We will engage with a hands-on activity that uses 3-D models and 2-D dynamic geometry software to explore a well-known geometric problem of optimization and rate of change. Through a spatial-visual approach, we explore an activity that highlights ‘big ideas’ such as how properties change during optimization, why an optimum is found where it is, as well as what (global conclusions) can be inferred by comparing (local) pairs of models. The activity affords a hands-on investigation of rates of change in volume with spatial-visual reasoning (and without calculation) – leading to an enriched sense of the process and encouraging reflection and connection amongst different approaches. Participants are encouraged to bring their portable computing devices to engage with the GSP sketches we will provide.

Bio: Walter Whiteley is Professor of Mathematics and member of the Graduate Program in Education at York University. For more than 40 years, he has practiced spatial reasoning in applied geometry and in his mathematics teaching and work with pre-service / in-service teachers. His observations include that: (i) spatial reasoning can be added to any area of mathematics – with positive impact; (ii) spatial reasoning is developed through regular practice; (iii) spatial reasoning remains malleable, at all ages. Recent projects include: a hands-on spatial reasoning course for pre-service teachers; and exploration of the decline (and maintenance) of spatial reasoning during aging.

Bio: Ami Mamolo is Assistant Professor at UOIT. She works with learners of all levels to explore how creative instructional approaches can be networked to foster conceptual growth, meaningful engagement, and enjoyment with mathematics. Her research explores ways of teaching math through issues of social justice, learning through mathematical paradoxes and ambiguities, relationships between teachers’ personal mathematics and their pedagogical decisions, as well as collaborative work with and Walter Whiteley and Robyn Ruttenberg on task design with spatial reasoning and digital modalities.