Abstract
This chapter revisits Clancey’s application of transactional perspectives to Lehrer and Schauble’s classroom episodes (“A Transactional Perspective on the Practice-Based Science of Teaching and Learning”). Interpreting these episodes with a focus on the specific and contingent role of disciplinary or content knowledge, children’s engagement, and the potential to improve teaching, Confrey identifies three key issues: (1) the role of competing conceptions, (2) typicality and bin size, and (3) variability, predictability, and spread. She then examines the applicability of Clancey’s theory to identifying such critical elements, and its potential to contribute to a practice-based science of teaching and learning.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bateson, G. (1972). Steps to an ecology of mind: Collected essays in anthropology, psychiatry, evolution, and epistemology. San Francisco: Chandler Publishing Co.
Ben-Zvi, D., & Garfield, J. (Eds.). (2004). The challenge of developing statistical literacy, reasoning and thinking. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Brown, A. (1992). Design experiments theoretical and methodological challenges in creating complex interventions in classroom settings. The Journal of the Learning Sciences, 2, 141–178, Lawrence Erlbaum Associates, Inc.
Confrey, J. (1990). The concept of exponential functions: A student’s perspective. In L. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 124–159). New York: Springer-Verlag.
Confrey, J. (2006). The evolution of design studies as methodology. In K. Sawyer (Ed.), Cambridge handbook of the learning sciences (pp. 135–151). New York: Cambridge University Press.
Confrey, J., & Makar, K. (2005). Critiquing and improving the use of data from high stakes tests with the aid of dynamic statistical software. In C. Dede (Ed.), Scaling up success: Lessons learned from technology-based educational improvement (pp. 198–226). San Francisco: Jossey Bass.
Confrey, J., & Maloney, A. (2007). A theory of mathematical modeling in technological settings. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modeling and applications in mathematics education: The 14th International Commission on Mathematical Instruction (ICMI) study (Vol. 10, pp. 57–68). New York: Springer Science.
diSessa, A. A. (2002). Students’ criteria for representational adequacy. In K. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 105–130). Dordrecht, The Netherlands: Kluwer Academic Publishers.
diSessa, A. A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. The Journal of the Learning Sciences, 13, 77–103.
Lehrer, R., & Pritchard, C. (2002). Symbolizing space into being. In K. Gravemeijer, R. Lehrer, H. J. van Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 59–86). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Lehrer, R., & Schauble, L. (2005). Developing modeling and argument in the elementary grades. In T. Romberg, T. Carpenter, & F. Dremock (Eds.), Understanding mathematics and science matters (pp. 29–53). Mahwah, NJ: Lawrence Erlbaum, Associates.
Lehrer, R., & Schauble, L. (2004). Modeling natural variation through distribution. American Educational Research Journal, 41, 635–679.
Meletiou, M. M. (2000). Developing students’ conceptions of variation: An untapped well in statistical reasoning. Austin, TX: University of Texas.
Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267–307). Hillsdale, NJ: Erlbaum.
Von Glasersfeld, E. (1991). Radical constructivism in mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Confrey, J. (2011). Making Sense of Practice in Mathematics: Models, Theories and Disciplines. In: Koschmann, T. (eds) Theories of Learning and Studies of Instructional Practice. Explorations in the Learning Sciences, Instructional Systems and Performance Technologies, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7582-9_19
Download citation
DOI: https://doi.org/10.1007/978-1-4419-7582-9_19
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7581-2
Online ISBN: 978-1-4419-7582-9
eBook Packages: Humanities, Social Sciences and LawEducation (R0)