San Diego University

This talk is on two fundamental questions: what is the mathematics that we should teach in school? and how should we teach it? The goal of the talk is twofold: to present a pedagogical stance on these two questions and to demonstrate this stance with an actual mathematical lesson. The stance is oriented within a broader theoretical framework, called DNR-based instruction in mathematics. The initials D, N, are R stand for three foundational instructional principles in the framework: duality, necessity, and repeated reasoning.

Guershon Harel is a Professor of Mathematics at the University of California, San Diego. Prior to joining the faculty at San Diego, he was faculty at Purdue University. Dr. Harel's research interests include the cognition and epistemology of mathematics and their implications to mathematics curricula and teacher education. This work focuses on advanced mathematical thinking, particularly the concept of proof, the learning and teaching of linear algebra, and the development of the multiplicative conceptual field. He is a member of the Special Interest Group of the Mathematical American Association on Research in Undergraduate Mathematics Education and recent contributions to MAA publications include "What is Mathematics? A Pedagogical Answer to a Philosophical Question" and "Mathematical Induction: Cognitive and Instructional Considerations." Dr. Harel was a principle investigator for The Rational Number Project, an NSF backed research project investigating student learning and teacher enhancement. Other projects include contributions the Algebraic Thinking Institute (ATI) at UCSD, an intensive summer professional development institute for high school algebra teachers, and to PUPA, NSF-funded research project on the development of students' proof understanding, production, and appreciation. Dr. Harel received his Ph.D. in Mathematics from Ben-Gurion University of the Negev. Currenlty he is on leave at the Illinois Institute of Technology.