Authority in students’ peer collaboration in statistics: an empirical study based on inferentialism
Abstract
Students’ peer collaboration efforts in mathematics and statistics is a topic that has increasingly gained attention in research. In any collaboration, authority relations play a role for how meaning is constituted: Whenever things are discussed and decisions are made, authority is involved in a sense that some arguments or persons may be more convincing and powerful than others. In this article, we investigate how authority changes dynamically in type and in distribution as groups of fifth grade students collaborate in data generation processes. We identify and categorize authority using an epistemological framework, which is based on the philosophical theory of inferentialism. The results show that the three different types of authority described in inferentialism are all identifiable in students’ collaborative work. We also find and categorize further types of authority connected to the statistics group work, some of which are hardly addressed in previous research.
References
Amit, M. & Fried, M. N. (2005). Authority and authority relations in mathematics education: a view from an 8th grade classroom. Educational Studies in Mathematics, 58 (2), 145-168. https://doi.org/10.1007/s10649-005-3618-2
Bakker, A., Ben-Zvi, D. & Makar, K. (2017). An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference. Mathematics Education Research Journal, 29 (4), 455-470. https://doi.org/10.1007/s13394-016-0187-x
Bakker, A. & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13 (1-2), 5-26. https://doi.org/10.1080/10986065.2011.538293
Ben-Zvi, D. (2007). Using wiki to promote collaborative learning in statistics education. Technology Innovations in Statistics Education, 1 (1), 1-18. https://doi.org/10.5070/T511000029
Brandom, R. B. (2000). Articulating reasons. An introduction to inferentialism. Cambridge: Harvard University Press. https://doi.org/10.4159/9780674028739
Brandom, R. B. (1994). Making it explicit: reasoning, representing, and discursive commitment. Cambridge: Harvard University Press.
Buzzelli, C. & Johnston, B. (2001). Authority, power, and morality in classroom discourse. Teaching and teacher education, 17 (8), 873-884. https://doi.org/10.1016/S0742-051X(01)00037-3
Cobb, P. & McClain, K. (2004). Principles of instructional design for supporting the development of students' statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 375-395). Dordrecht: Kluwer. https://doi.org/10.1007/1-4020-2278-6_16
Cobb, G. W. (1992). Teaching statistics. In L. A. Steen (Ed.), Heeding the call for change: suggestions for curricular action (pp. 3-43). Washington: Mathematical Association of America.
Cohen, E. G. & Lotan, R. A. (1995). Producing equal-status interaction in the heterogeneous classroom. American educational research journal, 32 (1), 99-120. https://doi.org/10.3102/00028312032001099
Engle, R. A., Langer-Osuna, J. M. & McKinney de Royston, M. (2014). Toward a model of influence in persuasive discussions: negotiating quality, authority, privilege, and access within a student-led argument. Journal of the Learning Sciences, 23 (2), 245-268. https://doi.org/10.1080/10508406.2014.883979
Engle, R. A. (2012). The resurgence of research into transfer: an introduction to the final articles of the transfer strand. Journal of the Learning Sciences, 21 (3), 347-352. https://doi.org/10.1080/10508406.2012.707994
Engle, R. A. & Conant, F. R. (2002). Guiding principles for fostering productive disciplinary engagement: explaining an emergent argument in a community of learners' classroom. Cognition and Instruction, 20 (4), 399-483. https://doi.org/10.1207/S1532690XCI2004_1
Freitas, E. de, Wagner, D., Esmonde, I., Knipping, C., Lunney Borden, L. & Reid, D. (2012). Discursive authority and sociocultural positioning in the mathematics classroom: new directions for teacher professional development. Canadian Journal of Science, Mathematics and Technology Education, 12 (2), 137-159. https://doi.org/10.1080/14926156.2012.679994
Friedrich, C. J. (Ed.). (1958). Nomos I: authority. Cambridge: Harvard University Press.
