Mathematics Teachers in Collaboration: A Commentary

2015

After an introduction on the importance of redefining the didactic system in the terms of a more global interpretation of the personal relationships which intertwine in it, we look at the general principals of “cooperative learning”, an educational strategy by social mediation in which the resources for the construction of knowledge are the students, who are called upon both to accomplish a disciplinary task and to develop social abilities. The role of the teacher remains fundamental, being the organiser and facilitator of the entire process. After the presentation of some didactic experiences carried out in the upper secondary school with the cooperative groups, some elements of the evaluation of the experiences carried out are put forth, also through the judgments expressed by the students themselves. At the end, note is made of some open problems which it seems necessary to confront. 1.

Proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education, 24, (vol 3, pp. 1439-1450). Columbus, OH: ERIC Clearinghouse. , 2002

In this paper I explore the challenges and possibilities for teacher learning in study groups by examining the typical discourse generated in one particular group. Special attention was paid to the teachers’ talk when doing mathematics together and when talking about their teaching practices and students’ work. When doing mathematics together, the examined group’s talk can be described as exploratory talk, that is talk characterized by speakers seeking and showing intellectual involvement; public disclosure of disagreements and confusion; and talk that is generative and collaborative. In contrast, the teachers' talk about their teaching and students' work can be categorized as expository talk, which can be characterized by the use of monologues; speakers seeking and giving approval; and the non-analytical or unproblematic narration of events. These are features of study group talk that seem important to attend to and study as these affect the participants’ learning opportunities and impact the design and leadership of teacher groups.

International Group for the Psychology of Mathematics Education, 2011

A common practice in mathematics professional development to enhance teachers’ content knowledge is to engage them in solving and discussing mathematics tasks. Yet, what is entailed in these experiences and how teacher discussions afford or constrain opportunities to develop teachers’ knowledge of mathematics is not fully understood. In this paper, the authors provide a research-based framework to analyze teachers’ mathematical productions (verbal reasoning and written inscriptions) used in collaborative mathematical work that illustrates the complexity of considering teachers’ opportunities to learn and how discussion of mathematics may or may not be resources for learning.

HAL (Le Centre pour la Communication Scientifique Directe), 2019

We aim to understand how primary teachers who participated in a lesson study developed their collaboration relationships. The research is qualitative and interpretive with a case study design. The results show that the involvement in moments of planning and analysis of the students' work, where teachers reflected on practice and for practice helped them to develop collaborative relationships, moving from storytelling and scanning to joint work. The teachers were encouraged to express their voices regarding their participation in the lesson study and this led to an increasing involvement in the group, favoring the development of their reflection and knowledge of mathematics teaching.

mai.liu.se

The value of mathematical dialogues between students and teachers is not restricted to the educational value for students. They are also fundamental for the teacher's ongoing professional development. This aspect is also connected to student's sense of responsibility-to the students awareness of that their mathematical activity is regarded as potentially valuable for the teacher's development of the education, and thus for the benefit of future students. Many years of teaching experience is not equivalent to high professional skill. Development of skill during years of teaching is strongly dependent on the reflective activity on the ongoing practice. How can such reflection be carried out? Student-teacher dialogues are probably essential material here, being traces of authentic mathematical thinking. We discuss action research, that targets teachers development by the practice, and the inspiring method of the dialogue seminar. The goal of this paper is to bring together dialogue, student thinking, teacher development, and reflection tools such as the dialogue seminar, aiming towards an extended version of mathematicsextended in conceptual direction. This version of mathematics should be generally available and become visible for example in the main exhibition venue of mathematics: the text books. Reflection on student-teacher practice may have an natural output as "conceptual mathematics"-mathematics "from the outside", which formulates observations of how mathematics works that are useful for teachers in their teaching. Conceptual mathematics is an intended remedy of the common and reasonable complain of students as mathematics being very fragmentized. The argumentation is based on the standpoint that mathematics requires more dialogue than other subjects, and not less, at it continues to be. This is due both to its abstract and hard-to-reach concepts and strange not-so-intuitive symbolic language.

