Investigating task design, classroom culture and mathematics learning: an enactivist approach
- 580 Downloads
- 2 Citations
Abstract
In this paper I introduce a methodological approach that can be useful for investigating relationships between mathematics tasks, mathematical classroom cultures and mathematics learning. This proposal responds to a need, identified in the literature, for “further research which uses alternative methods to understand student perspectives more fully, particularly in the context of innovative task design” (Ainley and Margolinas, Task design in mathematics education, Springer, Switzerland, 2015, p. 20). Influenced by enactivism, classroom cultures are characterised through patterns in students’ effective behaviours. Mathematics learning is defined as changes in effective behaviours which result from noticing features such as mathematical structure and which allow the learner to act differently in a given mathematical context. The following aspects were used as starting points to explore students’ behaviours and to characterise different cultures: active/passive, attentive/inattentive, working with others/working individually, freedom/constraint, giving correct answers/formulating explanations, knowing how and knowing why/remembering. Examples from two large-scale Mexican projects show how different tasks emerge in different contexts and how this emergence is interconnected with different patterns in effective behaviours and with mathematics learning. Characterising classroom cultures and sharing different ways of working in the classroom, which might give rise to different tasks, are offered as possibilities for taking students’ and teachers’ perspectives more fully into account in task design.
Keywords
Enactivism Mathematics classroom culture Mathematical tasks Mathematics learningReferences
- Ainley, J., & Margolinas, C. (2015). Accounting for student perspectives in task design. In A. Watson & M. Ohtani (Eds.), Task design in mathematics education (pp. 115–142). Switzerland: Springer.CrossRefGoogle Scholar
- Bartolini Bussi, M. G. (1998). Verbal interaction in the mathematics classroom: A vygotskian analysis. In H. Steinbring, M. G. Bartolini Bussi & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 65–84). Reston: NCTM.Google Scholar
- Bikner-Ahsbahs, A., & Janßen, T. (2013). Emergent tasks—Spontaneous design supporting in-depth learning. In Proceedings of ICMI Study22: Task Design in Mathematics Education (pp. 155–164). Oxford: Springer.Google Scholar
- Brousseau, G. (1997). Theory of didactical situations in mathematics (Edited and translated by N. Balacheff, M. Cooper, R. Sutherland & V. Warfield).Dordrecht: Kluwer.Google Scholar
- Clarke, D., & Mesiti, C. (2013). Writing the student into the task: agency and voice. In Proceedings of ICMI Study 22: Task Design in Mathematics Education (pp. 175–184). Oxford: SpringerGoogle Scholar
- Cobb, P., & Yackel, E. (1998). A constructivist perspective on the culture of the mathematics classroom. In F. Seeger, J. Voigt & U. Waschescio (Eds.), The culture of the mathematics classroom (pp. 158–190). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
- Coles, A. (2015). On enactivism and language: towards a methodology for studying talk in mathematics classrooms. ZDM Mathematics Education, 47(2), 235–246.CrossRefGoogle Scholar
- Coles, A., & Brown, L. (2013). Making distinctions in task design and student activity. In Proceedings of ICMI Study 22: Task Design in Mathematics Education (pp. 185–194). Oxford: Springer.Google Scholar
- Engeström, Y. (1998). Reorganizing the motivational sphere of classroom culture: an activity–theoretical analysis of planning in a teacher team. In F. Seeger, J. Voigt & U. Waschescio (Eds.), The culture of the mathematics classroom (pp. 76–103). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
- Gardner, K. (2013). Applying the phenomenographic approach to students’ conceptions of tasks. In C. Margolinas (Ed.), Task design in mathematics education (pp. 195–204). Oxford: Springer.Google Scholar
- Kieran, C., Doorman, M., & Ohtani, M. (2015). Frameworks and principles for task design. In C. Margolinas (Ed.), Task design in mathematics education (pp. 19–81). Oxford: Springer.CrossRefGoogle Scholar
- Lozano, M. D. (2004). Characterising algebraic learning: An enactivist longitudinal study. Unpublished doctoral dissertation, University of Bristol, Bristol.Google Scholar
- Margolinas, C. (Ed.). (2013). Proceedings of ICMI Study 22: Task Design in Mathematics Education. Oxford: Springer.Google Scholar
- Maturana, H., & Varela, F. (1992). The tree of knowledge: the biological roots of human understanding. Revised edition. Boston: Shambala.Google Scholar
- Radonich, P., & Yoon, C. (2013). Using student solutions to design follow-up tasks to model-eliciting activities. In Proceedings of ICMI Study 22: Task design in Mathematics Education (pp. 261–270). Oxford: Springer.Google Scholar
- Reid, D. A., & Mgombelo, J. (2015). Key concepts in enactivist theory and methodology. ZDM Mathematics Education, 47(2), 171–183.CrossRefGoogle Scholar
- Sandoval, I. T., Lozano, M. D., & Trigueros, M. (2006). Changes in the culture of the mathematics classrooms with the use of Enciclomedia, a national programme. In Proceedings of the 28th Conference of the North American Chapter of the Group for the Psychology of Mathematics Education (pp. 863–870). Mérida: PME-NA. ISBN: 970-702-202–7.Google Scholar
- Simmt, E., & Kieren, T. (2015). Three “moves” in enactivist research: a reflection. ZDM Mathematics Education, 47(2), 307–317.CrossRefGoogle Scholar
- Varela, F. (1999). Ethical know-how: action, wisdom and cognition. Stanford: Stanford University Press.Google Scholar
- Walkerdine, V. (1988). The mastery of reason: cognitive development and the production of rationality. London: Taylor & Frances/Routledge.Google Scholar