Exploring relationships between students’ individual ways of reasoning and normative ways of reasoning
Tipo de documento
Autores
Lista de autores
Gruver, John
Resumen
Through the lens of the emergent perspective (Cobb & Yackel, 1996), this study examined the nature and extent of variation in individuals’ ways of reasoning from ways of reasoning that were accepted by a classroom community. This was done by interviewing seven undergraduate students after they had participated in classroom discussions. In contrast to other studies that have examined this relationship, the individuals’ ways of reasoning were qualitatively different from the accepted ways of reasoning. This suggests that even if students actively participate in classroom discourse where students’ ideas are considered, debated, and refined, they may not meet the major conceptual goals of the unit. As such, I argue that the relationship between the nature of social interactions students participate in and their subsequent reasoning needs further study, if educators are going to successfully support student learning.
Fecha
2022
Tipo de fecha
Estado publicación
Términos clave
Discurso | Entrevistas | Normas socio-culturales | Razonamiento
Enfoque
Idioma
Revisado por pares
Formato del archivo
Referencias
Alagic, M., & Palenz, D. (2006). Teachers explore linear and exponential growth: Spreadsheets as cognitive tools. Journal of Technology and Teacher Education, 14(3), 633-649. Bauersfeld, H., Krummheuer, G., & Voight, J. (1988). Interactional theory of learning and teaching mathematics and related microethnographical studies. In H.-G. Steiner & A. Vermandel (Eds.), Foundations and Methodology of the Discipline of Mathematics Education (pp. 174–188). Proceedings of the TME Conference. Berezovski, T. (2004). An inquiry into high school students’ understanding of logarithms [Master Thesis, Simon Fraser University]. http://summit.sfu.ca/item/7821 Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18, 32-41. Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5-43. https://doi.org/10.1207/s15327833mtl0101_1 Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175-190. Cole, R., Becker, N., Towns, M., Sweeney, G., Wawro, M., & Rasmussen, C. (2012). Adapting a methodology from mathematics education research to chemistry education research: Documenting collective activity. International Journal of Science and Mathematics Education, 10(1), 193-211. Cole, M., & Wertsch, J. V. (1996). Beyond the individual-social antinomy in discussions of Piaget and Vygotsky. Human Development, 39(5), 250-256. Confrey, J. (1991). Learning to listen: A student’s understanding of powers of ten. In E. von Glasersfeld (Ed.), Radical Constructivism in Mathematics Education Library, vol. 7 (pp. 111-138). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47201-5_6 De Bock, D., van Dooren, W., Janssens, D., & Verschaffel, L. (2002). Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students’ errors. Educational Studies in Mathematics, 50, 311-333. Erlwanger, S. H. (1973). Benny’s conception of rules and answers in IPI Mathematics. Journal of Children’s Mathematical Behavior, 1, 7-26. Empson, S. B. (2003). Low-performing students and teaching fractions for understanding: An interactional analysis. Journal for Research in Mathematics Education, 34(4), 305-343. https://doi.org/10.2307/30034786 Glaser, B. G., & Strauss, A. L. (1967). The Discovery of Grounded Theory: Strategies for Qualitative Research. Aldine. Ginsburg, H. P. (1997). Entering the Child’s Mind: The Clinical Interview in Psychological Research and Practice. Cambridge University Press. Gruver, J. (2018). A trajectory for developing conceptual understanding of logarithmic relationships. Journal of Mathematical Behavior, 50, 1-22. https://doi.org/10.1016/j.jmathb.2017.12.003 Hershkowitz, R., & Jaworski, B. (2012). Book Review: A dialog in the footsteps of the book “A journey in mathematics education research—Insights from the work of Paul Cobb”; Erna Yackel, Koeno Gravemeijer and Anna Sfard (Eds.);(2011); A journey in mathematics education research—Insights from the work of Paul Cobb. Educational Studies in Mathematics, 81(3), 407-420. https://doi.org/10.1007/s10649-012-9406-x Hershkowitz, R., & Schwarz, B. B. (1999). The emergent perspective in rich learning environment: Some roles of tools and activities in the construction of socio-mathematical norms. Educational Studies in Mathematics, 39(1-3), 149- 166. 