Prospective elementary teachers’ beliefs about collaborative problem solving and dialogue in mathematics
Keywords:
prospective teachers, beliefs, collaborative problem solving, dialogueAbstract
This study is concerned with prospective elementary teachers’ beliefs about collaborative problem solving and dialogue in mathematics classroom. Participants (n=16) attended an undergraduate module titled Problem Solving in Primary Mathematics, which was specifically designed to provide them with opportunities in collaborative problem solving and dialogic activities. Students were invited to answer an open-ended questionnaire at the beginning and end of the course. In addition, at the end of the semester, students wrote individual reflective reports commenting on their experiences. Qualitative analyses revealed three areas of beliefs for which positive changes were observed: (a) dialogue and its relation to school mathematics, (b) the characteristics of a ‘good’ interlocutor, and (c) the importance of collaborative problem solving. This paper closes with a discussion concerning the implementations of our findings and suggestions for future research.
References
Aguirre, J., & Speer, N.M. (1999). Examining the relationship between beliefs and goals in teacher practice. The Journal of Mathematical Behavior 18(3), 327-56.
Albert, L. R., & Kim, R. (2013). Developing creativity through collaborative problem solving. Journal of Mathematics Education at Teachers College, 4, 32-38.
Alexander, R. (2008). Towards Dialogic Teaching: Rethinking classroom talk. York: Dialogos
Artzt, A.F., & Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and Instruction, 9(2), 137-175.
Barron, B. (2000). Achieving coordination in collaborative problem-solving groups. The Journal of the Learning Sciences, 9(4), 403-436.
Bauml, M. (2009). Examining the unexpected sophistication of preservice teachers’ beliefs about the relational dimensions of teaching. Teaching and Teacher Education, 25, 902-908.
Bennett, C. (2010). “It's hard getting kids to talk about math”. Helping new teachers improve mathematical discourse. Action in Teacher Education, 32(3), 79-89.
Bills, C., & Grey, E. (2001). The ‘particular’, ‘generic’ and ‘general’ in young children’s mental calculations”. In M. van den Heuval-Panhuizen (ed.), Proceedings of the 25th Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 2. (pp. 153–160). Utrecht: PME.
Bills, L. (2000). Politeness in teacher-student dialogue in mathematics: A socio-linguistic analysis. For the Learning of Mathematics, 20(2), 40-47.
Bjuland, R. (2004). Student teachers' reflections on their learning process through collaborative problem solving in geometry. Educational Studies in Mathematics, 55(1/3), 199-225.
Black, L. (2004). Teacher–pupil talk in whole-class discussions and processes of social positioning within the primary school classroom. Language and Education, 18 (5), 347-360.
Borasi, R. (1986). On the nature of problems. Educational Studies in Mathematics, 17(2), 125-141.
Brown, R,. & Hirst, E. (2007). Developing an understanding of the mediating role of talk in the elementary mathematics classroom. Journal of Classroom Interaction, 42(1), 18-28.
Carpenter, T.P., Franke, M.L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic & algebra in elementary school. Portsmouth, NH: Heinemann.
Chapman, O. (2003). Belief structure and inservice high school mathematics teacher growth. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 177–193). Doordrecht: Kluwer Academic Publishers.
Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing, PNA, 6(4), 135-146.
Charalambous, C. Y., Panaoura, A., & Philippou, G. (2009). Using the history of mathematics to induce changes in preservice teachers’ beliefs and attitudes: Insights from evaluating a teacher education program. Educational Studies in Mathematics, 71(2), 161-180.
Clarke, D.J. (2013). Contingent Conceptions of Accomplished Practice: The Cultural Specificity of Discourse in and about the Mathematics Classroom. ZDM: The International Journal in Mathematics Education 45(1), 21-33.
Cohen, L., Manion, L., & Morrison, K. (2013). Research methods in education. New York: Routledge.
Cohrssen, C., Church, A., & Tayler, C. (2014). Purposeful pauses: teacher talk during early childhood mathematics activities. International Journal of Early Years Education, 22, 169-183.
Duffin, J. (1986). Mathematics through classroom talk. Mathematics in School, 15(2), 10–13.
Forman, E. (1989). The role of peer interaction in the social construction of mathematical knowledge. International Journal of Educational Research, 13(1), 55-70.
Forman, E.A. (1989). The role of peer interaction in the social construction of mathematical knowledge. International Journal of Educational Research, 13(1), 55-70.
Goos, M., Galbraith, P., & Renshaw, P. (2002). Socially mediated metacognition: Creating collaborative Zones of Proximal Development in small group problem solving. Educational Studies in Mathematics, 49(2), 193-223.
Greiff, S., Holt, D.V, & Funke, J. (2013). Perspectives on Problem Solving in Educational Assessment: Analytical, Interactive, and Collaborative Problem Solving. The Journal of Problem Solving, 5(2), 71-91.
Hennessy, S., Rojas-Drummond, S., Higham, R., Márquez, A.M., Maine, F., Ríos, R.M., García-Carrión, R., Torreblanca, O., & José Barrera, M. (2016). Developing a coding scheme for analysing classroom dialogue across educational contexts. Learning, Culture and Social Interaction, 9, 16-44.
