MathWright.com
Title
The New Mathwright Library and Cafe
Description
James E. White received his Ph.D. from Yale University in 1972, as a student of William Massey, and has devoted the better part of his professional life to teaching mathematics, beginning at University of California, San Diego in 1972, and oscillating between teaching positions at Carleton College, Bates College, Kenyon College, and research positions at Jet Propulsion Labs, Institute for Academic Technology, and finally, his own consulting company, Bluejay Lispware, which operates the New Mathwright Library and Café on the web. He has held visiting positions at Harvey Mudd College, University of North Carolina, Chapel Hill, Naval Postgraduate School and Stetson University.
Early in his career, he became interested in the epistemological basis for the pedagogical styles that were in general use, and that interest led him to the Piagetian "constructivist" interpretation of the psychology of mathematics learning that is couched in his Genetic Epistemology. This has much in common with ideas expressed by the mathematicians: Poincare, Hadamard, and Hurewicz, and he found it to be consistent with his personal views.
On the genetic view, the learner actively constructs her knowledge by challenging old ideas, and assimilating new ones into increasingly stable "structures". Since it is difficult to translate this abstraction to pedagogical practice within the context of curricula that are organized around different (more behavioral) premises, he began to look for ways to structure lower level mathematics courses around the constructive activity of the learners. It quickly became apparent that, for a strategy like this to work, the students would need heuristic tools that would help them form coherent pictures of the mathematical processes and constructions under discussion, and that would allow them quickly to test their understanding by showing them the answers to the questions they asked.
