Hopefully you can help me. "How does young children's logico mathematical knowledge develop?" Thank you so much!
This is a big topic, but recent research in cognitive science
is giving some new insights.
There is so much we do not know. We do, however, know now that
many assumptions made in the past, including assumptions by
people like Piaget, are probably wrong.
The way these abilities are embodied in the brain is not,
itself, 'logical' or predicted by thought experiements on
what could have worked. When answering the question
Is 7x5 > 26?
we do NOT calculate 7x5=? Typical adults do the first
question more rapidly than the second, with a different
part of the brain than they do the second!
- 3 day old babies can do some arithmetic (with numbers
1,2,3). That is, we are typically born with some capacities
which will be used in mathematics and other areas. Some of
this is shared with animals.
- the parts of the brain active in many parts of mathematics
are NOT the language parts, but the parts involved in vision,
in eye-hand coodination (manipulation, planning, ... ).
So what Howard Gardner might call the logico mathematical
intelligence is only part of what is used in doing mathematics
(and for some mathematicians, is not the major part).
- the brain we use to do math and science, is a brain evolved
long before math and science existed. We must be reusing brain
patterns and circuits evolved for other purposes, reshaping
connections, and reusing pieces.
- Areas like spatial reasoning seem to be influenced by
physical experience and practice. Alternatively, the same
prebuild abilities show up in sports and in math.
- there are intriguing experients that indicate that early
musical experience (listening, learning piano, ... ) improve
spatial temporal reasoning - abilities used in parts of
mathematics, but again not linked to language.
Go to Math Central