DNR’s
Definition of “Mathematics” and Its Pedagogical Consequences; Focus on
the Transition between Proof Schemes

Plenary Speaker

Guershon Harel

University of California, San Diego

Current teaching practices tend to view
mathematics in terms of subject matter, such as definitions, theorems,
proofs, problems and their solutions, not in terms of the conceptual
tools that are necessary to construct such mathematical objects.
This talk has two main goals: The first goal is to define these two
categories of knowledge and explain why both categories are
needed. The definitions and explanations are oriented within a
theoretical perspective called DNR-based
instruction in mathematics. Central to DNR is the distinction between way of understanding and way of thinking and the definition
of “mathematics” in terms of these two constructs. The second
goal is to discuss curricular and instructional implications of this
definition, in particular, and of DNR, in general. While examples
from different areas of mathematics will be presented, the focus will
be on proof, more specifically on the transition from empirical proof
schemes to deductive proof schemes.