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  • 1.
    Eckert, Andreas
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Agency as a tool in design research collaborations2017In: PROCEEDINGS OF THE TENTH CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION (CERME10) / [ed] Dooley, T Gueudet, G, DUBLIN CITY UNIV GLASNEVIN CAMPUS, INST EDUCATION , 2017, p. 3666-3673Conference paper (Refereed)
    Abstract [en]

    The aim in this paper is to shed light on interactional aspects of researcher and practitioner collaboration in design research in mathematics education. Symbolic interactionism is used to gain understanding of interactional aspects as it has potential to take both individual and social aspects of the interaction into account. Aims and agencies are in focus of the retrospective analysis of the collaboration between two researchers and two practitioners as they collaborate to develop instructional design. The analysis show how referring to authoritative disciplines as the mathematics community influence agency and therefore has great potential to influence how the negotiation of meaning progress and participants acts. I argue that agency could be viewed as an indirect tool that has the potential to direct the collaboration when designing tasks based on what aim different actors put in the foreground.

  • 2.
    Eckert, Andreas
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Contributing to develop contributions: - a metaphor for teaching in the reform mathematics classroom2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis aims at contributing to the theoretical research discourse on teaching mathematics. More precise, to explore a teacher’s role and actions while negotiating meaning of mathematical objects in discursive transformative practices in mathematics. The focus is to highlight the teacher as an active contributor to the classroom mathematical discourse, having an important role in shaping the mathematics. At the same time, the teacher is acknowledged as an individual who learns and develops as a lesson and semester progress.

    Three research papers illustrate the state, at that time, of an inductive analysis of three teachers, teaching a series of lessons based on probability theory at two Swedish primary schools. The teachers worked together with the students to explore an unknown sample space, made up out of an opaque bottle with coloured marbles within that showed one marble at each turn of the bottle. They had to construct mathematical tools together to help them solve the mystery. The analysis focused on teacher–student interactions during this exploration, revealing complex connections in the process of teaching.

    The three papers presented the development of a theoretical framework named Contributing to Develop Contributions (CDC). The frameworks’ fundamental idea is that teachers learn as they teach, using the teaching metaphor learning to develop learning. That metaphor was developed, in light of the ongoing empirical analysis, into CDC by drawing on a theoretical idea that learning can be viewed as contributing to the collaborative meaning making in the classroom. Teaching and teacher learning are described and understood as reflexive processes in relation to in-the-moment teacher-student interaction.

    Contributing to develop contributions consists of three different ways of contributing. The analytical categories illustrate how students’ opportunities to contribute to the negotiation of mathematical meaning are closely linked to teachers’ different ways of contributing. The different ways are Contributing one’s own interpretations of mathematical objects, Contributing with others’ interpretations of mathematical objects, and Contributing by eliciting contributions. Each way of contributing was found to have the attributes Transparency, Role-taking and Authority. Together, these six categories show teacher– student interaction as a complex dynamical system where they draw on each other and together negotiate meaning of mathematical objects in the classroom.

    This thesis reveals how the teaching process can be viewed in terms of learning on different levels. Learning as thought of in terms of contributing to the negotiation of meaning in the moment-to-moment interaction in the classroom. By contributing you influence the collective’s understanding as well as your own. A teacher exercises and develops ways of contributing to the negotiation of meaning of mathematical objects, in order to develop students’ contributions. In a wider perspective, the analysis showed development over time in terms of transformation. The teachers were found to have transformed their understanding of classroom situations in light of the present interactions. Contributing to the negotiation of meaning in the classroom was understood as a process in such transformation, in the ever ongoing becoming of a mathematics teacher. 

