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Re: [ARUME] Piaget, Vygotsky, and ?
Self-regulatory thinking (self-regulation) has its origins in the work of
Piaget and was developed by Inhelder and Karmiloff-Smith (re metaprocedural
organisation) - see references below.
I have synthesised the works of metacognition (major definitions by Alan
Schoenfeld and Anne Brown) into three areas:
1. Knowledge-of
2. Self-regulation
3. other-regulation (socially constructed)
My thesis summarises these works and develops self-regulatory thinking by
developing a model of thinking referring to the analysis of Reflection,
Organisation, Monitoring and Extraction of mental resources (ROME).
References and literature review can be found at
http://users.ox.ac.uk/~heg/thesis/
especially
http://users.ox.ac.uk/~heg/thesis/Chapter2/Chapter2.htm
Others:
Brown, A. L. (1987) 'Metacognition, executive control, self-regulation, and
other more mysterious mechanisms', in F. E. Weinert and R. H. Kluwe (Eds.),
Metacognition, Motivation and Understanding, 65-116. Hillsdale, NJ: Lawrence
Erlbaum.
Inhelder, B., Sinclair, H., & Bovet, M. (1974) Learning and the development
of cognition. Cambridge, MA: Harvard University Press.
Karmiloff-Smith, A. (1979a) 'Micro- and macro- developmental changes in
language acquisition and other representational systems' in Cognitive
Science, 3, 91-118.
Karmiloff-Smith, A. (1979b) 'Problem-solving construction and
representations of closed railway circuits' in Archives of Psychology, 47,
37-59.
Piaget, J. (1976). The grasp of consciousness (S. Wedgwood, Trans.).
Cambridge MA: Harvard University Press.
Piaget, J. (1978). Success and understanding (A. J. Pomerans, Trans.).
Cambridge MA: Harvard University Press.
Piaget, J., & Inhelder, B. (1963). The child's concept of space. London:
Routledge and Kegan Paul. Prentice Hall. Publishing Company.
Concept image was introduced by Vinner and Tall in 198. Some references:
Tall, D. O. & Vinner , S., (1981) Concept image and concept definition in
mathematics with particular reference to limits and continuity, Educational
Studies in Mathematics, 22 (2), 125-147.
Vinner, S. (1983) Concept definition, concept image and the notion of
function. International Journal of Mathematical Education in Science and
Technology, 14, 239-305.
Vinner, S. & Dreyfus, T. (1989) Images and definitions for the concept of
function. In Journal for research in Mathematics Education,. 20 , 356-366.
regards
Stephen
-----------------------------------------------------------------
Dr. Stephen Hegedus
Centre for Mathematics Education Research
Department of Educational Studies
University of Oxford
15 Norham Gardens
Oxford OX2 6PY
UK
Tel: +44 (0) 1865 274259
Fax: +44 (0) 1865 274027
E-mail: heg@ermine.ox.ac.uk
URL: http://users.ox.ac.uk/~heg
----- Original Message -----
From: Margaret Morrow <morrowml@PLATTSBURGH.EDU>
To: <ARUME-LIST@ENTERPRISE.MAA.ORG>
Sent: 20 March 2000 18:55
Subject: Re: [ARUME] Piaget, Vygotsky, and ?
> Could Stephen Hegedus please give a couple of references on
> "self regulatory thinking" in Mathematics and "concept image"?
> Thanks!
> Margaret Morrow
> (Mathematics,
> SUNY Plattsburgh.
>
> Quoting Stephen Hegedus
> <stephen.hegedus@EDUCATIONAL-STUDIES.OXFORD.AC.UK>:
>
>
> > I have begun to see certain advances in understanding the
> learning of
> > mathematics by examining self-regulatory thinking (as a form
> of
> > metacognition) from a theoretical perspective. I also see
> substantial
> > cognitive mathematical theories such as concept image being
> reshaped by the
> > cognitive growth of meta-mathematical thinking.
>
> > For example, I see concept image as a brilliant piece of
> insight in to the
> > learning of mathematics but it might be too broad (and too
> rich) a
> > structure. Through examining the role of symbol, building and
> constructing
> > on theories (yet again) such as Deacon, then we see images
> within images or
> > images/experiences which overlap. Whilst these areas are
> fuzzy it might be
> > worthwhile to study them. Example, the multi-dimensional
> purpose of
> > thinking
> > geometrically and/or algebraically in doing simple integral
> calculus.
>