Variation theory and teaching experiences as tools to generate knowledge about teaching and learning mathematics – the case of pre-service teachers
Abstract
The theory-practice divide in teacher education is commonly viewed as there are two separate entities – theory and practice. However, in practice-based research approaches, theory is commonly integrated with existing practical knowledge with the aim to deepen teachers’ knowledge about practice or to create new knowledge. In this study, we examine 30 pre-service teachers taking part in a 5-week course in a teacher education program in Sweden, in which an action-research approach termed Learning study was used to deepen the pre-service teachers’ thinking and reasoning about mathematics teaching in order to develop primary student learning. Variation theory was used as a tool to support the pre-service teachers’ reflections on how different ways of structuring the mathematical content are related to student learning outcomes. This research aims to illustrate how the integration of theory and teaching experiences from the 5-week mathematics education course supported pre-service teachers’ generation of knowledge about teaching and learning mathematics. In this study, we regard mathematical tasks created by the pre-service teachers and used in the lessons as generated knowledge about the practice of teaching. Data were collected during the course and consist of written reports about task refinements in the pre-service teachers’ lessons. We identified five different ways of re-designing the tasks: expanding tasks, making tasks more explicit, making tasks less explicit, bringing metaphors and representations to the foreground, and creating new tasks.
References
Ax, J., Ponte, P. & Brouwer, N. (2006). Action research in initial teacher education: an explorative study. Educational Action Research, 16 (1), 55-72. https://doi.org/10.1080/09650790701833105
Brante, G., Holmqvist Olander, M., Holmquist, P.-O. & Palla, M. (2015). Theorising teaching and learning: pre-service teachers' theoretical awareness of learning. European Journal of Teacher Education, 38 (1), 102-118. https://doi.org/10.1080/02619768.2014.902437
Cheng, C. K. (2014). Learning study: nurturing the instructional design and teaching competency of pre-service teachers. Asia-Pacific Journal of Teacher Education, 42 (1), 51-61. https://doi.org/10.1080/1359866X.2013.869546
Davies, P. & Dunnill, R. (2008). "Learning study" as a model of collaborative practice in initial teacher education. Journal of Education for Teaching, 34 (1), 3-16. https://doi.org/10.1080/02607470701773408
Denscombe, M. (2017). The good research guide: for small-scale social research projects (sixth edition.). Open University Press.
Dewey, J. (1904). The relation of theory to practice in education. In C. A. McMurry (Ed.), The third yearbook of the national society for the scientific study of education. Part I. (pp. 9-30). The University of Chicago Press. https://doi.org/10.1177/016146810400500601
Durden, G. (2018). Improving teacher learning: variation in conceptions of learning study. International Journal for Lesson and Learning Studies, 7 (1), 50-61. https://doi.org/10.1108/IJLLS-09-2017-0041
Elliott, J. (2012). Developing a science of teaching through lesson study. International Journal for Lesson and Learning Studies, 1 (2), 108-125. https://doi.org/10.1108/20468251211224163
Goodson, I. & Hargreaves, A. 1996. Teachers' professional lives. Routledge.
Huang, R., Takahashi, A. & Ponte, J. P. da (Eds.) (2019). Theory and practice of lesson study in mathematics: an international perspective. Springer. https://doi.org/10.1007/978-3-030-04031-4_28
Ko, P. Y. (2012). Critical conditions for pre-service teachers' learning through inquiry: the learning study approach in Hong Kong. International Journal for Lesson and Learning Studies, 1 (1), 49-64. https://doi.org/10.1108/20468251211179704
Korthagen, F. A. J. (2010). The relationship between theory and practice in teacher education. In P. Peterson, E. Baker & B. McGaw, (Eds.), International Encyclopedia of Education (pp. 669-675). Elsevier. https://doi.org/10.1016/B978-0-08-044894-7.00638-2
Kullberg, A., Runesson, U. & Marton, F. (2017) What is made possible to learn when using the variation theory of learning in teaching mathematics? ZDM, 49 (4), 559-569. https://doi.org/10.1007/s11858-017-0858-4
Lai, M. Y. & Lo-Fu, Y. W. P. (2013). Incorporating learning study in a teacher education program in Hong Kong: a case study. International Journal for Lesson and Learning Studies, 2 (1), 72-89. https://doi.org/10.1108/20468251311290141
Lampert, M. (2010). Learning teaching in, from, and for practice: What do we mean? Journal of teacher education, 61 (1-2), 21-34. https://doi.org/10.1177/0022487109347321
Larssen, D. L. S., Cajker, W., Mosvold, R., Bjuland, R., Helgevold, N. et al. (2018). A literature review of lesson study in initial teacher education: perspectives about learning and observation. International Journal for Lesson and Learning Studies, 7 (1), 8-22. https://doi.org/10.1108/IJLLS-06-2017-0030
Lo, M. L., Pong, W. Y. & Chik, P. P. M. (2005). For each and everyone. Catering for individual differences through learning studies. Hong Kong University Press. Loughran, J. (2006). Developing a pedagogy of teacher education: understanding teaching and learning about teaching. Taylor & Francis.
