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Traditional thinking about teachable moments (TMs) sees in TMs only spontaneity and curricular independence. This makes TMs mysterious in origin and irrelevant to planned lessons. Possible meanings of ‘teachable moment’ may be expanded by taking spontaneity and curricular independence as variables – predictability and curricular relevance – not absolute properties. Interpreting TMs as theoretical constructs yields four varieties of TMs (Circumstantial, Collateral, Conventional, and Creatable). Each type is a TM because all express the educational energy characteristic of TMs; but each expresses it differently under varying environmental conditions. Creatable TMs convert traditional metaphysical mysteries into a solvable epistemological puzzle about creating in classrooms the educational energy we already know exists in nature. This opens opportunity to study teaching from a measurable perspective.