Howe, C., & Abedin, M. (2013). Classroom dialogue: a systematic review across four decades of research. Cambridge Journal of Education, 43(3), 325-356.
Iiskala, T., Vauras, M., Lehtinen, E., & Salonen, P. (2011). Socially shared metacognition of dyads of pupils in collaborative mathematical problem-solving processes. Learning and Instruction, 21, 379-393.
Joshua, T. (2008). Teacher-initiated talk and student oral discourse in a second language literature classroom: a sociocultural analysis, Unpublished PhD Thesis, The University of Iowa, USA.
Kersaint, G., Thompson, D.R., & Petkova, M. (2013). Teaching mathematics to English language learners. New York, NY: Routledge.
Kroll, D.L, Masingila, J.O., & Mau, S.T. (1992). Cooperative problem solving: But what about grading? The Arithmetic Teacher, 39(6), 17-23.
Kvale, S., & Brinkmann, S. (2009). InterViews: Learning the craft of qualitative research interviewing. London: SAGE Publications.
Langer-Osuna, J.M. (2016). The social construction of authority among peers and its implications for collaborative mathematics problem solving. Mathematical Thinking and Learning, 18(2), 107-124.
Lee, J.E., & Kim, K.T. (2016). Pre-service teachers’ conceptions of effective teacher talk: their critical reflections on a sample teacher-student dialogue. Educational Studies in Mathematics. Advance online publication, DOI: 10.1007/s10649-016-9710-y
Mercer, N., & Littleton, K. (2007). Dialogue and the Development of Children’s Thinking: A sociocultural approach. London: Routledge.
Mercer, N. (1996). The quality of talk in children’s collaborative activity in the classroom. Learning and Instruction, 6, 359-377.
Middleton, J.A. (1999). Curricular influences on the motivational beliefs and practices of two middle school mathematics teachers: A follow-up study. Journal for Research in Mathematics Education, 30, 349-358.
Miles M.B., & Huberman, M. (1994). Qualitative data analysis: A sourcebook of new methods. Beverly Hills, CA: SAGE.
Ng, W., Nicholas, H., & Williams, A. (2010). School experience influences on pre-service teachers’ evolving beliefs about effective teaching. Teaching and Teacher Education, 26(2), 278-289.
Nussbaum, M. (2011). Argumentation, Dialogue Theory, and Probability Modeling: Alternative Frameworks for Argumentation Research in Education. Educational Psychologist, 46(2), 84-106.
Nystrand, M., Wu, L.L., Gamoran, A., Zeiser, S., & Long, D.A. (2003). Questions in time: Investigating the structure and dynamics of unfolding classroom discourse. Discourse Processes, 35(2), 135–196
OECD (2013). Draft collaborative problem solving framework. Available at https://www.oecd.org/pisa/pisaproducts/Draft%20PISA%202015%20Collaborative%20Problem%20Solving%20Framework%20.pdf
Pirie, S.E.B., & Schwarzenberger, R.L.E. (1988). Mathematical discussion and mathematical understanding. Educational Studies in Mathematics, 19, 459-470.
Potari, D. (2001). Primary mathematics teacher education in Greece: reality and vision. Journal of Mathematics Teacher Education, 4(1), 81-89.
Ramsey, C., & Langrall, C.W. (2016). Promoting mathematical argumentation. Teaching Children Mathematics, 22(7), 413-419.
Robson, C. (2011). Real world research. Sussex: Wiley.
Smith, J. (2010). Talk, thinking and philosophy in the primary classroom. Exeter: Learning Matters.
Strauss, A. L., & Corbin, J. M. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. London: SAGE.
Stylianides, A.J., & Stylianides, G.J. (2014). Impacting positively on students’ mathematical problem solving beliefs: An instructional intervention of short duration. The Journal of Mathematical Behavior, 33, 8-29.
Tatsis, K., & Koleza, E. (2008). Social and socio-mathematical norms in collaborative problem-solving. European Journal of Teacher Education, 31(1), 89-100.
Thompson, A.G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 105-127.
Tobin, K. (1986). Effects of Teacher Wait Time on Discourse Characteristics in Mathematics and Language Arts Classes. American Educational Research Journal, 23(2), 191-200.
Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
Wadlington, E. (1993). Integrating writing and cooperative problem solving in elementary mathematics methods classes. Teacher Education Quarterly, 20(3), 121-127.
Webb, N.M. (1991). Task-related verbal interaction and mathematics learning in small groups. Journal for Research in Mathematics Education, 22(5), 366-389.
Wells, G. (1999). Dialogic Inquiry: Towards a Sociocultural Practice and Theory of Education. Cambridge: Cambridge University Press.
Yackel, E., Cobb, P., & Wood, T. (1991). Small-group interactions as a source of learning opportunities in second-grade mathematics. Journal for Research in Mathematics Education, 22(5), 390-408.
Zsoldos-Marchis, I. (2015). Changing pre-service primary-school teachers’ attitude towards mathematics by collaborative problem solving. Procedia - Social and Behavioral Sciences, 186, 174-182.
Zuengler, J., & Cole, K. (2005). Language socialization and second language learning. In E. Hinkel (ed.), Handbook of research in second language teaching and learning (pp. 301-316). Mahwah, NJ: Lawrence Erlbaum.
