Re: The abstract (contd.)

From: Peter Moxhay (
Date: Thu May 05 2005 - 03:49:49 PDT

Noel wrote:

> But if it is the genesis of the generalization that matters for
> Davydov, then it is less clear to me.

Yes, that it why it is unclear to me what kind of generalization is
being formed by the students described in Jurow's paper. Are they
picking out a pattern in data, or are they really identifying some
fundamental relation? Are they doing empirical or theoretical
abstraction and generalization. (Or doesn't it matter?)

Another problem I have in reading the paper is that mathematical
generalization is often discussed in term of some broad class of
mathematical problems or tasks.


- the students solve a large number of particular problems in order to
generalize (come up with the general method for solving all problems of
the class), or

- by solving a single, paradigmatic problem they "from the start" solve
all problems of the given class.

The second case would correspond to the case of theoretical or
contentful generalization. This kind of description was made by
Rubinshtein, and also discussed by Krutetskii, and picked up on by

I have difficulty applying this picture to Jurow's article: What is the
larger class of problems of which the guppy population problem is a
particular case? How can we say the students have generalized unless
they have been shown to have solved this larger class of problems?

Any ideas?


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