Psychology of learning mathematics
Notes - 21/3/00
Vygotsky - Problems of Method
(Background of current psychology) Stimulus-response experiments are
sufficient for experiments on lower psychological functions.
Qualitative distinction between animal and human behaviour. (p.60)
(Note: historical distinction - may be objectionable to some parts of
ecology movement. Counterpoint Tepper: some humans behave like animals and
some animals behave like humans.)
Engels: approaches to understanding human history. (p.60)
(Vygotsky's source: Engels "Dialectics of nature", p.172)
- Naturalistic approach: "only nature affects human beings and
only natural conditions determine historical development."
- Dialectical approach: "while admiting the influence of nature
on man, asserts that man, in turn, affects nature and creates
through his changes in nature new natural conditions for his
Stimulus-response methods in psychology are similar to naturalistic
approaches in history. "Both see the relation between human behaviour and
nature as unidirectionally reactive." (p.61)
Alternative methods are necessary for higher psychological functions.
Vygotsky highlights three principles:
"The search for method becomes one of the most important problems of the
entire enterprise of understanding the uniquely human forms of
psychological activity. In this case, the method is simulateously
prerequisite and product, the tool and the result of the study." (p.65)
- Analyzing processes, not objects. Psychological processes cannot
be considered as fixed objects, as they are undergoing change. It is
therefore important to trace the historical development of the
process. ("To study something historically means to study it in the
process of change", pp.64-65)
- Explanative vs. descriptive. By analogy with biological
distinction between phenotype and genotype, Lewin contrasts the
external features of a phenomenon with the internal processes that
give rise to the phenomenon. Two phenomena may have the same
external appearance but have different internal causes (and vice
versa). "Thus, psychologoical analysis in our sense rejects nominal
descriptions and seeks instead to determine causal-dynamic
relations. However, such explanation would also be impossible if we
ignored the external manifestations of things. By necessity,
objective analysisincludes a scientific explanation of both external
manifestations and the process under study". (p.63)
- Problem of "fossilized behaviour". "...processes that have gone
through a very long stage of historical development and have become
fossilized." (p.63) It is necessary to reconstruct the processes
in the development of a particular psychological function.
Example: psychology of complex choice responses.
Usual theory considers that the response time in these experiments is equal
to the arithmetic sum of the time of the simple reaction plus
the discrimination plus the choice. Instead experiments show that times for
complex choice and simple reaction experiments can be equal. One problem is
the subjects need to learn the experiment. Early trials, (in which the
learning process may be evident) are discarded in order of find an average
response time for the activity.
Consequences for tests of divergent-convergent thinking.
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