The nature of spontaneity in high quality mathematics learning experiences

Spontaneity has been linked to high quality learning experiences in mathematics (Csikszentmihalyi & Csikszentmihalyi, 1992; Williams, 2002).This paper shows how spontaneity can be identified by attending to the nature of social elements in the process of abstracting (Dreyfus, Hershkowitz, & Schwarz, 2001). This process is elaborated through an illustrative example—a Year 8 Australian male student who scaffolded his learning by attending to images in the classroom that were intended for other purposes. Leon’s cognitive processing was not ‘observable’ (Dreyfus et al., 2001) in classroom dialogue because Leon ‘thought alone’. Post-lesson videostimulated reconstructive interviews facilitated study of Leon’s thought processes and extended methodological techniques available to study thinking in classrooms.<br />