Thursday, 19 September 2019
Lecture Theatre 1, Brooks Building
As a young student, I marveled at the capacity of mathematical symbols to anticipate local and cosmic physical events. How is that possible? What kind of miraculous written notations and alchemies were those that appeared to decode secrets of the universe? I was also in awe about understanding them: how do we come to learn about them? What is the nature of thought that allows thinking them?
Many years later, I continue to wonder about these questions and others that equally resist all attempts to reach closure. Awareness of the vainness of seeking final answers is a vital spring for all that we learn, as it helps us circumvent the traps of dogmatism. After a few decades of research on mathematics learning, I will portray current orientations of work that seem to me insightful and productive. In this talk, I will elaborate on two of them:
1. Bodies and Imaginaries
An ancient philosophical enigma is the apparent inexistence of mathematical entities; for example, perfect lines or circles cannot be seen, touched, or heard. And yet, imperfect and perceivable drawn or written diagrams are critical to figure out their properties and relations.
Elizabeth Grosz and other contemporary philosophers are reviving ideas from the Stoics about bodies and imaginaries. It seems to me that these can support us think anew the old enigma. I will reflect on this possibility on the basis of two episodes with students learning projective geometry.
2. Conversations with Materials
Conversation with materials, including diagrams, seems to be a misnomer. How is it possible to converse with things that do not speak, do not wait for their turns to respond, and do not argue for or adopt thoroughgoing commitments? If the notion of conversation with materials is to have any sustenance, it must refer to a type of conversation that can also happen among people.
I will propose that this kind of conversations appear to be well characterized by what Maurice Blanchot has called 'plural speech', and illustrate this with episodes involving making and mathematics.
To conclude, I will share emerging pedagogical visions for the learning of mathematics in informal settings, which coalesce interdisciplinary strands, including mathematics, art, architecture, and crafts.
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