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Grasping spatial gestalts as figures is mathematizing of space. Arranging the properties of a parallelogram such that a particular one pops up to base the others on it in order to arrive at a definition of parallelogram, that is mathematizing the conceptual field of the parallelogram.

— Hans Freudenthal Mathematics as an Educational Task (1973)

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More quotes by Hans Freudenthal

Horizontal mathematising leads from the world of life to the world of symbols.

Revisiting Mathematics Education (1991)

Angles are measured by arcs, such that 360° and 2π correspond to each other.

Mathematics as an Educational Task (1973)

Vertical mathematising is the most likely part of the learning process for the bonds with reality to be loosened and eventually cut.

Revisiting Mathematics Education (1991)

Educational technique needs a philosophy, which is a matter of faith rather than of science.

Hans Freudenthal (1977)

No scientist is as model minded as is the statistician; in no other branch of science is the word model as often and consciously used as in statistics.

The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961)

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Quote text and notes from Wikiquote: Hans Freudenthal (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.