Investigating task design, classroom culture and mathematics learning: an enactivist approach

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.