Phenomenal Mathematics at University Level
Plenary Speaker
John Mason
Open
University & University of Oxford
Every mathematical topic has components which can contribute to or address three of the traditional strands of the human psyche: cognition (awareness,), enaction (behaviour) and affect (emotion). These three strands form a framework for elaborating the Structure of a Topic. The framework can contribute to planning teaching by acting as a reminder about aspects of the topic. It can also provide an analytical tool for researching learners' appreciation and understanding of a topic.
Reaching out to the full complexity of the human psyche contributes not only to learning as such, but to the perception of what mathematics is and can be. For many students, especially those on service courses, mathematics is a collection of tools for answering questions in the learner's preferred discipline. But we know mathematics as a way of thinking, as a way of perceiving, as a way of being. Mathematics can be used to make mathematical sense of phenomena in the world, but to do this, learners need to make sense of mathematics: literally, to engage their senses.
I shall outline uses of the Structure of a Topic Framework, focusing on the affective-emotional strand, and propose the conjecture that every mathematical topic in the undergraduate mathematics curriculum can be introduced as a way of making sense of some phenomena. These phenomena may be manifested in the material world, or in the virtual world of e-screens. By presenting phenomena which generate surprise or intrigue, learners are not only drawn to engage with the topic, but also have a sense of what the topic is for and why it might be useful, and experience mathematical sense making as a stimulating and challenging activity.