Martina Metz

Digging Beneath Dual Systems Theory and the Bicameral Brain: Abductions About the Human Psyche From Experience in Mathematical Problem Solving

Abstract Using a phenomenological stance, the chapter invites readers to undertake a variety of mathematical and pedagogic tasks. These are used as the basis for conjectures about the human psyche that draw upon ancient psychology and underpin both dual systems theory ( Kahneman, 2012 ) and the notion of a bicameral brain ( Jaynes, 1976 ; McGilchrist, 2009 ) as explanations for the behavior of students studying and exploring mathematics. Both of these theories are extended in order to integrate emotions into the picture, using ancient descriptions of a sixfold structure of the human psyche.

Dynamic Responsive Pedagogy: Implications of Micro-Level Scaffolding

In mathematics education, scaffolding is often viewed as a mechanism to provide temporary aid to learners to enhance mathematical understanding. Micro-level scaffolding is process by which the teacher returns the student(s) to a conceptual point where scaffolding is not needed. Then the teacher creates a series of incrementally more complex tasks leading to the original task. This process is dynamic, as it often requires multiple steps, and it is responsive because involves moment-by-moment assessment, which shapes each increment. In this paper, we present data on how experienced teachers in the Math Minds Initiative employ micro-level scaffolding. Implications of micro-level scaffolding are discussed.

Attending and Responding to What Matters: A Protocol to Enhance Mathematics Pedagogy

University of Calgary Werklund School of Education, Galileo Educational Network, Navigator, Centaur Products Inc., Marathon Oil