By Hans Freudenthal
The release ofa new publication sequence is usually a not easy eventn ot just for the Editorial Board and the writer, but additionally, and extra really, for the 1st writer. either the Editorial Board and the writer are delightedt hat the 1st writer during this sequence isw ell in a position to meet the problem. Professor Freudenthal wishes no advent toanyone within the arithmetic schooling box and it truly is quite becoming that his e-book can be the 1st during this new sequence since it used to be in 1968 that he, and Reidel, produced the 1st factor oft he magazine Edu cational experiences in arithmetic. Breakingfresh floor is consequently not anything new to Professor Freudenthal and this booklet illustrates good his excitement at this type of job. To be strictly right the ‘ground’ which he has damaged here's now not new, yet aswith arithmetic as a tutorial activity and Weeding and Sowing, it is very the newness oft he demeanour during which he has conducted his research which supplies us with such a lot of clean views. it's our purpose that this new ebook sequence may still supply those that paintings int he rising self-discipline of mathematicseducation with a necessary source, and at a time of substantial quandary in regards to the complete arithmetic cu rriculum this booklet represents simply such source. ALAN J. BISHOP handling Editor vii a glance BACKWARD AND a glance ahead males die, structures final.
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Additional resources for Didactical Phenomenology of Mathematical Structures (Mathematics Education Library)
Realistic contexts require a much broader reference set – actually but also potentially by their openness, by the potentiality of extending. The reason why this phenomenological analysis is less relevant for mathematics than for applications (for instance, probability, where it originated) is to be found in the peculiarities that distinguish mathematical language from the vernacular, in which applications are usually formulated. I shall return to these peculiarities, but I will anticipate the most essential one: The variables of mathematical language are omnivalent in principle; letters can indicate anything, whereas any restriction of domain must be made explicit.
Remembering length during long periods remains a difficult AS AN E X A M P L E : L E N G T H 21 task. As for myself, I am often surprised that relations of length differ greatly from what I remember they should be. Comparing objects side by side gains precision in the course of development: the ruler is laid close to the line to be measured, while observing the prescription to aim perpendicularly to the line. The connection between “length” and “distance” is stressed, and the weight is shifted to “distance” if one of the objects to be compared, or both of them, bear marks by which the ends of the objects to be compared can be indicated.
The mathematical objects are nooumena, but a piece of mathematics can be experienced as a phainomenon; numbers are nooumena, but working with numbers can be a phainomenon. Mathematical concepts, structures, and ideas serve to organise phenomena – phenomena from the concrete world as well as from mathematics – and in the past I have illustrated this by many examples**. By means of geometrical figures like triangle, parallelogram, rhombus, or square, one succeeds in organising the world of contour phenomena; numbers organise the phenomenon of quantity.
Didactical Phenomenology of Mathematical Structures (Mathematics Education Library) by Hans Freudenthal