01 SES 07 B, Collaborative Approaches to Professional Learning
The purpose of this paper is to shed light on how Edda, a classroom teacher in elementary school, learned to deal with conflicting views about mathematics teaching and –learning at her new school. The aim is to explore how her participation in a developmental research project with six teachers and a mathematics teacher educator enabled her to resolve her disagreement with her colleagues. The goal with the research project was to identify approaches to teacher education that could support teachers in meeting the needs of diverse learners in the mathematics classroom. Edda’s contribution to the project added to the understanding of the problems teachers meet when they enter a new professional community where the culture differs from what they expected.
The theories that guided the study are sociocultural, in the Vygotskian sense, that individual cognition develops when people change their ways of understanding, perceiving, noticing and thinking through shared efforts with others (Vygotsky, 1978). During this development, they build on the cultural practices and traditions of communities such that participation is seen as both a social process and a personal experience (Lave & Wenger, 1991). When developing learning communities where the diverse background of the participants is respected, everyone’s contributions must be valued. Jaworski (2006) argues that collective learning develops through a mutually reflexive process of knowledge growth between individuals and a community in which co-learning partnership is cultivated. Thus, through the process of sharing experiences and developing norms, the community provides supportive structures for individual inquiry and acts to mediate knowledge so that knowledge grows within the community, as well as for each individual.
Askew (2015) argues that in order to foster an inclusive approach in attending to diverse learners needs, it is important to begin with learning communities, rather than taking the individual as the starting point for planning learning experiences. In these communities, teachers work with the collective construction of mathematical knowledge while still ultimately addressing the needs of the individuals within that community. This is the position I took in working with teachers when attending to their different needs for improving their teaching.
Reflecting on and in one’s own practice is an essential feature of teacher development and in inquiring into one’s teaching. In a community of inquiry according to Jaworski (2008) the inquiry is seen both as a tool for developing practice and as a way of being in practice, and thus, inquiry becomes a norm of a community of practice. When individuals are encouraged to look critically at their own practices and to modify these through their own learning-in-practice, there will be a shift from “community of practice” to “community of inquiry”. Through the shift a perspective emerges in which reflective development of practice by practitioners, individually or in groups, can be seen to result in the development of community.
The participants in the study belong to different communities, within a complex landscape of learning (Wenger-Trayner & Wenger-Trayner, 2015), that all affect how we interpret the learning that developed within our community and thus our own individual development as mathematics teachers and a teacher educator. The teachers’ background and the experience they bring into our community, shape our collaborative work.
Modes of inquiry A model of a developmental research cycle as put forth by Goodchild (2008) was used as the framework for the research project. In this model there are two interconnected cycles of development and research that model a linked dialectical growth of theory and practice. In the developmental process the teachers were supported to reflect on their mathematics teaching as well as their own way of working with mathematics. Seven teachers in grades 5-7 in two neighbouring schools and a mathematics teacher educator (the author of this paper) met at workshops on a monthly basis for three years. They solved mathematics problems together and shared and discussed their experiences of researching into their own teaching and learning. The teacher educator assured dialectical growth of theory and practice and urged the teachers to take lead in shaping the developmental process within their learning community. A narrative of each of the teachers was developed throughout the project, based on the stories they told at workshops and in interviews (Clandinin, 2013). These stories are their first-person identity stories, which formed the basis for the narratives the teacher educator wrote. Each teacher read and commented on her own narrative, which then became a second-person identity story. Finally the teacher educator wrote a third-person identity story of each of the teachers (Sfard & Prusak, 2005). Data sources Data was collected of videotapes from workshops, audiotapes from interviews and notes from classroom observations. To learn about the teachers’ visions for the project and the cultures in their mathematics classrooms the teacher educator interviewed them and observed their classrooms three times. The analysis of the results started at the outset of the study as a spiral of analysis developed over time (Creswell, 2007).
Results The workshops were based on the participants’ expectations for the project. They wanted to learn about collaborative approaches to mathematics teaching and how to teach for relational understanding (Skemp, 1976). To begin with the focus was much on the teachers’ own explorations with mathematical problems and discussions about their diverse approaches to solving them. As the project progressed the teachers gradually took the lead in deciding what to focus on at each workshop. When Edda joined the project she was new at her school and found it difficult to adjust to the culture in the school where emphasis was placed on rote learning and memorizing of facts in mathematics classes. She underlined the significance of teaching for under¬standing and tried to approach her teaching in a variety of ways to encourage her pupils’ understanding. She sought to develop her teaching by drawing on what she learned at the workshops where she was always active, engaging with the other teachers on how she solved different problems. When Edda was empowered to rethink her own way of solving mathematical problems she started to pay attention to the communication in her classroom and focus on the learning of her pupils. Her teaching habits changed as by the end of the project she placed more emphasis on inquiry based approaches than she did at the outset. This was also reflected in the other participants’ work. Conflicts about effective ways of learning mathematics were resolved by careful considerations of children’s diverse ways of learning. One major concern was how to resolve conflicts concerning established norms about mathematics teaching and learning. The results of this project showed that in future research conflicts from the advent of new communities can be resolved through close collaboration with the communities of practices already present within the teachers’ schools.
Askew, M. (2015). Diversity, inclusion and equity in mathematics classrooms: From individual problems to collective possibility. In A. Bishop, H. Tan, & T. N. Barkatsas (Eds.), Diversity in mathematics education: Towards inclusive practices (pp. 129–145). Cham: Springer. Doi: 10.1007/978-3-319-05978-5 Clandinin, D. J. (2013). Engaging in narrative inquiry. Walnut Creek: Left Coast Press. Creswell, J. W. (2007). Qualitative inquiry & research design: Choosing among five approaches. Thousand Oaks: Sage. Goodchild, S. (2008). A quest for a ‘good research’: The mathematics teacher educator as a practitioner researcher in a community of inquiry. In B. Jaworski, & T. Wood (Eds.), The international handbook of mathematics teacher education. Vol. 4: The mathematics teacher educator as a developing professional (pp. 201–220). Rotterdam: Sense Publishers. Jaworski, B. (2006). Theory and practice in mathematics teaching development: Critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education, 9(2), 187–211. Jaworski, B. (2008). Building and sustaining inquiry communities in mathematics teaching development. In K. Krainer, & T. Wood (Eds.), The international handbook of mathematics teacher education. Vol. 3: Participants in mathematics teacher education (pp. 309–330). Rotterdam: Sense Publishers. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press. Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytical tool for investigating learning as culturally shaped activity. Educational Researcher, 34(4), 14–22. Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 76(1), 4–14. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. M. Cole, V. John-Steiner, S. Scribner, & E. Souberman (Eds. and trans.). Cambridge: Harvard University Press. Wenger-Trayner, E., & Wenger-Trayner, B. (2015). Learning in a landscape of practice: A framework. In E. Wenger-Trayner, M. Fenton-O'Creevy, S. Hutchinsn, C. Kubiak, & B. Wenger-Trayner (Eds.), Learning in landscapes of practice: Boundaries, identity, and knowledgeability in practice-based learning (pp. 13–29). London: Routledge.
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