Impetus to explore: approaching operational deficiency optimistically

‘Impetus to explore’ is studied through post-lesson video-stimulated student interviews. This impetus focuses ‘spontaneous’ decisions to explore unfamiliar mathematics. Uncertainty, quests for elegance and curiosity have been found to contribute to this impetus. This study identified other contributing factors: inability to undertake the teacher’s task, ‘optimistic explanatory style’ (Seligman, 1995), and identifying relevant complexities (Williams, 2002). Explanatory style affects how a person perceives successes and failures. Enactment of optimism in this study illuminated its role in creating an impetus to explore. Re-conceptualising ‘operational deficiency’ (Chen & Siegler, 2000) to include absence of resources to undertake a task illuminated a task design feature that can increase exploration.