Garfield, J. & Ben-Zvi, D. (2008). Developing students' statistical reasoning: connecting research and teaching practice. New York: Springer.
Gore, J. M. (1996, November). Understanding power relations in pedagogy. Paper presented at the joint meeting of the Australian Association for Research in Education and the Educational Research Association, Singapore.
Gore, J. M. (1994, April). Power and pedagogy: an empirical investigation of four sites. Paper presented at the annual meeting of the American Educational Research Association, New Orleans.
Hufferd-Ackles, K., Fuson, K. C. & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for research in mathematics education, 35 (2), 81-116. https://doi.org/10.2307/30034933
Inglis, M. & Mejia-Ramos, J. P. (2008). How persuaded are you? A typology of responses. Research in Mathematics Education, 10 (2), 119-133. https://doi.org/10.1080/14794800802233647
Konold, C., Higgins, T., Russell, S. J. & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88 (3), 305-325. https://doi.org/10.1007/s10649-013-9529-8
Krummheuer, G. (2015). Methods for reconstructing processes of argumentation and participation in primary mathematics classroom interaction. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education. Examples of methodology and methods (pp. 51-74). Dordrecht: Springer. https://doi.org/10.1007/978-94-017-9181-6_3
Krummheuer, G. (2000). Mathematics learning in narrative classroom cultures: studies of argumentation in primary mathematics education. For the learning of mathematics, 20 (1), 22-32. https://doi.org/10.1007/BF02655655
Langer-Osuna, J. M. (2017). Authority, identity, and collaborative mathematics. Journal for Research in Mathematics Education, 48 (3), 237-247. https://doi.org/10.5951/jresematheduc.48.3.0237
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. https://doi.org/10.1080/10986065.2016.1148529
Langer-Osuna, J. M. (2011). How Brianna became bossy and Kofi came out smart: understanding the trajectories of identity and engagement for two group leaders in a project-based mathematics classroom. Canadian Journal of Science, Mathematics and Technology Education, 11 (3), 207-225. https://doi.org/10.1080/14926156.2011.595881
Lemke, J. L. (1990). Talking science: language, learning, and values. Norwood: Ablex.
Makar, K., Bakker, A. & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13 (1-2), 152-173. https://doi.org/10.1080/10986065.2011.538301
Mercer, N. (1996). The quality of talk in children's collaborative activity in the classroom. Learning and instruction, 6 (4), 359-377. https://doi.org/10.1016/S0959-4752(96)00021-7
Metz, M. H. (1978). Clashes in the classroom: the importance of norms for authority. Education and Urban Society, 11 (1), 13-47. https://doi.org/10.1177/001312457801100102
Noorloos, R., Taylor, S. D., Bakker, A. & Derry, J. (2017). Inferentialism as an alternative to socioconstructivism in mathematics education. Mathematics Education Research Journal, 29 (4), 437-453. https://doi.org/10.1007/s13394-017-0189-3
O'Connor, M. C. & Michaels, S. (1996). Shifting participant frameworks: orchestrating thinking practices in group discussion. In D. Hicks (Ed.), Discourse, learning, and schooling, (pp. 63-103). 63-103. New York: Cambridge University Press. https://doi.org/10.1017/CBO9780511720390.003
Oyler, C. (1996). Sharing authority: student initiations during teacher-led read- alouds of information books. Teaching and Teacher Education, 12 (2), 149-160. https://doi.org/10.1016/0742-051X(95)00028-I
Oyler, C. & Becker, J. (1997). Teaching beyond the progressive-traditional dichotomy: sharing authority and sharing vulnerability. Curriculum Inquiry, 27 (4), 453-467. https://doi.org/10.1080/03626784.1997.11075502
Resnick, L. B., Michaels, S. & O'Connor, C. (2010). How (well structured) talk builds the mind. In D. Preiss & R. Sternberg (Eds.), Innovations in educational psychology: perspectives on learning, teaching and human development (pp. 163-194). New York: Springer.
