Norton A. (2009) Re-solving the Learning Paradox: Epistemological and Ontological Questions for Constructivists. For the Learning of Mathematics 29(2): 2–7. Fulltext at http://cepa.info/327

Norton A.
(

2009)

Re-solving the Learning Paradox: Epistemological and Ontological Questions for Constructivists.
For the Learning of Mathematics 29(2): 2–7.
Fulltext at http://cepa.info/327
This paper addresses the learning paradox, which obliges radical constructivists to explain how cognition can advance from a lower level of reasoning to a higher one. Although the question is at least as old as Plato, two major flaws have inhibited progress in developing solutions: the assumption that learning is an inductive process, and the conflation of epistemological and ontological questions. I adopt a radical constructivist perspective and present a few related solutions from previous mathematics education literature. I then provide a new solution that relies on Peirce’s theory of abduction and Piaget’s theory of operational schemes. However, with the learning paradox resolved, an ontological paradox remains: If individuals construct their mathematical realities based on their personal actions and experiences, how can we explain the predictive power of scientific hypotheses that are based on this mathematics?

Stern J. M. (2007) Cognitive constructivism, eigen-solutions, and sharp statistical hypotheses. Cybernetics & Human Knowing 14(1): 9–36. Fulltext at http://cepa.info/1277

Stern J. M.
(

2007)

Cognitive constructivism, eigen-solutions, and sharp statistical hypotheses.
Cybernetics & Human Knowing 14(1): 9–36.
Fulltext at http://cepa.info/1277