From: Wolff-Michael Roth (mroth@uvic.ca)
Date: Sun May 01 2005 - 17:19:58 PDT

Hi all,
further to my earlier note about our (Western) tendency to celebrate a
certain form of abstraction--Piaget, too, celebrated this particular

Hegel asked the rhetorical question, "Who thinks abstractly?" and then,
after saying in French "Sauve qui peut" answers his question, "Only the
uneducated." You can find his piece on the net. But essentially,
Marxist philosophers and psychologists picked up on this and speak of
ascension from abstract to concrete, from the general knowledge of the
uneducated to the detailed and particular, contextualized knowledge of
the specialist.

My sense is that the expert is expert because s/he has many ways for
concretely realizing the possibilities in the general (genetic
developmentally, the abstract of the uneducated is always prior to the
concrete of the expert). Our phenomenologically oriented research
framed expertise in terms of Spielraum, room to maneuver, which
increases with experience and familiarity of the subject|object unit
(e.g., Roth, Lawless, & Masciotra, 2001).

More to this point, a phenomenological analysis of my own mathematical
experience shows that I mastered the unknown problem as it became
increasingly concrete and less abstract (Roth, 2001). It would be
interesting for me to go back and rewrite the piece now from the CHAT
perspective on concrete and abstract.

I hope others, too, will read this months article and write on this
interesting issue.


Roth, W.-M. (2001). Phenomenology and mathematical experience.
Linguistics & Education, 12(2), 239252.
Roth, W.-M., Lawless, D., & Masciotra, D. (2001). Spielraum and
teaching. Curriculum Inquiry, 31(2), 183207.

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