Abstract
In this paper, we explore the relationship between scaffolding, dialogue, and conceptual breakthroughs, using data from a design-based research study that focuses on the development of understanding of probability in 10–12 year old students. The aim of the study is to gain insight into how the combination of scaffolding for content using technology and scaffolding for dialogue can facilitate conceptual breakthroughs. We analyse video-recordings and transcripts of pairs and triads of students solving problems using the TinkerPlots software with teacher interventions, focusing on moments of conceptual breakthrough. Data show that dialogue scaffolding promotes both dialogue moves specific to the context of probability and dialogue in itself. This paper focuses on episodes of learning that occur within dialogues framed and supported by dialogue scaffolding. We present this as support for our claim that combining scaffolding for content and scaffolding for dialogue can be effective in students’ conceptual development. This finding contributes to our understanding of both scaffolding and dialogic teaching in mathematics education by suggesting that scaffolding can be used effectively to prepare for conceptual development through dialogue.
Similar content being viewed by others
References
Bakhtin, M. M. (1981). The dialogic imagination: four essays by M.M. Bakhtin (trans: Emerson, C., & Holquist, M.). Austin: University of Texas Press.
Bakhtin, M. M. (1986). Speech genres and other late essays (trans: McGee, V. W.) Austin: University of Texas Press.
Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. In A. Rossman & B. Chance (Eds.), Proceedings of the seventh international conference on teaching of statistics (CD-ROM), Salvador, Bahia, Brazil, 2–7 July, 2006. Voorburg: International Statistical Institute.
Bruner, J. (1985). Vygotsky: A historical and conceptual perspective. In J. V. Wertsch (Ed.), Culture, communication, and cognition: Vygotskian perspectives (pp. 21–34). Cambridge: Cambridge University Press.
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32, 9–13.
Dawes, L., Mercer, N., & Wegerif, R. (2000). Thinking together: a programme of activities for developing speaking, listening and thinking skills for children aged 8–11. Birmingham: Imaginative Minds.
Dillon, J. T. (Ed.). (1988). Questioning and discussion: a multidisciplinary study. Norwood: Ablex.
Fernández, M., Wegerif, R., Mercer, N., & Rojas-Drummond, S. M. (2001). Re-conceptualizing “scaffolding” and the zone proximal development in the context of symmetrical collaborative learning. Journal of Classroom Interaction, 36, 40–54.
Fitzallen, N., & Watson, J. (2010). Developing statistical reasoning facilitated by TinkerPlots. In C. Reading (Ed.), Proceedings of the eight international conference for teaching statistics. Lbjubjana: International Statistical Institute.
Francisco, J. M., & Maher, C. A. (2005). Conditions for promoting reasoning in problem solving: insights from a longitudinal study. Journal of Mathematical Behavior, 24, 361–372.
Guzdial, M. (1994). Software-realized scaffolding to facilitate programming for science learning. Interactive Learning Environments, 4, 1–44.
Horvath, J., & Lehrer, R. (1998). A model-based perspective on the development of children’s understanding of chance and uncertainty. In S. P. LaJoie (Ed.), Reflections on statistics: agendas for learning, teaching, and assessment in K-12 (pp. 121–148). Mahwah: Lawrence Erlbaum.
Kazak, S., Wegerif, R., & Fujita, T. (2013). ‘I get it now!’ Stimulating insights about probability through talk and technology. Mathematics Teaching, 235, 29–32.
Kazak, S., Wegerif, R., & Fujita, T. (2015). The importance of dialogic processes to conceptual development in mathematics. Educational Studies in Mathematics,. doi:10.1007/s10649-015-9618-y.
Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6, 59–98.
Konold, C., Harradine, A., & Kazak, S. (2007). Understanding distributions by modeling them. International Journal of Computers for Mathematical Learning, 12, 217–230.
Konold, C. & Kazak, S. (2008). Reconnecting data and chance. Technology innovations in statistics education, vol. 2. http://repositories.cdlib.org/uclastat/cts/tise/vol2/iss1/art1. Accessed 10 December 2008.
Konold, C. & Miller, C. D. (2011). TinkerPlots2.0: dynamic data exploration. Emeryville: Key Curriculum.
Konold, C., Pollatsek, A., Well, A., Lohmeier, J., & Lipson, A. (1993). Inconsistencies in probabilistic reasoning of novices. Journal for Research in Mathematics Education, 24, 392–414.
Lee, H. S., Angotti, R. L., & Tarr, J. (2010). Making comparisons between observed data and expected outcomes: students’ informal hypothesis testing with probability simulation tools. Statistics Education Research Journal, 9(1), 68–96.
Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13, 152–173.
Mercer, N. (2000). Words and minds: how we use language to think together. London: Routledge.
Mercer, N. (2004). Sociocultural discourse analysis: analysing classroom talk as a social mode of thinking. Journal of Applied Linguistics, 1, 137–168.
Polaki, M. V. (2002). Using instruction to identify key features of Basotho elementary students’ growth in probabilistic thinking. Mathematical Thinking and Learning, 4, 285–313.
Pratt, D. (2000). Making sense of the total of two dice. Journal of Research in Mathematics Education, 31, 602–625.
Pratt, D., Johnston-Wilder, P., Ainley, J., & Mason, J. (2008). Local and global thinking in statistical inference. Statistics Education Research Journal, 7(2), 107–129.
Quintana, C., Reiser, B. J., Davis, E. A., Krajcik, J., Fretz, E., Duncan, R. G., et al. (2004). A scaffolding design framework for software to support science inquiry. Journal of the Learning Sciences, 13, 337–386.
Reiser, B. J. (2004). Scaffolding complex learning: the mechanisms of structuring and problematizing student work. Journal of the Learning Sciences, 13, 273–304.
Rojas-Drummond, S. M., & Mercer, N. (2003). Scaffolding the development of effective collaboration and learning. International Journal of Educational Research, 39, 99–111.
Smit, J. & Van Eerde, H. A. A. (2011). A teacher’s learning process in dual design research: learning to scaffold language in a multilingual mathematics classroom, ZDM—The International Journal on Mathematics Education, 43, 889–900.
Smit, J., Van Eerde, H. A. A., & Bakker, A. (2013). A conceptualisation of whole-class scaffolding. British Educational Research Journal, 39, 817–834.
Vygotsky, L. S. (1978). Mind in society: the development of higher mental processes. Cambridge: Harvard University Press.
Vygotsky, L. S. (1986). Thought and language (trans: Kozulin, A.). Cambridge: MIT Press.
Watson, J. M., & Moritz, J. B. (2003). A longitudinal study of students’ beliefs and strategies for making judgments. Journal for Research in Mathematics Education, 34, 270–304.
Wegerif, R. (2007). Dialogic, education and technology: expanding the space of learning. New York: Springer.
Wegerif, R. (2011). From dialectic to dialogic: a response to Wertsch and Kazak. In T. Koschmann (Ed.), Theorizing practice: theories of learning and research into instruction practice (pp. 201–222). New York: Springer.
Wegerif, R. (2013). Dialogic: education for the internet age. New York: Routledge.
Wood, D., Bruner, J., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry and Allied Disciplines, 17, 89–100.
Acknowledgments
This research was supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme to S. Kazak and R. Wegerif. We would also like to acknowledge the generous support of the schools, teachers and students who worked with us on this project.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kazak, S., Wegerif, R. & Fujita, T. Combining scaffolding for content and scaffolding for dialogue to support conceptual breakthroughs in understanding probability. ZDM Mathematics Education 47, 1269–1283 (2015). https://doi.org/10.1007/s11858-015-0720-5
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11858-015-0720-5