Effects of variations in task design on mathematics teachers’ learning experiences: a case of a sorting task
The goal of the study presented in this article was to examine how variations in task design may affect mathematics teachers’ learning experiences. The study focuses on sorting tasks, i.e., learning tasks that require grouping a given set of mathematical items, in as many ways as possible, according to different criteria suggested by the learners. We present an example of a sorting task for which the items to be grouped are related to basic concepts of analytical geometry that are connected to the notion of loci of points. Based on a design experiment of three iterations with practicing secondary school mathematics teachers, we report on intended and enacted objects of learning inherent in three versions of the task. Empirically based suggestions are drawn about design of sorting tasks that potentially evoke desirable learning experiences.
KeywordsDesign experiment Sorting tasks Task design Teacher professional development Variation theory
- Askew, M., Brown, M., Rhodes, V., Wiliam, D., & Johnson, D. (1997). Effective teachers of numeracy: Report of a study carried out for the Teacher Training Agency. London: King’s College, University of London.Google Scholar
- Cooney, T. J., & Krainer, K. (1996). Inservice mathematics teacher education: The importance of listening. In A. J. Bishop, et al. (Eds.), International handbook of mathematics education (pp. 1155–1185). Dordrecht: Kluwer Academic Publishers.Google Scholar
- Dolev, L. (2012). Considerations in the design of learning tasks for teachers: The case of classification of mathematical items. Unpublished Ph.D. dissertation. Technion – Israel Institute of Technology.Google Scholar
- Friedlander, A., & Dreyfus, T. (1991). Is the graph of y = kx straight? The Mathematics Teacher, 84(7), 526–531.Google Scholar
- Goren, B. (2006). Mathematics (for 5 credit point curriculum). Part 7 (questionnaire 035007). Tel Aviv: Author (in Hebrew).Google Scholar
- Gu, L., Huang, R., & Marton, F. (2004). Teaching with variation: A Chinese way of promoting effective mathematics learning. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders. Singapore: World Scientific Publishing.Google Scholar
- Howard, A. (1988). Calculus: With analytic geometry. New York, NY: Wiley.Google Scholar
- Koichu, B., Zaslavsky, O., & Dolev, L. (2013b). Effects of variations in task design using different representations of mathematical objects on learning: A case of a sorting task. In C. Margolinas, J. Ainley, J. B. Frant, M. Doorman, C. Kieran, A. Leung, M. Ohtani, P. Sullivan, D. Thompson, A. Watson, & Y. Yang (Eds.), Proceedings of ICMI Study 22 Task Design in Mathematics Education (pp. 463–472). Oxford: Oxford University Press.Google Scholar
- Lai, M. Y., & Murray, S. (2012). Teaching with procedural variation: A Chinese way of promoting deep understanding of mathematics. International Journal for Mathematics Teaching and Learning. http://www.cimt.plymouth.ac.uk/journal/lai.pdf. Retrieved 18 Nov 2013.
- Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Erlbaum.Google Scholar
- NCTM (National Council of Teachers of Mathematics). (2000). Principles and standards for teaching mathematics. Reston, VA: NCTM.Google Scholar
- Swan, M. (2011). Designing tasks that challenge values, beliefs and practices: A model for the professional development of practicing teachers. In O. Zaslavsky & P. Sullivan (Eds.), Constructing knowledge for teaching secondary mathematics. New York: Springer.Google Scholar
- Tirosh, D., & Wood, T. (Eds.). (2008). The international handbook of mathematics teacher education (Vol. 2). Rotterdam: Sense Publishers.Google Scholar
- Wiersma, W. (1995). Research methods in education (6th ed.). Massachusetts: Allyn and Baker.Google Scholar
- Zaslavsky, O. (2008a). Attention to similarities and differences: A fundamental principle for task design and implementation in mathematics education. Presented at the Topic Study Group on Task Design and Analysis (TSG34) at ICME-11. http://tsg.icme11.org/document/get/290. Retrieved 19 July 2012.
- Zaslavsky, O. (2008b). Meeting the challenges of mathematics teacher education through design and use of tasks that facilitate teacher learning. In T. Wood, P. Sullivan, D. Tirosh, K. Krainer, & B. Jaworski (Eds.), The international handbook on mathematics teacher education, 4 (pp. 93–114). The Netherlands: Sense Publishers.Google Scholar
- Zaslavsky, O., & Sullivan, P. (Eds.). (2011). Constructing knowledge for teaching: Secondary mathematics tasks to enhance prospective and practicing teacher learning. New York: Springer.Google Scholar