Ryve, A. (2006). Approaching mathematical discourse: two analytical frameworks and their relation to problem solving interactions (PhD thesis). Departement of Mathematics and Physics, Mälardalen University.
Schindler, M., Hußmann, S., Nilsson, P. & Bakker, A. (2017). Sixth-grade students' reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis. Mathematics Education Research Journal, 29 (4), 471-492. https://doi.org/10.1007/s13394-017-0202-x
Schindler, M. & Joklitschke, J. (2016). Designing tasks for mathematically talented students. In K. Krainer & N. Vondrová (Eds.), Proceedings of CERME 9 (pp. 1066-1072). Retrieved from https://hal.archives-ouvertes.fr/hal-01287313/document
Schindler M. & Seidouvy A. (2019) Informal inferential reasoning and the social: understanding students' informal inferences through an inferentialist epistemology. In G. Burrill & D. Ben-Zvi (Eds.), Topics and trends in current statistics education research (pp. 153-171). Cham: Springer. https://doi.org/10.1007/978-3-030-03472-6_7
Seidouvy, A., Helenius, O. & Schindler, M. (2018). Data generation in statistics - both procedural and conceptual. An inferentialist analysis. In J. Häggström, Y. Liljekvist, J. Bergman Ärlebäck, M. Fahlgren & O. Olande (Eds.), Perspectives on professional development of mathematics teachers. Proceedings of MADIF 11 (pp. 191-200). Gothenburg: SMDF.
Seidouvy, A. & Schindler, M. (2019). An inferentialist account of students' collaboration in mathematics education. Mathematics Education Research Journal, 1-21. doi: 10.1007/s13394-019-00267-0 https://doi.org/10.1007/s13394-019-00267-0
Sfard, A. & Kieran, C. (2001). Cognition as communication: rethinking learning-by-talking through multi-faceted analysis of students' mathematical interactions. Mind, Culture, and Activity, 8 (1), 42-76. https://doi.org/10.1207/S15327884MCA0801_04
Skemp, R. R. (1979). Intelligence, learning, and action: a foundation for theory and practice in education. Chinchester: Wiley.
Spring, J. H. (1999). Wheels in the head: educational philosophies of authority, freedom, and culture from Socrates to human rights. Mahwah: McGraw-Hill College.
Stein, M. K., Engle, R. A., Smith, M. S. & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: five practices for helping teachers move beyond show and tell. Mathematical thinking and learning, 10 (4), 313-340. https://doi.org/10.1080/10986060802229675
Vergnaud, G. (1996). The theory of conceptual fields. In L. P. Steffe & P. Nesher (Eds.), Theories of mathematical learning (pp. 219-239). Mahwah: Lawrence Erlbaum.
Vergnaud, G. (1982). A classification of cognitive tasks and operations of thought involved in addition and subtraction problems. In T. P. Carpenter, J. Moser & T. A. Romberg (Eds.), Addition and subtraction: a cognitive perspective (pp. 39-59). Hillsdale: Lawrence Erlbaum https://doi.org/10.4324/9781003046585-4
Vogel, M. (2009). Experimentieren mit Papierfröschen. Praxis der Mathematik in der Schule, 51 (26), 22-30.
Wagner, D. & Herbel-Eisenmann, B. (2014). Mathematics teachers' representations of authority. Journal of Mathematics Teacher Education, 17 (3), 201-225. https://doi.org/10.1007/s10857-013-9252-5
Weber M. (1947) The types of authority and imperative co-ordination. In A. M. Parsons & T. Parsons (Eds.), The theory of social and economic organization (pp. 324-423). New York: The Free Press.
Welker, R. (1992). The teacher as expert: a theoretical and historical examination. Albany: SUNY Press.
Wells, G. (2007). Semiotic mediation, dialogue and the construction of knowledge. Human Development, 50 (5), 244-274. https://doi.org/10.1159/000106414
Wertsch, J. V. (1998). Mind as action. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780195117530.001.0001
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