Using energy dynamics to explore the process of making sense and the role of multiple selves in the teaching and learning of mathematics
This is an enquiry into what is beneath energy dynamics (in a psychological sense) experienced in teaching and learning and how these dynamics can be manipulated. It draws on ideas from disparate fields such as psychology, art and literature, to develop an integrated explanatory framework. This is then probed and refined in a mathematics education context. This thesis explores being in, and manipulating an emotional state and its associated energy. It enquires into how the aesthetic nature of
... sthetic nature of emotions interrelates with intensity of emotions experienced as felt arousal. Based on the conjecture that being in a state is the result of having made sense of some input that triggers one into that state, the question 'how did I get into that state' is asked. It explores what happens in the process of making sense and the virtual places where grouped and accumulated past experiences are stored as Multiple Selves. In this process the roles and existence of assumptions, expectations, disturbances, foci of attention, being in an inappropriate Self or being in a 'fitting' Self, and experiencing flow is explored. Significant consequences for teaching and learning are investigated, including the notion of developing mathematical thinking. Juxtaposing and transposing all these ideas offers a complex metaphorical model, a multi-layered, multi-faceted framework that can be used in the analysis of teaching and learning in general. It also offers a structure and direction for developing and analysing task design in particular. It presents a tool to manipulate emotional and cognitive states, to recognize and possibly understand strange behaviour within students and oneself. This thesis uses phenomenological philosophical methods and a pragmatic way of working within the Discipline of Noticing. What is offered is an articulation of the integrated sense I have made, in the expectation of affording possibilities for readers to notice energy dynamics within themselves and offering a framework for doing so.