Abstract
This chapter explores the learning experienced by teachers engaged in algebra reform inquiry. The chapter describes two ways of using video episodes in the analysis of learning practices acquired through teaching. First, we perform a comparative analysis of two episodes that involve guided inquiry during whole-group discussion by the same students, taught by the same teacher at a distance of two years. Acquired practices are analyzed by quantifying “initiation–response–evaluation” statements made by the students and the teacher. The analysis sheds light on changes in practices and norms taking place over time. Second, we use the same two video episodes in a qualitative comparative analysis of two groups of teachers reflecting on the video episodes. One group of participants consists of teachers engaged in teaching the same reform algebra curriculum, the second of algebra teachers using traditional methods of teaching algebra in secondary school. The episodes motivated the first group to analyze their own tensions and dilemmas that the newly learned practices introduced. The major attempts of participants of the second group were to “fix” what they perceived to be the reality in ways that coincided with their practices.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Cazden, C. B. (1988). Classroom discourse. The language of teaching and learning. Heinemann Portsmouth, NH.
Chazan, D., & Ball, D.(1999). Beyond being told not to tell. For the Learning of Mathematics, 19, 2–10.
Chazan, D., & M. Schnepp (2002). Methods, goals, beliefs, commitments and manner in teaching: Dialogue against a calculus backdrop. Social Constructivist Teaching, 9, 171–195.
Chazan, D., Callis, S., & Lehman, M. (2008). Embracing reason: Egalitarian ideals and the teaching of high school mathematics. New York, NY: Routledge.
Elikan, S. (1999). Characterization of computers’ supported inquiry discussions in mathematics classrooms. M.A. Thesis. University of Haifa, Israel. (in Hebrew).
Herbst, P. G. & D. Chazan (2003). Exploring the practical rationality of mathematics teaching through coversations about videotaped episodes: the case of engaging students in proving. For the Learning of Mathematics, 23(1): 14–2.
Kieran, C., & Yerushalmy, M. (2004). Research on the role of technological environments in algebra learning and teaching. In K. Stacey, H. Shick, & M. Kendal (Eds.), The future of the teaching and learning of Algebra. ICMI Study-12 Volume (pp. 99–152). Dordrecht, the Netherlands: Kluwer.
Lampert, M., & Ball, D. (1998). Teaching, multimedia, and mathematics: Investigations of real practice. The practitioner inquiry series. New York, NY: Teachers College Press.
Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.
Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 1, 29–63.
Leikin, R., & Rota, S. (2006). A case study on the development of teacher’s proficiency through teaching. Mathematics Education Research Journal, 18(3), 44–68.
Leikin, R. (2005). Teachers’ learning in teaching: Developing teachers’ mathematical knowledge through instructional interactions. The paper presented at the 15th ICMI Study: The Professional Education and Development of Teachers of Mathematics. http://stwww.weizmann.ac.il/G-math/ICMI/log_in.html
Levenberg, I. (1995). Teacher’s diary. Journal for Mathematics Teachers (ALEE') 17, 73–77 (in Hebrew).
Lindsay, J. S. (1990). Classroom discourse analysis: A review of the literature with implications for educational evaluation. Journal of Research and Development in Education, 23, 107–116.
National Council of Teachers of Mathematics (1989, 2000). Principles and standards for school mathematics. Reston, VA: NCTM.
Nemirovsky, R. (1996). A functional approach to algebra: Two issues that emerge. In Bednarz, N., Kieran, C., & Lee, L. (eds.), Approaches to algebra: Perspectives for research and teaching (pp. 295–316). Dordrecht, the Netherlands: Kluwer.
Pimm, D. (1996) ‘This is so’: A text on texts. In A. J. Bishop et al. (Eds.), International handbook of mathematics education (pp. 371–409). Dordrecht, the Netherlands: Kluwer.
Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10, 123–140.
Schifter, D. (1996). What’s happening in math class? Envisioning new practices through teacher narratives. New York, NY: Teachers College Press.
Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 44–49.
Stacey, K., & Kendal, M. (2004). Algebra: A world of difference, In: K. Stacey, H. Shick, & M. Kendal (Eds.), The future of the teaching and learning of algebra. The 12th ICMI Study (pp. 329–346), Dordrecht, the Netherlands: Kluwer.
Visual Math: Algebra (1995). Center for educational technology, Ramat-Aviv. http://www.cet.ac.il/math-international/visualizing.htm
Wood, T. (1995). An emerging practice of teaching. In P. Cobb & Bauersfeld, H. (Eds), The emergence of mathematical meaning. Interaction in classroom cultures (pp. 203–228). Hillsdale, N.J: Erlbaum.
Yerushalmy, M., & Chazan, D. (2008). Technology and curriculum design: The ordering of discontinuities in school algebra. In L. English et al. (Eds.), Handbook of international research in mathematics education (2nd edn., pp. 806–837). New York, NY: Routledge.
Yerushalmy, M., Elikan, S., & Chazan, D. (2000). Discussions in the Mathematics Classroom. Multimedia package (Video and Documents). University of Haifa and Center for Educational Technology, Ramat-Aviv, IL.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Yerushalmy, M., Elikan, S. (2010). Exploring Reform Ideas for Teaching Algebra: Analysis of Videotaped Episodes and of Conversations About Them. In: Leikin, R., Zazkis, R. (eds) Learning Through Teaching Mathematics. Mathematics Teacher Education, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3990-3_10
Download citation
DOI: https://doi.org/10.1007/978-90-481-3990-3_10
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3989-7
Online ISBN: 978-90-481-3990-3
eBook Packages: Humanities, Social Sciences and LawEducation (R0)