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 Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper- elementary mathematics classrooms. The Elementary School Journal, 102, 59- 80. Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple Perspectives on Mathematics Teaching and Learning (pp. 19- 44). Greenwood Publishing Group. Miles, M. B., & Huberman, A. M. (1994). Qualitative Data Analysis. Sage Publications. National Council of Teachers of Mathematics. (2014). Principles to Actions: Ensuring Mathematical Success for All. Author. Pang, J. (2000). Implementing Student-Centered Instruction in Korean and the U.S. Elementary Mathematics Classrooms. Retrieved from http://eric.ed.gov/?id=ED441672 Rasmussen, C., Wawro, M., & Zandieh, M. (2015). Examining individual and collective level mathematical progress. Educational Studies in Mathematics, 88(2), 259-281. https://doi.org/10.1007/s10649-014-9583-x Roy, G. J. (2008). Prospective Teachers’ Development of Whole Number Concepts and Operations During a Classroom Teaching Experiment [Doctoral dissertation, University of Central Florida]. https://stars.library.ucf.edu/cgi/viewcontent.cgi?article=4562&context=etd 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 Stephan, M., Cobb, P., & Gravemeijer, K. (2003). Coordinating social and individual analyses: Learning as participation in mathematical practices. In N. Pateman (Ed.), Supporting Students’ Development of Measuring Conceptions: Analyzing Students’ learning in social context. Journal for Research in Mathematics Education Monograph Number 12 (pp. 67-102). The National Council of Teachers of Mathematics. Stephan, M., & Rasmussen, C. (2002). Classroom mathematical practices in differential equations. The Journal of Mathematical Behavior, 21(4), 459-490. https://doi.org/10.1016/s0732-3123(02)00145-1 Strauss, A. L. (1987). Qualitative Analysis for Social Scientists. Cambridge University Press. Strauss, A. L., & Corbin, J. (1990). Basics of Qualitative Research: Grounded Theory Procedures and Techniques. Sage Publications. Strauss, A. L., & Corbin, J. (1994). Grounded theory methodology: An overview. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of Qualitative Research (pp. 273-285). Sage Publications. Tabach, M., Hershkowitz, R., Rasmussen, C., & Dreyfus, T. (2014). Knowledge shifts and knowledge agents in the classroom. The Journal of Mathematical Behavior, 33, 192-208. https://doi.org/10.1016/j.jmathb.2013.12.001 Voigt, J. (1995). Thematic patterns of interaction and sociomathematics norms. In P. Cobb & H. Bauersfeld (Eds.), Emergence of Mathematical Meaning: Interaction in Classroom Culture (pp. 163-201). Lawrence Erlbaum. von Glasersfeld, E. (1984). An introduction to radical constructivism. In P. Watzlawick (Ed.), The Invented Reality (pp. 17-40). Norton. von Glasersfeld, E. (1992). Constructivism reconstructed: A reply to Suchting. Science and Education, 1, 379-384. Wawro, M. (2011). Individual and collective analyses of the genesis of student reasoning regarding the invertible matrix theorem in linear algebra [Doctoral dissertation, University of California San Diego]. https://escholarship.org/uc/item/30g0b1g1. Wenger, E. (1998). Communities of Practice: Learning, Meaning, and Identity. Cambridge University Press. Wertsch, J. V. (1991). Voices of the Mind: A Sociocultural Approach to Mediated Action. Harvard University Press. Yackel, E. (2001). Explanation, Justification and Argumentation in Mathematics Classrooms. In Proceedings of the PME25. http://eric.ed.gov/?id=ED466631