Over the last three decades research in beliefs, and affect more generally, has developed into a significant field of study. It attempts to make sense of teachers’ and students’ understandings of mathematics, of its teaching and learning, and of themselves as doers, teachers, and learners of mathematics and of how these understandings relate to classroom practice. Studies of these issues have been published widely and in the most prestigious journals and book series. However, belief research is still confronted with significant conceptual and methodological problems. I suggest that this is at least in part due to the dominant conceptualization of individual functioning in belief research, one that is based on acquisitionism with its emphasis on human action as an enactment of previously reified mental entities. In the present chapter I build on social practice theory and symbolic interactionism to rephrase key issues of belief research, especially that of the relationship between beliefs and practice, in more participatory terms. The suggestion is to shift the focus from beliefs to the pre-reified processes that are said to give rise to them. This leads to more dynamic understandings of learning and lives in mathematics classrooms and serves to overcome some of the conceptual and methodological problems of the field.
The relationship between acquisitionism and participationism is a challenge in research on and with teachers. This study uses a patterns-of-participation framework (PoP), which aims to develop coherent and dynamic understandings of teaching as well as to meet the conceptual and methodological problems of other approaches. The paper presents PoP theoretically, but also illustrates its empirical use. It presents a novice teacher, Anna, who often engages with mathematics and with aspects of ‘the reform’ in ways that link well with how she builds relationships with her students and positions herself in her team of teachers. However, in other situations her engagement with mathematics is overshadowed by her involvement in other practices. The study suggests that there is some potential in PoP in spite of methodological difficulties.
There is evidence for recommendations to link mathematics teacher education (MTE) closely to school mathematics and to emphasise proving why rather than proving that when teaching reasoning and proof (R&P) in schools. In spite of that we suggest not to take the implication that MTE focuses on proving why to extremes. We outline the background, framework, and results of a pilot to an intervention study that seeks to address the problems of R&P in MTE. The results suggest that teachers face more problems with R&P than expected and have difficulties just selecting situations from school in need of a mathematical justification, let alone developing justifications and supporting their students’ learning of R&P. This supports our suggestion that a dual emphasis on proving that and proving why is needed in MTE
Developing Research in Mathematics Education is the first book in the series New Perspectives on Research in Mathematics Education, to be produced in association with the prestigious European Society for Research in Mathematics Education. This inaugural volume sets out broad advances in research in mathematics education which have accumulated over the last 20 years through the sustained exchange of ideas and collaboration between researchers in the field. An impressive range of contributors provide specifically European and complementary global perspectives on major areas of research in the field on topics that include:the content domains of arithmetic, geometry, algebra, statistics, and probability;the mathematical processes of proving and modeling;teaching and learning at specific age levels from early years to university;teacher education, teaching and classroom practices;special aspects of teaching and learning mathematics such as creativity, affect, diversity, technology and history;theoretical perspectives and comparative approaches in mathematics education research.This book is a fascinating compendium of state-of-the-art knowledge for all mathematics education researchers, graduate students, teacher educators and curriculum developers worldwide.
There are two sets of backgrounds to the presentation. First, it is generally acknowledged that the frameworks used in research shape the results obtained in fundamental ways. However, it is not always made clear how conceptual or theoretical frameworks are conceptualised, in what ways competing frameworks differ from one another, and what role a particular framework plays in a study. Second, research on and with mathematics teachers has since the beginning of the 1980s had a dual focus on understanding teachers’ acts and meaning-making and solving what is often referred to as the problems of implementation. However, more often than not studies are based on acquisitionist interpretations of human functioning, and the more participatory stance increasingly adopted in other lines of research in mathematics education is rarely considered.
In the first part of the session Jeppe discusses the notion of a conceptual framework and presents an approach to analysing and comparing frameworks. He presents a framework called Patterns of Participation (PoP) that adopts a participatory perspective on teaching and teacher learning, and he compares it with other lines of research conducted on and with teachers. In line with social practice theory, PoP views classroom practice as a social phenomenon, but seeks to re-centre the individual, rather than a particular practice, in the analysis. One moral of the story is that PoP offers a valuable, complementary perspective on learning to teach; another that the implementation metaphor often used in research on and with teachers does not do justice to the complexity of teaching.
In the second part of the session Charlotte introduces how she and her colleagues have adapted the Japanese method of Lesson Study (LS) to work with teachers at a school in a Copenhagen suburb. Doing so they interpret teacher learning in PoP terms. Research into how LS contributes to teachers’ professional development often seeks to identify connections between features of the method and teacher learning. However, many such studies focus on and try to document teacher learning without accounting theoretically for what is meant by the term of teacher learning. Using PoP, Charlotte will give a theoretical account of one mathematics teachers’ learning by analysing changes in his participation during the collaborative LS-processes.
DELTA 2.0 er en ny og helt opdateret udgave af Delta, der i ti år har været brugt i matematiklærernes grund-, efter- og videreuddannelse.DELTA 2.0 er del af serien MATEMATIK FOR LÆRERSTUDERENDE.Ud over DELTA 2.0 består serien af fem bøger med fokus på matematisk indhold: to om Tal, algebra og funktioner, to om Geometri og en om Stokastik, hvortil kommer en bog om elever med særlige behov i matematikundervisningen. Bøgerne i serien er et ambitiøst forsøg på at sammentænke de matematikfaglige aspekter af læreruddannelsen med fagdidaktiske og professionsrettede overvejelser.DELTA 2.0 er seriens almene fagdidaktik. Der er også fagdidaktiske overvejelser i de øvrige bøger i serien, men de er knyttet til specifikt matematisk indhold. DELTA 2.0 behandler mere generelle matematikdidaktiske problemstillinger som læringsteoretiske overvejelser i forbindelse med matematik, centrale aspekter af det at undervise i matematik og digitale teknologier som værktøj til at støtte elevers faglige læring af matematik. Det er en gennemgående idé i DELTA 2.0 at formulere matematikdidaktiske fokuspunkter, som i særlig grad er vigtige for lærere at reflektere over.DELTA 2.0 henvender sig ikke blot til lærerstuderende, men kan også anvendes i matematiklærernes efter- og videreuddannelse, fx diplom-, kandidat- eller masteruddannelser. Desuden vil matematiklærere kunne finde inspiration til udvikling af egenundervisning.
The study reported in this paper concerns the tensions and conflicts that teachers experience while they enact a new set of reform-oriented curricular materials into their classrooms. Our focus is οn the interactions developed in two groups of teachers in two schools for a period of a school year. We use Activity Theory to study emerging contradictions and we elaborate on the construct of dialectical opposition to understand the nature of these contradictions and their potential for teacher learning. We provide evidence that discussions about contradictions and their dialectical character in the two groups support teachers to engage differently in mathematics teaching and learning and carry potentials for shifts in the practices that evolve in their classrooms. Our study addresses empirically in the context of mathematics teaching the philosophical claim about the role of contradictions as a driving force for any dynamic system.