Human ecology
Mathematics education
Psychology of learning mathematics
Notes
Notes - 16/2/00
Zone of proximal development
"... the distance between the actual development level as determined by
independent problem solving and the level of potential development as
determined through problem solving under adult guidance or in collaboration
with more capable peers." Zygotsky (1978, p.86)
Lev S. Vygotsky (1978) "Mind in society", Harvard UP, Cambridge
Edited by Michael Cole, Vera John-Steiner, Sylvia Scribner, Ellen Souberman
Contents...
Part I. Basic theory and data
- 1. Tool and symbol in child development
- 2. The development of perception and attention
- 3. Mastery of memory and thinking
- 4. Internalization of higher psychological functions
- 5. Problems of method
Part II. Educational Implications
- 6. Interaction between learning and development
- 7. The role of play in development
- 8. The prehistory of written language
Internalization is the "internal reconstruction of an external operation."
(p.56) Internalization consists of a series of transformations...
- (a) An operation that initially represents an external activity
is reconstructed and begins to occur internally
- (b) An interpersonal process is transformed into an
intrapersonal one.
- (c) The transformation of an interpersonal process into an
intrapersonal one is the result of a long series of developmental
events.
Self and mutual as consequences of natural selection.
- Selfish behaviour (T.H.Huxley)
- Mutual aid (Kropotkin)
Definitions of self and mutual reflexivity
- Self reflexivity. The self changes (and is changed by) its
abiotic surroundings?
- Mutual reflexivity. The self changes (and is changed by) its
biotic surroundings - by other selves. (Examples: prisoner's
dilemma?, internal uncertainty model)
Internalization as an example of (mutual) reflexivity. Identification of
reflexivity with internal uncertainty and with the internal perspective in
psychology.
Sixth form subjects chosen by convergers and divergers.
History
- Extreme divergers: 7
- Mild divergers: 15
- All-rounders: 17
- Mild convergers: 3
- Extreme convergers: 2
Modern languages
- Extreme divergers: 3
- Mild divergers: 18
- All-rounders: 26
- Mild convergers: 7
- Extreme convergers: 0
Mixed courses
- Extreme divergers: 4
- Mild divergers: 1
- All-rounders: 14
- Mild convergers: 4
- Extreme convergers: 0
Classics
- Extreme divergers: 1
- Mild divergers: 2
- All-rounders: 3
- Mild convergers: 7
- Extreme convergers: 3
Physical science
- Extreme divergers: 3
- Mild divergers: 12
- All-rounders: 33
- Mild convergers: 37
- Extreme convergers: 19
Biology
- Extreme divergers: 1
- Mild divergers: 4
- All-rounders: 14
- Mild convergers: 4
- Extreme convergers: 3
"The converger is the boys who is substantially better at the intelligence
test than he is at the open-ended tests; the diverger is the reverse. In
addition are the all-rounders , the boys who are more or less equally good
(or bad) on both types of test. As a matter of convenience, I define 30 per
cent of my usual schoolboy sample as convergers, 30 per cent as divergers,
and leave the remaining 40 per cent in the middle as all-rounders."
(Hudson, 1966, p.55)
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Created 22/3/00
Last modified