Abstract
This article examines unifying factors among diverse problems of understanding in several fields. Certain misunderstandings in science, mathematics, and computer programming display strong structural analogies with one another. Even within one of these domains, however, not all misunderstandings are structurally similar. To explain the commonality and variety, four levels of knowledge are posited: (a) content, (b) problem-solving, (c) epistemic, and (d) inquiry. Through analysis of several examples, it is argued that misunderstandings have causes at multiple levels, with highly domain-specific causes predominant at the “content” level and somewhat more general causes at the other levels. The authors note that education characteristically neglects all but the content level, describe successful interventions at all levels, and urge more attention in education to integration across the levels.
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