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Re: Only 45% of the students were prepared for math
Posted:
Mar 24, 2006 9:10 PM
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In article <25o822pt3oh9p6jjqq70ietqgasccq929h@4ax.com>,
Guess who <notreally.here@here.com> wrote:
>On 24 Mar 2006 11:22:36 -0500, hrubin@odds.stat.purdue.edu (Herman
>Rubin) wrote:
>>In article <m4p522tsf03cd3aq84fm1spqnugkge7oac@4ax.com>,
>>Guess who <notreally.here@here.com> wrote:
>>>On 23 Mar 2006 11:33:53 -0500, hrubin@odds.stat.purdue.edu (Herman
>>>Rubin) wrote:
>>>>Concepts and structure need to come EARLY, so the students
>>>>can know why, and not just how.
>>>Not so; certainly not necessarily so, and far too sweeping a
>>>generalisation. You lose almost everyone if you pontificate. The
>>>young are generally not ready for theory simply due to the fact that
>>>they are very young, but might grasp it later when they have more
>>>detail to put to that theory.
>>Do you mean you cannot teach grammatical structure to
>>someone who has not learned a language? Nonsense.
>In what language to you teach it then?
One needs very little of a language. Scientists have
demonstrated that little vocabulary is learned before
the idea of grammatical structure is managed; there
has been an argument, with data to back it, that
children earlier than one year, with zero vocabulary,
can comprehend grammatical ideas.
Once one has an adequate amount to use to communicate,
entirely foreign grammar can be taught.
>>You do not understand concepts. They are NOT the same as
>>theory; one can learn the theory and have no understanding
>>of the concepts, and vice versa.
>Don't be speculative about what I do or do not know. I *taught*
>concepts. I *argued* that is was lack of knowledge and understanding
>of concepts that made the difference, being not surprised even when my
>own daughter showed a decided lack of that knowledge in her studies in
>physics.
What are the unrelated concepts of the integers, which
I have been mentioning? They do need to be tied together,
but they are totally distinct concepts. There are other
conceptual extensions, but these are very basic.
Also, the classical Euclidean geometry used intuition
only for the axioms (including some unstated ones), and
then was completely formal. This does not mean that SOME
"geometric intuition" may not be helpful; however, I saw
early that it was a mistake to rely on this, despite the
standard pedagogical saw about the importance. This is
the case even in many "geometric" situations.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
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