Abstract
Interactive problem solving and learning are priorities in contemporary education, but these complex processes have proved difficult to research. This project addresses the question “How do we optimise social interaction for the promotion of learning in a mathematics classroom?” Employing the logic of multi-theoretic research design, this project uses the newly built Science of Learning Research Classroom (ARC-SR120300015) at The University of Melbourne and equivalent facilities in China to investigate classroom learning and social interactions, focusing on collaborative small group problem solving as a way to make the social aspects of learning visible. In Australia and China, intact classes of local year 7 students with their usual teacher will be brought into the research classroom facilities with built-in video cameras and audio recording equipment to participate in purposefully designed activities in mathematics. The students will undertake a sequence of tasks in the social units of individual, pair, small group (typically four students) and whole class. The conditions for student collaborative problem solving and learning will be manipulated so that student and teacher contributions to that learning process can be distinguished. Parallel and comparative analyses will identify culture-specific interactive patterns and provide the basis for hypotheses about the learning characteristics underlying collaborative problem solving performance documented in the research classrooms in each country. The ultimate goals of the project are to generate, develop and test more sophisticated hypotheses for the optimisation of social interaction in the mathematics classroom in the interest of improving learning and, particularly, student collaborative problem solving.
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26 July 2017
An erratum to this article has been published.
References
Australian Chamber of Commerce Industry, & Business Council of Australia. (2002). Employability skills for the future. Canberra: Department of Education, Science and Training.
Australian Department of Education and Training. (2012). Australian core skills framework. Canberra: Commonwealth of Australia.
Bruner, J. S. (1990). Acts of meaning. Cambridge: Harvard University Press.
Cao, Y., Clarke, D., & Xu, L. H. (2010). Qifa Shi teaching: Confucian heuristics. In M. M. F. Pinto & T. F. Kawasaki (Eds.), Proceedings of the 34th conference of the International Group for the Psychology in mathematics education (Vol. 1, pp. 232–234). Belo Horizonte: PME.
Chan, M. C. E., & Clarke, D. J. (2017). Entangled modes of social interaction in student collaborative problem solving of open-ended mathematical tasks. ZDM-The International Journal on Mathematics Education, (in press).
Clarke, D. J. (1996). Assessment. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 327–370). Dordrecht: Kluwer Academic Publishers.
Clarke, D. J. (Ed.). (2001). Perspectives on practice and meaning in mathematics and science classrooms. Dordrecht: Kluwer Academic Publishers.
Clarke, D. J. (2011). Open-ended tasks and assessment: The nettle or the rose. In B. Kaur & K. Y. Wong (Eds.), Assessment in the mathematics classroom (pp. 131–163). Singapore: World Scientific.
Clarke, D. J. (2013a). Contingent conceptions of accomplished practice: The cultural specificity of discourse in and about the mathematics classroom. ZDM-The International Journal on Mathematics Education, 45(1), 21–33. doi:10.1007/s11858-012-0452-8.
Clarke, D. J. (2013b). International comparative research into educational interaction: Constructing and concealing differences. In K. Tirri & E. Kuusisto (Eds.), Interaction in educational domains (pp. 5–22). Rotterdam: Sense Publishers.
Clarke, D. J., & Helme, S. (1998). Context as construction. In O. Björkqvist (Ed.), Mathematics teaching from a constructivist point of view (pp. 129–147). Vasa: Faculty of Education, Åbo Akademi University.
Clarke, D. J., & Sullivan, P. (1990). Is a question the best answer? Australian Mathematics Teacher, 46(3), 30–33.
Clarke, D. J., & Sullivan, P. (1992) Responses to open-ended tasks in mathematics: Characteristics and implications. In W. Geeslin, & K. Graham (Eds.), Psychology of Mathematics Education (Vol. 1, pp. 137–144). Durham, NH: University of New Hampshire.
Clarke, D. J., Xu, L. H., Arnold, J., Seah, L. H., Hart, C., Tytler, R., et al. (2012). Multi-theoretic approaches to understanding the science classroom. In C. Bruguière, A. Tiberghien, & P. Clément (Eds.), E-book proceedings of the ESERA 2011 biennial conference: Part 3 (pp. 26–40). Lyon: European Science Education Research Association.
Clarke, D. J., Xu, L. H., & Wan, M. E. V. (2013). Spoken mathematics as an instructional strategy: The public discourse of mathematics classrooms in different countries. In B. Kaur, G. Anthony, M. Ohtani, & D. Clarke (Eds.), Student voice in mathematics classrooms around the world (pp. 13–31). Rotterdam: Sense Publishers.
