Special Colloquium
Jennifer A. Kaminski
Center for Cognitive Science, Ohio State University
Acquisition of Mathematical Concepts: What instantiations promote transfer of conceptual knowledge across isomorphs?
Abstract: A fundamental question for any mathematics instructor is "what choice of
instantiation most effectively facilitates acquisition of a given concept?"
Effective instantiations must promote two processes: learning and transfer.
Learning is evidenced by demonstration of knowledge in the context of initial
learning. Transfer is the application of prior knowledge to a novel situation.
Specific cognitive mechanisms underlie transfer; and these mechanisms are
influenced by extraneous information in the learning context. A series of
experiments examined the effects on learning and transfer of both concrete and
abstract instantiations. Undergraduate and middle school students learned
different instantiations of a mathematical group. Students who learned an
abstract, generic instantiation successfully learned the concept and
transferred their knowledge to a novel isomorphic domain. Students who learned
a concrete instantiation were unable to transfer. These results argue that
some concrete instantiations can provide a leg-up in the learning process.
However, this benefit comes at the cost of transfer. Particularly for
mathematical concepts, whose very nature allows unlimited instantiations, this
is a high price to pay.
Tuesday February 28, 2006 at 11:00 AM in SEO 636