Adult Students\u27 Reasoning in Geometry: Teaching Mathematics through Collaborative Problem Solving in Teacher Education

This article reports research that is concerned with pre-service teachers2 working collaboratively in a problem-solving context without teacher involvement. The aim is to focus on the students’ heuristic strategies employed in the solution process while working on two problems in geometry. Two episodes from the dialogues in one group of students with limited mathematical backgrounds have been chosen to illustrate some mathematical movement throughout the group meetings, from working with the first problem to working with the second one. The findings reveal that three categories of strategies, visualising, monitoring, and questioning, play an important role in order to make progress with the problems. As a preparation for working on the two problems, metacognitive training in combination with cooperative learning was introduced to the students throughout a month. The study indicates that these critical components in the design of the instructional context stimulated the students with limited background in mathematics to improve their problem-solving skills. The analysis has particularly focused on the important role of the process writer that provokes the mathematical discussion by generating utterances categorised as looking-back questions. By recapitulating the solution process or the last idea introduced in the dialogue, the process writer stimulated the establishment of a common ground for the further discussion. The article also deals with issues of teacher involvement in students’ mathematical discussions in collaborative working groups

Lesson study in teacher education: Learning from a challenging case

Whereas most studies of lesson study in teacher education seem to report on success stories, this article investigates a negative case. From an implementation of lesson study in Norwegian teacher education, we analyse data from a mathematics group that struggled with their implementation. Analysis of data from group interviews, mentoring sessions and teaching the research lesson indicates that several crucial aspects of lesson study were missing. The student teachers did not formulate a research question for their research lesson, they did not focus on observing pupil learning, and their lesson was not organized to make pupil learning visible.acceptedVersio

The work of positioning students and content in mathematics teaching

International audienceWhereas other studies have applied positioning theory to analyses of teaching and learning mathematics, this paper takes a practice-based approach to unpack what positioning in mathematics teaching might entail. From analysis of a shared video where a teacher leads a mathematical discussion of the naming of a fraction on the number line, we unpack the work of continually balancing attention to the mathematical content with positioning of students in their relation to each other, to the teacher, and to the mathematical content

Teachers’ perspectives on collaboration with didacticians to create an inquiry community

A research and development project, Learning Communities in Mathematics (LCM) was designed to create opportunities for ‘co-learning inquiry’ between mathematics teachers in eight schools and didacticians in a university in Norway (UiA). The focus has been on improving mathematics teaching and learning at school levels from lower primary to upper secondary and on the developmental processes and partnerships involved. A central aim was to create a community of inquiry through which aspects of mathematics teaching and learning could be explored, and through which both teachers and didacticians could learn in practice. Theoretically, ‘Community of Inquiry’ derives from ‘Community of Practice’ as expounded by Lave andWenger, and particularlyWenger’s concept of ‘belonging’. The project included three, one-year phases of joint activity. At the end of Phase II, didacticians led focus group interviews with teacher teams to gain insights into schools’ and teachers’ perceptions of the project and its activity. We report on insights into how teachers thought about the activities of the project and what an inquiry community looks like in terms of the learning of those involved. We relate this back to the theoretical perspectives of communities of practice and inquiry

Lærerstudenters utvikling av matematikklæreridentitet

I løpet av fire års utdanning skal grunnskolelærerstudenter utvikle seg til å bli lærere. Dette handler ikke bare om å tilegne seg kunnskap; det handler om å utvikle yrkesidentitet. Lærerstudenters identitetsutvikling blir påvirket på ulike måter, og i denne artikkelen bruker vi kulturhistorisk aktivitetsteori for å analysere en gruppe lærerstudenters dialoger før og etter en praksisperiode. Gjennom studentenes refleksjoner – som belyser noen eksempler på praksiserfaringer – ser vi mulige spor av utvikling av yrkesidentitet. I artikkelen diskuteres det også om denne utviklingen kan påvirkes av motsetninger som oppstår når lærerstudenter skal være deltakere i ulike aktivitetssystemer.acceptedVersio

Professional mathematics teacher identity: analysis of reflective narratives from discourses and activities

This article focuses on the methodological use of reflective narratives from discourses and activities of an experienced primary teacher as evidence of her professional identity. The teacher’s reflective narratives emerge from her participation in a 3-year developmental and research project, Learning Communities in Mathematics, conducted at the University of Agder (UiA) in Norway. As background for our study, we firstly present the teacher in action with her sixth-grade pupils in a mathematics lesson, and then analyse selected clusters of reflective narratives from different empirical situations in the project. We have identified four identity indicators, which have been elaborated and organised thematically, related to the teacher’s engagement and critical alignment in the community of participants: (1) Positioning in relation to pupils, (2) Reflecting on developing a workshop model in teaching, (3) Integrating and expanding models of teaching and (4) Challenging positioning in relation to didacticians. These indicators provide evidence of the teacher’s professional identity. We suggest that the emergence of these indicators also gives empirical evidence of professional teacher identity development

Teachers’ perspectives on collaboration with didacticians to create an inquiry community

This article was published in the journal, Research in Mathematics Education [Routledge © British Society for Research into Learning Mathematics]. The definitive version is available at: http://www.tandfonline.com/doi/abs/10.1080/14794800902732209A research and development project, Learning Communities in Mathematics (LCM) was designed to create opportunities for ‘co-learning inquiry’ between mathematics teachers in eight schools and didacticians in a university in Norway (UiA). The focus has been on improving mathematics teaching and learning at school levels from lower primary to upper secondary and on the developmental processes and partnerships involved. A central aim was to create a community of inquiry through which aspects of mathematics teaching and learning could be explored, and through which both teachers and didacticians could learn in practice. Theoretically, ‘Community of Inquiry’ derives from ‘Community of Practice’ as expounded by Lave andWenger, and particularlyWenger’s concept of ‘belonging’. The project included three, one-year phases of joint activity. At the end of Phase II, didacticians led focus group interviews with teacher teams to gain insights into schools’ and teachers’ perceptions of the project and its activity. We report on insights into how teachers thought about the activities of the project and what an inquiry community looks like in terms of the learning of those involved. We relate this back to the theoretical perspectives of communities of practice and inquiry

An Activity Theory View on Learning Studies

The final publication is available at www.springerlink.com.Learning study has been used by many to develop exemplary teaching in school, and this approach has recently been adopted for use in kindergarten as well. When using such approaches in different settings than they were intended for, several challenges potentially arise. This article discusses the implementation of a learning study approach in a Norwegian kindergarten setting and employs activity theory as a framework for this theoretically based analysis. Several potential limitations of the approach are discussed and suggestions for further development are made. Differences between the learning culture of Norwegian kindergartens and, in particular, the view on learning in the theoretical framework of learning studies is emphasized

Learning professional noticing by co-planning mathematics instruction

At the core of ambitious mathematics teaching involves using knowledge of students’ mathematical thinking when facilitating and leading mathematical discussions. A teacher’s ability to productively use this knowledge depends on his/her noticing expertise. This study explores in-service teachers’ opportunities to develop their ability to notice through a practice-based approach to professional development. Fourteen Norwegian elementary-school teachers collaborate with teacher educators in learning cycles of enactment and investigation, where the overarching aim is to learn to enact ambitious mathematics teaching. This study investigates what this innovative approach enables teachers to work on when co-planning to notice. The findings suggest that the co-planning discussions focused on particular students’ mathematical thinking (focused noticing) and on both students’ mathematical thinking and teacher’s pedagogy (extended noticing).publishedVersio