Marton, F. (2015). Necessary condition of learning. Routledge. https://doi.org/10.4324/9781315816876
Marton, F. & Booth, S. (1997). Learning and awareness. Lawrence Erlbaum.
McGarr, O., O'Grady, E. & Guilfoyle, L. (2017). Exploring the theory-practice gap in initial teacher education: moving beyond questions of relevance to issues of power and authority. Journal of Education for Teaching, 43 (1), 48-60. https://doi.org/10.1080/02607476.2017.1256040
McIntosh, A. (2008). Förstå och använda tal: en handbok. National Centre for Mathematics Education, University of Gothenburg.
McMahon, M., Forde, C. & Dickson, B. (2015). Reshaping teacher education through the professional continuum. Educational Review, 67 (2), 158-178. https://doi.org/10.1080/00131911.2013.846298
Morris, A. K. & Hiebert, J. (2011). Creating shared instructional products: an alternative approach to improving teaching. Educational Researcher, 40 (1), 5-14. https://doi.org/10.3102/0013189X10393501
Mårtensson, P. (2019). Learning to see distinctions through learning studies: critical aspects as an example of pedagogical content knowledge. International Journal for Lesson and Learning Studies, 8 (3), 196-211. https://doi.org/10.1108/IJLLS-10-2018-0069
Nuthall, G. (2004). Relating classroom teaching to student learning: a critical analysis of why research has failed to bridge the theory-practice gap. Harvard Educational Review, 74 (3), 273-306. https://doi.org/10.17763/haer.74.3.e08k1276713824u5
Pang. M. F. & Ki, W. W. (2016). Revisiting the idea of "critical aspects". Scandinavian Journal of Educational Research, 60 (3), 323-336. https://doi.org/10.1080/00313831.2015.1119724
Pang, M. F. & Marton, F. (2003). Beyond "lesson study" - comparing two ways of facilitating the grasp of economic concepts. Instructional Science, 31 (3), 175-194. https://doi.org/10.1023/A:1023280619632
Royea, D. & Nicol, C. (2019). Pre-service teachers' experiences of learning study: learning with and using variation theory. Educational Action Research, 27 (4), 564-580. https://doi.org/10.1080/09650792.2018.1515094
Runesson, U. & Gustafsson, G. (2012). Sharing and developing knowledge products from learning study. International Journal for Lesson and Learning Studies, 1 (3), 245-260. https://doi.org/10.1108/20468251211256447
Skolverket. (2019). Läroplan för grundskolan, förskoleklassen och fritidshemmet 2011 (reviderad 2019). Skolverket.
Skott, J., Jess, K. & Hansen, H. C. & Lundin, S. (2010). Matematik för lärare. Delta Didaktik. Gleerups Utbildning.
Stenhouse. L. (1981). What counts as research? British Journal of Educational Studies, 2, 103-114. https://doi.org/10.1080/00071005.1981.9973589
Sugrue, C. (1997). Student teachers' lay theories and teaching identities: their implications for professional development. European Journal of Teacher Education, 20 (3), 213-225. https://doi.org/10.1080/0261976970200302
Thompson, P. W. (2008). Conceptual analysis of mathematical ideas: some spadework at the foundations of mathematics education. In O. Figueras et al. (Eds.), Proceedings of PME 32 (pp. 31-49). PME. http://www.igpme.org/publications/current-proceedings/
Turu, M. (2017). Initial teacher education: exploring student teachers' experiences in a physics learning study. Leeds Beckett University. https://eprints.leedsbeckett.ac.uk/id/eprint/3948/
Watson, A. & Mason, J. (2006). Seeing an exercise as a single mathematical object: using variation to structure sense-making. Mathematical Thinking and Leaning, 8 (2), 91-111. https://doi.org/10.1207/s15327833mtl0802_1
Watson, A. & Mason, J. (2007). Taken-as-shared: a review of common assumptions about mathematical tasks in teacher education. Journal of Mathematics Teacher Education, 10 (4-6), 205-215. https://doi.org/10.1007/s10857-007-9059-3
Wood, K. (2013). A design for teacher education based on a systematic framework of variation to link teaching with learners' ways of experiencing the object of learning. International Journal for Lesson and Learning Studies, 2 (1), 56-71. https://doi.org/10.1108/20468251311290132
Wood, P., Larssen, D. L. S., Helgevold, N. & Cajkler, W. (2019) (Eds.). Lesson study in initial teacher education: principles and practices. Emerald Publishing.´https://doi.org/10.1108/9781787567979
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