New ICMI studies series, 2024

Research suggests that collaborative professional development has the potential for impactful effects on teaching practices and student achievement . Yet, the OECD's most recent Teaching and Learning International Survey (TALIS) data show a comparatively low percentage of teachers participating in collaborative professional learning activities (OECD, 2019). This chapter examines the involvement of four mathematics teachers in collaborative groups, with the aim of: (i) understanding the kinds of opportunities for learning that these groups provided and the impact that they had; (ii) synthesising insights from the teachers' participation in these groups to inform the ways that mathematics teachers might work and learn in collaborative groups in the future. The four teachers were invited to participate in a Plenary Panel at the ICMI Study 25 Conference, where they shared accounts of their collaborative group work and learning. Each teacher was asked to report on three areas, including: the context, purpose and design of the collaboration; outcomes of the collaboration; particular

ZDM, 2013

In her overview of trends in mathematics education research, Anna suggests that ''the last few years have been the era of the teacher as the almost uncontested focus of researchers' attention' ' (p. 409, emphasis in original). Since then the research interest in teachers has certainly not diminished, as evidenced by the high and growing number of conference papers, journal articles, and monographs in the field as well as by the emphasis on teachers and teacher education in recent handbooks on mathematics education. It is a characteristic feature of most of this research that it is conducted within one of the three relatively distinct fields of teachers' knowledge, teachers' beliefs (or affect more generally), and teacher identity. Despite the unquestionable advances in each of the three fields, there is a somewhat surprising disconnect between them, leading to an incoherent view of the teacher and her or his role in instruction. This seems to be due not only to the different objects of investigation, but at least in part to different theoretical and methodological assumptions leading to qualitatively different units of analysis. Notwithstanding the differences within each of the three fields, research practices among them appear to particularly differ in their ways of dealing with (1) the relationships between individual and social understandings of teacher development and the role of the teacher for classroom practice, and (2) the relationship between theory and practice, especially the expectations with regard to impact on instruction and student learning.

2017

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Introduction to the papers of TWG18: International research on mathematics teacher education and professional development Stefan Zehetmeier, Laurinda Brown, Maria Mellone, Leonor Santos, Gulseren Karagoz Akar

2019

Since its birth in the aftermath of CERME10, discussions in TWG19 concentrated on identifying its research territory and on creating opportunities for collaboration among the participants beyond the conference sessions. These discussions led to shifting the focus of the group on mathematics teaching and teacher practice (s) and to an initiative of working on shared data that fueled fruitful explorations related to conceptualizations and theorization of mathematics teaching. The participants’ contributions and the work carried out during CERME11 sessions challenged further the core ideas of how mathematics teaching can be defined and studied while an emerging distinction between teaching as an activity and teaching as work stimulated further the group’s discussions.

I believe the key problems in the preparation of teachers of mathematics are related to inadequate visions of the purposes of education and of the role of mathematics teachers as educators. Prospective and in-service teachers of mathematics should be always reflecting on changes in education, which result from profound changes in society particularly those in the demographic scenario, in production, in information, and in communication. I will elaborate on the purposes of education and on the role of mathematics teachers as educators.

… and Development of …, 2009

HAL (Le Centre pour la Communication Scientifique Directe), 2017

2016

The paper deals with teacher education in the institutional context, using the Meta-Didactical Transposition framework (based on Chevallard theory of transposition) for analysing the processes of researchers and teachers working together in designing tasks of an educational programme, training teachers in these tasks, and following them while experimenting the same tasks with their students. The research aim of the paper is to describe the features of the practices of these communities, to identify them as community of design and community of experimentation, according to the praxeologies they put into action in the processes of designing, training, experimenting. Particularly, this study is referred to a research and educational programme on MERLO (Meaning Equivalence Reusable Learning Objects) items, a didactical tool for involving students in group/individual activities that involve deep understanding in mathematics and assessing them. Résumé: Cet article concerne la formation de...

Teachers and Teaching, 1997

This paper describes research into the beliefs and practices established over time by teachers, who had been engaged in an innovative 'mathematical investigations' school program, based on the use of exploratory software. The theoretical framework perceives the teacher as an active mediator of innovation, constructing and reorganizing a personal pedagogy. Interview and detailed observational classroom data were collected and analyzed, synthesizing qualitative and quantitative interpretations of teachers' comments in the classroom. The results show that teachers refer to a variety of aspects of the learning situations in which they intervene rather than just the mathematical concepts and ideas. They adopt multiple roles in the classroom and are influenced by the values of the educational system. The ways in which these issues influence teaching and learning of the mathematical concepts at hand is considered. The nature of teacher beliefs and the ways in which they may influence their practice is questioned.

2011

To address the shortage of mathematics teachers in England, serving teachers, qualified in subjects other than mathematics yet teaching secondary mathematics, were eligible to participate in a Mathematics Development Programme for Teachers (MDPT) commissioned and funded by the Teacher Development Agency (TDA). A research project was set up to investigate how teachers in our 2010-11 cohort developed into mathematics teachers within this Programme. This report indicates how (1) learning new mathematics, (2) developing a view on the nature of mathematics and (3) teaching mathematics in different ways, contribute to a mathematics teacher identity, yet there was a discrepancy between the teachers' espoused confidence in being a mathematics teacher and their technical mathematical competence.