By Hans Freudenthal
The release ofa new ebook sequence is often a not easy eventn ot just for the Editorial Board and the writer, but in addition, and extra fairly, 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 really is relatively becoming that his publication 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 flooring is hence not anything new to Professor Freudenthal and this booklet illustrates good his excitement at one of these job. To be strictly right the ‘ground’ which he has damaged here's no longer new, yet aswith arithmetic as an instructional job and Weeding and Sowing, it is extremely the newness oft he demeanour during which he has performed his research which supplies us with such a lot of clean views. it really is our purpose that this new booklet sequence should still supply those that paintings int he rising self-discipline of mathematicseducation with a vital source, and at a time of substantial situation concerning the entire arithmetic cu rriculum this e-book represents simply such source. ALAN J. BISHOP dealing with 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)
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.
10–11. THE METHOD 31 Consider the number concept “three” and the geometrical concept “straight”. Before the child masters these words, he can be familiar with what they mean: clapping his hands thrice and running straight to a goal if it is suggested to him (the enactive phase); sorting out cards with three objects or straight lines pictured on them (the ikonic phase). Mastering the word three (or straight) means he is in the symbolic phase, since “three” as a word is a symbol for the concept three (or “straight” is for straight).
Likewise in the sequel I will not clearly separate phenomenology and didactical phenomenology from each other. As promised in the preface I would not sacrifice readability to systematics. Where did I look for the material required for my didactical phenomenology of mathematical structures? I could hardly lean on the work of others. I have profited from my knowledge of mathematics, its applications, and its history. I know how mathematical ideas have come or could have come into being. From an analysis of textbooks I know how didacticians judge that they can support the development of such ideas in the minds of learners.