Who Puts the ‘Active’ into ‘Active Learning’?

Learning is here considered to have taken place when someone has developed the habit, propensity, and disposition to attend productively to things not previously noticed, and in ways not previously experienced, to do with some specific and particular content. ‘Active learning’ sounds like a tautology, but was introduced as a contrast to the more passive activity of students sitting in lectures listening and transcribing mathematics written on a board or screen onto their own paper. The stance taken here is that effective and efficient learning involves active engagement in activity, but includes enculturation through being in the presence of a relative expert¹ who themselves is manifesting mathematical thinking, not simply passing on the records of the results of previous mathematical thought. Such ‘passivity’ does not necessarily require intention. Following Bennett² actions are here taken to involve three agents or impulses: initiating, responding, and reconciling or mediating. All three agents are thus active, but in different ways. Interactions intended to contribute to learning are considered to be actions, and so involve three agents: learner, teacher (in some manifestation), and mathematical content, all within a culture or ethos. Since there are six different ways in which the triple of agents can be assigned to the triple of impulses, six different modes are possible. Analysing these modes sheds light on different ways in which learning could be said to be ‘active’. Activity takes place within a mode of interaction. Again following Bennett, effective activity is here taken to require appropriate relationships among the gap between current state and intended goal, the resources available, and the tasks set.

¹Vygotsky (1978) pointed out that ‘higher psychological processes’ are first encountered in others.

²Bennett (1993); see also Shantock Systematics Group (1975)