11 quotes
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)
Learners should be allowed to find their own levels and explore the paths leading there with as much and as little guidance as each particular case requires.
Didactical Phenomenology of Mathematical Structures (1983)
Space and the bodies around us are early mental objects... Name-giving is a first step towards consciousness.
Mathematics as an Educational Task (1973)
Geometry is grasping space. And since it is about the education of children, it is grasping that space in which the child lives, breathes and moves. The space that the child must learn to know, explore, conquer, in order to live, breathe and move better in it.
Mathematics as an Educational Task (1973)
Logic is usually understood nowadays as a study of certain formal systems, though in former times there were philosophers who held that the subject matter of logic was the formal rules of human thought.
No doubt once it was real progress when developers and teachers offered learners tangible material in order to teach them arithmetic of whole number... The best palpable material you can give the child is its own body.
Mathematics as an Educational Task (1973)
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.
Mathematics as an Educational Task (1973)