Hans Freudenthal - Revisiting mathematics education

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

Hans Freudenthal

[Guided reinvention is] striking a subtle balance between the freedom of inventing and the force of guiding, between allowing the learner to please himself and asking him to please the teacher. Moreover, the learner's free choice is already restricted by the re of reinvention. The learner shall invent something that is new to him but well-known to the guide.

Hans Freudenthal

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

Hans Freudenthal