“The general aim of my book has been but to point out a way in which a solution of these numerous problems (behavior and development) can be attained. The nature of mental development as it has been revealed to us is not the bringing together of separate elements, but the arousal and perfection of more and more complicated configurations in which both the phenomena of consciousness and the functions of the organism go hand in hand.”

—  Kurt Koffka

Kurt Koffka. Growth of the Mind. An Introduction to Child Psychology. New York: Harcourt, Brace, 1924. p. 388 (2013 edition)

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Kurt Koffka 12
German psychologist 1886–1941

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“No mathematical idea has ever been published in the way it was discovered. Techniques have been developed and are used, if a problem has been solved, to turn the solution procedure upside down, or if it is a larger complex of statements and theories, to turn definitions into propositions, and propositions into definitions, the hot invention into icy beauty. This then if it has affected teaching matter, is the didactical inversion, which as it happens may be anti-didactical.”

Hans Freudenthal (1905–1990) Dutch mathematician

Rather than behaving anti-didactically, one should recognise that the learner is entitled to recapitulate in a fashion of mankind. Not in the trivial matter of an abridged version, but equally we cannot require the new generation to start at the point where their predecessors left off.
Source: The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961), p. ix

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