of numerous authors that it is necessary to identify and correct specific difficulties in the school environment. Qualitative analyzes partially open the implications for school practice, which indicate the existence of students who are more difficult to master mathematics, but also the fact that the extra work of teachers with them significantly influences the elimination of existing difficulties. By considering the aforementioned aspects of classroom practice and their impact on students' achievement in mathematics, further research was opened that would more specifically address the contexts and modes of mathematics instruction, with particular attention to the existence of students with specific difficulties in mathematics and the key role of teachers in their recognition.

Mathematics Curriculum Evaluation

Many current and prospective teachers, policy makers, and members of the public view mathematics as neutral and objective, and they expect mathematics teaching and teacher education to be neutral as well. But what would it mean to think of mathematics teacher education as politically neutral? Below we consider some questions that we see as highlighting why mathematics teacher education cannot be neutral. We are not the first to raise these issues, but we appreciate the opportunity to discuss and reflect on them among a community of mathematics teacher educators. Although these questions have always been relevant, we see their importance growing in the face of the increased mathematization of our world and a highly polarized political landscape with a seemingly increased public acceptance of oppressive discourse and actions (Potok, 2017).

As announced in the editorial of the last issue of Volume 10, I am delighted to assume the role of Chief Editor of the Journal of Mathematics Teacher Education (JMTE). Barbara Jaworski, the outgoing chief editor, outlined the achievements of her custodianship of JMTE. The journal, established by Tom Cooney, has grown to a well-respected forum for the publication of articles of interest to mathematics teacher educators. There have been close to 400 articles submitted in the most recent three year period, with acceptance rates less than 20%, which is testimony to the popularity of the journal, the rigorous reviewing, and to the high standards that have been established by Tom and Barbara. It is indeed an honour for me to follow in the footsteps of such outstanding educators, and I thank Barbara for ensuring the journal has such strong standing. I also thank Terry Wood for her wonderful contribution to the journal. Terry was an associate editor for six years, and was always at the forefront of discussions on the discipline of mathematics teacher education. The standing of the journal is very much due to the contribution of Terry in supporting authors, and indeed her support of the other associate editors. I am delighted that Konard Krainer and Dina Tirosh are continuing as associate editors and so maintaining their continuity, and using the wealth of their experience and expertise in supporting authors. We also welcome two new associate editors: Olive Chapman, from the University of Calgary, maintains the northern American perspective, and Anne Cockburn, from the University of East Anglia, continues to represent a British view of mathematics education and teacher education. We thank the editorial board (see http://www.springer.com/east/home/education/ teachers+%26+teaching?SGWID=5-40411-70-35669386-detailsPage=journal|editorialBoard) for their continued support of the Journal, and to the reviewers for the time and effort they contribute on behalf of authors. One of the first actions of the new editorial team was to review the objectives of JMTE. After consideration of the current objectives, and discussion of alternative emphases, we