Ernst von Glasersfeld's answers
October 1999

Put Your Questions to Ernst von Glasersfeld



From: "Víctor M. Hernández L."
Subject: Conjecture

Professor Ernst von Glasersfeld:

From time to time I take again the wires of a conjecture:
1. As you probably know, Mandelbrot´s work introduce us to a new geometric objects called fractals, usually generated applying recursively a simple procedure (or algotirhm) to its own outputs, by means of wish it may produce the most complicated sets ever viewed before, including those who have rational dimentions. Consequently, we have new instruments to see, think and describe the world´s objects surrounding us.
2. From my point of view, the human cognition is in somewhat manner the most intrincated and complex space ever the human intend to see, think and describe as and intelligible object, in order to develope it conciently from a didactical point of view
3. This description is a conditio sine qua non the didactical efforts can have some viable concretions lying on it.
4. The conjecture is thinking in the mother language as the prototype action or procedure that a person applying it recursively on his (or her) daily life as the outputs of the procedure, can develope the enormous complexity we can name as the human cognition.

¿Could you share with us some theoretical or practical elements to reject this conjecture?
In other case, ¿Could you share with us some papers or references to get closer in develope some didactical consequences for mathematical education?

Best from Hermosillo, Sonora. Mexico.

In advance, thanks for your time and attention ...

Víctor M. Hernández L.

Dear Mr. Hernandez,

I, too, have great respect for Benoit Mandelbrot and his invention of  fractals. I don't think, however, that this new instrument enables us "to describe the world's objects surrounding us". Rather, with this instrument  we generate patterns that enable us to sistematize areas of experience that formerly showed no regularities at all. In my view, fractals are a new way  of SEEING, and they have no more independent "existence" that numbers - or a coast line, which is one of Mandelbrot's favorite examples (where exactly should you draw the coast line when the tides shift it all the time, when  waves keep moving up and down on beeches and there are millions of rocks of which you cannot say whether they belong to the land or the sea? But it's nevertheless a useful fiction). I agree that "thinking in language" is a powerful tool (and manifestation) OF cognition; but the source of cognition itself is our mysterious capabilty of  REFLECTING and constructing regularities in our experience.
On the question of mathematics education, here are some references:
L.P.Steffe, E.von Glasersfeld, J.Richards, & P.Cobb (Eds.), Children's  counting types: Philosophy, theory, and application. New York: Praeger, 1983.
L.P.Steffe (Ed.), Epistemological foundations of mathematical experience.  New York: Springer, 1991.
von Glasersfeld, E. (Editor). Radical constructivism in mathematics education. Dordrecht: Kluwer 1991

Best wishes,

Ernst von Glasersfeld.




From: Shu Ching Yang
Subject: request for paper

Dear Prof. Glasersfeld

I am interested in your paper, "Learning as a constructive activity", which appeared in In J. C. Bergeron and N. Herscovics (Eds.), Proceedings of the Fifth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 41-69). Montreal: University of Montreal. Unfortunately,

I was unable to locate this proceedings from my country. Is it possible for you to either send me through attached file or a paper copy.

Thank you very much.

Sincerely yours,

Shu Ching Yang
Graduate Institute of Education
National Sun Yat-sen University
70 Lien-hai Rd. Kaohsiung, Taiwan
804 ROC



Dear Mr. Shu Ching Yang,

I will send yu a copy of the paper you requested by ordinary mail because I do not have the text in my computer.



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