Rethinking Formalisms in Formal Education

Abstract

I explore a belief about learning and teaching that is commonly held in education and society at large that nonetheless is deeply flawed. The belief asserts that mastery of formalisms—specialized representations such as symbolic equations and diagrams with no inherent meaning except that which is established by convention—is prerequisite to applied knowledge. A formalisms first (FF) view of learning, rooted in Western dualist philosophy, incorrectly advocates the introduction of formalisms too early in the development of learners’ conceptual understanding and can encourage a formalisms-only mind-set toward learning and instruction. I identify the prevalence of FF in curriculum and instruction and outline some of the serious problems engendered by FF approaches. I then turn to promising alternatives that support progressive formalization, problem-based learning, and inquiry learning, which capitalize on the strengths of formalisms but avoid some of the most costly problems found in FF approaches.

Notes

The claims in this article are about formal educational settings. Informal and extracurricular education may follow different guidelines (e.g., L. B. Resnick, 1987) and tend to treat formalisms in a different manner (e.g., Rose, 2004).

In unpublished research, Kurt VanLehn found that participants in his studies on learning systems dynamics treat stock and flow diagrams as abstract representations rather than in a concrete or iconic manner (personal communication, June 28, 2011).

This exact point was made by an anonymous reviewer, whom I wish to acknowledge.