Rethinking Formalisms in Formal Education

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.