  • 3.
    Eckert, Andreas
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    The potential of a grounded theory approach to study teaching probability2014In: Proceedings of the NinthInternational Conference on Teaching Statistics (ICOTS9, July, 2014), Flagstaff, Arizona, USA: Sustainability in statistics education / [ed] Makar, K., de Sousa, B., & Gould R., International statistical institute , 2014Conference paper (Other academic)
    Abstract [en]

    An important part of teaching probability is teachers interacting with students about probability.Most of these interactions do not occur anywhere else but inside the classroom so that is where weshould research teacher knowledge for future development of teacher training and professionaldevelopment. To accomplish this I propose a research methodology founded on the theoreticalassumptions of symbolic interactionism combined with a grounded theory approach. The purposeof this paper is to outline such a research methodology that focuses on teaching as classroominteraction between teachers and students. The discussion aims to emphasize the possibilities bythis way of studying teachers’ knowledge for teaching probability and refine the methodologicalconstruct. Examples used are from lessons where two teachers work with unknown sample spacesand interact with students regarding chance, variation and the importance of sampling.

  • 4.
    Eckert, Andreas
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Nilsson, Per
    Linnaeus University, Faculty of Technology, Department of Mathematics, Department of Mathematics Education.
    Contextualizing Sampling: Teaching Challenges and Possibilities2013In: Proceedings of the Eight Conference of European Research in Mathematics Education, European Society for Research in Mathematics Education, 2013Conference paper (Refereed)
    Abstract [en]

    The aim of the present paper is to shed light on mathematical knowledge for teaching probability. In particular we investigate critical instances when a teacher tries to keep track on the idea of sampling and random variation by allocating the discussion to an everyday context. The analysis is based on a certain episode of a longer teaching experiment. The analytical construct of contextualization was used as a means to provide structure to the qualitative analysis performed. Our analysis provides insight into the nature and role of teachers’ knowledge of content and teaching. In particular, the study suggests the idea of a meta-contextual knowledge that teachers need to develop in order to keep track of the intended object of learning when allocating their teaching to an everyday context. 

  • 5.
    Eckert, Andreas
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Nilsson, Per
    Örebro University.
    Introducing a symbolic interactionist approach on teaching mathematics: The case of revoicing as an interactional strategy in the teaching of probability2017In: Journal of Mathematics Teacher Education, ISSN 1386-4416, E-ISSN 1573-1820, Vol. 20, no 1, p. 31-48Article in journal (Refereed)
    Abstract [en]

    This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher’s role in the negotiation of meaning. Using methods inspired by grounded theory, patterns of teachers’ interaction are categorized. The results show how teachers’ actions, interpretations and intentions form interactional strategies that guide the negotiation of meaning in the classroom. The theoretical case of revoicing as a teacher action, together with interpretations of mathematical objects from probability theory, is used to exemplify conclusions from the proposed perspective. Data are generated from a lesson sequence with two teachers working with known and unknown constant sample spaces with their classes. In the lessons presented in this article, the focus is on negotiations of the meaning of chance. The analysis revealed how the teachers indicate their interpretations of mathematical objects and intentions to the students to different degrees and, by doing so, create opportunities for the students to ascribe meaning to these objects. The discussion contrasts the findings with possible interpretations from other perspectives on teaching.

  • 6.
    Seidouvy, Abdel
    et al.
    Örebro University, Sweden.
    Eckert, Andreas
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Designing for responsibility and authority in experiment based instruction in mathematics: The case of reasoning with uncertainty2017In: PROCEEDINGS OF THE TENTH CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION (CERME10) / [ed] Dooley, T Gueudet, G, DUBLIN CITY UNIV GLASNEVIN CAMPUS, INST EDUCATION , 2017, p. 3740-3747Conference paper (Refereed)
    Abstract [en]

    This study examines principles of task design concerning the concept of uncertainty in the area of statistics. A purpose is to promote and support students reasoning competency involving the aspects authority and responsibility. By using inferential role semantics as a background theory, we examine students' reasoning by means of how they show authority and responsibility for statements in the reasoning process. Statistical tasks where students generate and analyze their own data formed the basis for this pilot study conducted with seventh grade students in Sweden. The students were able to reflect on how their actions and consequences of their actions influence their reasoning with uncertainty. The study describes the findings, and presents principles to inform the design of innovative learning environments that promote authority and responsibility in reasoning in the domain of uncertainty.

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