John Mason (2011) Explicit and Implicit Pedagogy: variation theory as a case study, Smith, C. (Ed.) Proceedings of the British Society for Research into Learning Mathematics 31(3) November 2011
Variation theory proposes that learners must experience variation in the critical aspects of a concept, within limited space and time, in order for the concept to be learnable. But the presence of variation does not in itself guarantee that that variation will be experienced. As Kant implied, a sequence of experiences does not guarantee an experience of that sequence. Implicit variation theory assumes that the presentation of variation is sufficient in order for learners to learn what is intended, whereas explicit variation theory incorporates some degree of explicitness in the interaction between teacher and student. The conjecture is proposed that tension between explicitness and implicitness is present in all attempts both to implement theories in practice and to justify or analyse pedagogical choices using theories, of whatever kind.
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