COAG [Council of Australian Governments]. (2008). National education agreement. Barton: Author.
Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13–20.
Cobb, P., & Bowers, J. (1999). Cognitive and situated learning perspectives in theory and practice. Educational Researcher, 28(2), 4–15.
Cohen, L., Manion, L., & Morrison, K. (2013). Research methods in education (7th ed.). Hoboken: Taylor and Francis.
Dunbar, R. I. M. (1998). The social brain hypothesis. Evolutionary Anthropology, 6(5), 178–190. doi:10.1002/(sici)1520-6505(1998)6:5<178::aid-evan5>3.0.co;2-8.
Greeno, J. G. (1997). On claims that answer the wrong questions. Educational Researcher, 26(1), 5–17. doi:10.2307/1176867.
Griffin, P. E., McGaw, B., & Care, E. (Eds.). (2012). Assessment and teaching of 21st century skills. Dordrecht: Springer.
Holton, D., & Clarke, D. (2006). Scaffolding and metacognition. International Journal of Mathematical Education in Science and Technology, 37(2), 127–143. doi:10.1080/00207390500285818.
Kim, H. S., & Markus, H. R. (2002). Freedom of speech and freedom of silence: An analysis of talking as a cultural practice. In R. A. Shweder, M. Minow, & H. R. Markus (Eds.), Engaging cultural differences: The multicultural challenge in liberal democracies (pp. 432–452). New York: Russell Sage Foundation.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.
Lerman, S. (2001). Cultural, discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics. Educational Studies in Mathematics, 46(1/3), 87–113.
Lobato, J., Clarke, D., & Ellis, A. B. (2005). Initiating and eliciting in teaching: A reformulation of telling. Journal for Research in Mathematics Education, 36(2), 101–136. doi:10.2307/30034827.
Lodico, M. G., Spaulding, D. T., & Voegtle, K. H. (2010). Methods in educational research from theory to practice (2nd ed.). Hoboken: Wiley.
MCEECDYA [Ministerial Council for Education Early Childhood Development and Youth Affairs]. (2008). Melbourne declaration on educational goals for young Australians. Carlton South, Victoria, Australia: Author.
Mercer, N. (2013). The social brain, language, and goal-directed collective thinking: A social conception of cognition and its implications for understanding how we think, teach, and learn. Educational Psychologist, 48(3), 148–168. doi:10.1080/00461520.2013.804394.
Ministry of Education of the People’s Republic of China. (2011). 义务教育数学课程标准 [Compulsory education mathematics curriculum standards]. Beijing: Author.
OECD [Organisation for Economic Co-operation and Development]. (2013). Synergies for better learning: An international perspective on evaluation and assessment. Paris: Author.
Packer, M. J., & Goicoechea, J. (2000). Sociocultural and constructivist theories of learning: Ontology, not just epistemology. Educational Psychologist, 35(4), 227–241.
Sfard, A., Forman, E., & Kieran, C. (2001). Learning discourse: Sociocultural approaches to research in mathematics education. Educational Studies in Mathematics, 46(1/3), 1–12.
Sullivan, P., & Clarke, D. J. (1988). Asking better questions. Journal of Science and Mathematics Education in South East Asia, 11, 14–19.
Sullivan, P., & Clarke, D. J. (1991). Catering to all abilities through “good” questions. The Arithmetic Teacher, 39(2), 14–18. doi:10.2307/41194944.
Sullivan, P., & Clarke, D. J. (1992). Problem solving with conventional mathematics content: Responses of pupils to open mathematical tasks. Mathematics Education Research Journal, 4(1), 42–60. doi:10.1007/bf03217231.
Suri, H., & Clarke, D. (2009). Advancements in research synthesis methods: From a methodologically inclusive perspective. Review of Educational Research, 79(1), 395–430. doi:10.3102/0034654308326349.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press.
Acknowledgements
This research is supported under Australian Research Council’s Discovery Projects funding scheme (Project number DP170102541). The pilot study from which this project is building on was supported by the Science of Learning Research Centre funded by the Australian Research Council (ARC-SR120300015).
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The original version of this article was revised: In Fig. 3, the centrally located characters “C, c, a, m” were included in error and form no part of the intended diagram.
An erratum to this article is available at https://doi.org/10.1007/s13394-017-0221-7.
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Chan, M.C.E., Clarke, D. & Cao, Y. The social essentials of learning: an experimental investigation of collaborative problem solving and knowledge construction in mathematics classrooms in Australia and China. Math Ed Res J 30, 39–50 (2018). https://doi.org/10.1007/s13394-017-0209-3
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DOI: https://doi.org/10.1007/s13394-017-0209-3