Inducing Mathematical Flow

Abstract

The concept of mathematical flow is introduced in this thesis and is defined as experiencing flow whilst engaged in mathematics. Flow (Csikszentmihalyi, 1975) is a state of concentration and complete focus on a complex task. Typically the person is working near the edge of their skill set. During flow experiences people lose track of time, are unaware of their surroundings, feel competent and in control, have no fear of failure, and often achieve at their personal best. Popular examples of flow involve artists, musicians, rock climbers and writers. In educational research flow has been connected with Vygotsky’s (1987) Zone of Proximal Development (ZPD). The ZPD is a space in which people can succeed with help, which I argue, can facilitate entry into a state of flow. The acquisition of new skills and information through the ZPD can provide the impetus to enter and sustain a state of flow. Within this state of flow a learner may develop a new level of understanding, or achieve a goal. I make the assumption that mathematical flow experiences have a positive effect on mathematical achievement and motivation. Additionally these experiences may have a positive impact on students’ post-school mathematical engagement and achievement. A preliminary study to verify or dispel my idea of a specific mathematical flow resulted in the confirmation of the concept. The main study was an intervention which aimed to induce mathematical flow in school students. The data revealed that some pedagogical practices tend to inhibit mathematical flow whilst others do not. Open ended tasks with a low entry and high ceiling were identified as having the potential to induce flow. Furthermore, the physical environment can be designed to support mathematical flow. I conclude with the pedagogical changes I will make in my own practice due to this research. These changes may be interpreted as suggestions for teachers who wish to induce mathematical flow amongst their students. I argue that the pedagogical pursuit of mathematical flow is likely to have a positive impact on students learning experiences, regardless of the number or intensity of the mathematical flow experiences induced.