Pre-service teachers using the Knowledge Quartet as a tool to analyse and reflect on their own teaching

International audienceThis paper reports a qualitative study of the post-lesson reflections of two pre-service teachers in Norway. During their third school placement, Nora and Mia volunteered to use the Knowledge Quartet to analyse and reflect on their own mathematics teaching. Comparing the nature of their reflections at the start and at the end of the placement, we find that Nora and Mia exhibit some development, focusing more on mathematical content at the end of the study than in the beginning. Factors that can influence their reflections are discussed: their own experience of mathematics and their beliefs about mathematics seemed to play an important role in how they interpreted and made use of the framework

A Tripartite Cooperation? The Challenges of School-University Collaboration in Mathematics Teacher Education in Norway

One goal of Norway’s new primary teacher education programme of 2010 was improved school placement: the relationship between the teacher education institution, practice schools and pre-service teachers was to be formalized as a tripartite cooperation. However, in the area of mathematics education, cooperation is not straightforward: tensions arise because of pre-service teachers’ prior experience and beliefs, and differences between university college training and school practice. This paper reports on questionnaire data and focus group interviews with first-year pre-service teachers and their mentors following school placement. It illustrates the complexity of the partners hip and its impact on pre-service teachers’ professional development in the area of mathematics.Norges forskningsråd 21226

Prospective teachers navigating intersecting communities of practice: early school placement

An issue of particular concern in mathematics teacher education is the relationship between theory and practice, and the nature of university–school partnerships. We report here on results from a research project answering the call for a more systematic understanding of the practice learning context. The study focuses on the new Norwegian elementary teacher education programme and highlights the difficulties involved in connecting theory and practice and how prospective teachers may be supported in this respect. Focus group interviews involving 51 first-year prospective teachers and 25 teacher–mentors investigated early school placements, specifically prospective teachers’ positions in the classroom as teachers of mathematics, and the ways in which the mentoring relationship supported their developing role. Taking a communities of practice perspective, we found that the idea of movement across intersecting and sometimes conflicting communities of practice is helpful in aiding our understanding of the difficulty of connecting theory and practice. Additionally, variations in mentoring styles and perceptions of prospective teachers’ mathematics and pedagogic knowledge competencies play a part in some prospective teachers’ difficulties in taking up a role as legitimate peripheral participant in the school. We conclude by considering ways in which prospective teachers might be better supported to cope with school placement

The mathematics teacher educator as broker: boundary learning

International audienceWe analyse how two co-teaching mathematics teacher educators (MTEs) describe and justify the enactment of their theory of change in a course for practicing teachers. Applying concepts from Communities of Practice, we identify a shared view of the key boundary objects highlighted in the design of the course in our two MTEs, alongside divergent but complementary means of brokering learning at the boundary during enactment. Prominent in our analysis is a working relationship in which one MTE brokering through coordination appears to allow the other to work towards radical transformation, by seeking confrontation that allows her to define the problem space. We consider the implications of this dynamic for their emphasis on teaching as a pair

The mathematics teacher educator as broker: boundary learning

We analyse how two mathematics teacher educators (MTEs) describe, justify and enact their theory of change in a course for practicing teachers that they co-teach. Applying concepts from Communities of Practice, we identify a shared view of the key boundary objects highlighted in the design of the course in our two MTEs, alongside divergent but complementary means of brokering learning at the boundary during enactment. Prominent in our analysis is a working relationship in which one MTE brokering through coordination appears to allow the other to work towards radical transformation, by seeking confrontation that allows her to define the problem space. We consider the implications of this dynamic for their emphasis on teaching as a pair

Making changes in school as a mathematics expert teacher: framing problems of practice

We address the interplay between research and practice in terms of expert teachers’ roles in “cascading” their learning from professional development courses to their colleagues in school. Focusing on five teachers who have participated in two different professional development courses in Norway, we analyse how they frame problems of practice involving colleagues’ practice, despite the fact that the role of “expert” sits uneasily for teachers working within Norway’s flat social structure. We argue that expert teachers’ ability to identify successful ways of working with colleagues through relational agency enables them to see as fully actionable problems of practice that stem from other teachers’ practice even in the absence of a shared problem of practice

Exploring the Interplay between Conceptualizing and Realizing Inquiry—The Case of One Mathematics Teacher’s Trajectory

Inquiry, an approach that departs from traditional mathematics teaching, empowers students through active participation and increased accountability in exploration, argumentation, evaluation, and communication of mathematical ideas. There is broad research consensus on the benefits of inquiry-based approaches to teaching and learning mathematics, including their potential to support equitable mathematics classrooms. While research has separately explored teachers’ conceptions of inquiry and their efforts to enact the practice, little is known about the interplay between mathematics teachers’ conceptions and enactment, and how it could be harnessed in professional development. In this study, we follow Alex, an experienced upper secondary mathematics teacher unfamiliar with inquiry, as he participates in a one-semester professional development course that draws on inquiry in multiple ways. His trajectory towards learning to teach through inquiry is revealed through patterns and shifts in his reflections and classroom actions. Our findings reveal significant developments in Alex’s conception of inquiry and in how he realizes it in his classroom, identifying three paths that illuminate his inquiry trajectory: the teacher’s role in inquiry interactions, a growing idea of inquiry, and orchestrating whole-class situations. In the interplay between enacting and reflecting, he moves from distributing authority separately between himself and ‘the students’ (as one unit) to fostering shared authority, a key aspect of empowerment, between himself and his students (as multiple voices) in both groupwork and whole-class episodes

Challenges in Enacting Classroom Dialogue

In this article, we report on the challenges of enacting a dialogic approach to teaching mathematics. Using the five principles and three repertoires of dialogic teaching as theoretical framework, we draw on interviews and classroom observations of a secondary-school teacher who aspired to teach mathematics through dialogue. We analysed his accounts and videos of his lessons to identify his strategies for dialogic teaching and challenges in implementing these. We found that the usefulness of strategies for dialogue changed over time and that some challenges were manifestations of tensions between the five principles, and thus intrinsic to dialogic teaching. Specifically, concerns for broad participation needed to be balanced against concerns for mathematical content, while the pursuit of a specific mathematical goal – the purposeful principle – lead to missed opportunities for chaining ideas into coherent lines of thinking and understanding – the cumulative principle

Teacher learning towards equitable mathematics classrooms: reframing problems of practice

This study responds to the debate on understanding and evaluating teacher learning in professional development programmes, with particular reference to the development of equitable mathematics classrooms. Conducted in the context of a year-long PD mathematics programme for primary teachers in Norway, designed to disrupt teachers’ assumptions about mathematics pedagogy and how it relates to students’ mathematical thinking, this study takes teachers’ entry goals as its point of departure. Sixteen teachers participated in interviews at the end of the course. Using Horn and Garner’s (2022) account of the situated development of pedagogic judgement as a lens for analysis of teachers’ reflections on their learning, we report on the shift in their ‘problems of practice’ towards actionable concerns about student inclusion. We argue that this shift underpins a fundamental change in their assumptions on teaching and learning and a critical stance towards their own professional practice, suggesting an important indicator of what constitutes sustainable professional development for critical mathematics education