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Mathematics and theory of knowledge
Posted:
Aug 14, 1999 5:52 PM
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Newton Liebniz is of course absolutely right. (Sporting such a name
how could he be wrong). Those kinds of generalities are just so much
mathematical snake oil no matter the good intentions. Perhaps the fact
that there is still an awful large amount of snake oil sold in this
country is in fact a comment on the basic educational failures that
are reflected in math instruction.
What is needed is a firm foundation in hard concrete reality, a
reality that exists outside ourselves, outside our brains, and exists
if we perceive it or not. That firm foundation is among scientists
called a theory of knowledge. Unfortunately all too many theories are
offered that are not based on reality or at base on impressionisticaly
grasped bits and pieces of reality put together in much the same way
as Zim's poem.
I would suggest a good starting point being readings in the history
of science and as well, and more specifically, readings in the history
of math. Since these historys, the good ones at least, reflect the
actual historical, read historical in this context as material or
concrete, development of science and math it must reveal the actual
connections between ideas and the material world which we try to
describe through the discipline of math or other sciences.
Then it would be a lot harder to be impressed or trapped by the
rhetoric of the rank impressionism Mr. Liebniz so rightly protests.
Unfortunately for some here it is already too late, the desire being
to deal only with math without the interconnections math concepts have
to the science of our world as a whole and in its parts.
Jack Jersawitz
On 12 Aug 99, Newton Leibniz wrote re. Good intentions, but `Zim
mathematics' is not mathematics.:
> I know you have good intentions, but the `mathematics you describe
is
> either a) not mathematics, or b) has been and is still being studied
> intensively. For instance, the proposal that we study `space is
not
> novel. One could characterize the whole field of mathematics as
the
> study of space (in a very general sense). If you mean that we
should
> have our elementary students study geometry, then you would be
> correct. American elementary students are at the very bottom when
> compared with other countries on subjects like geometry and
> measurement (see Stevenson and Stigler, TIMSS report).
>
> You seem to be promoting a theory of information. There is work in
> that area you should know about. A good first reference is "The
> Mathematical Theory of Communication" by Claude E. Shannon and
Warren
> Weaver (Shannon is considered the `father of this field). Some of
> your other ideas seem to be referring to another concept called
> `situation theory. This is not mathematical theory, it is more of
a
> logical system for modeling information (it is unable to predict -
an
> essential part of any mathematical theory). A good reference here
> would probably be "The Situation in Logic" by Jon Barwise. Another
> author you can reference is Keith Devlin (he writes popular books on
> mathematics and logic). Both of these topics are interesting in
their
> own right, and I encourage you to read up on them, however, neither
of
> them are appropriate at the K-12 level as part of a mathematics
> curriculum. The reason is that the first one is an application of
> mathematics (it should be a computer science course) and the second
> one is still being worked out by professors of logic.
>
> You also seem to have trouble expressing your ideas. Poems are
nice,
> but they leave much up to interpretation which is not an effective
way
> to communicate your `mathematics. You talk about everything,
> anything, and nothing without really defining how you wish to use
> them. You also use +,-,x,/ symbols without defining them. For
> instance, A x B means something completely different than
> multiplication of numbers when A and B are matrices. Until you
> provide more concrete details, most of your statements are complete
> gibberish.
>
> I know this is some pretty harsh criticism, but my reasons for
> delivering it to this forum is not to humble you. It is to say
that
> much of the material I read on theories of education contain prose
> similar to yours (especially constructivism). Well intentioned
> educational theorist using ill-defined concepts, poor logic, and
> anecdotal evidence are somehow fooling many teachers into believing
> theories that, if you sat and thought about the it for more than 2
> seconds, doesnÂt make any sense whatsoever. If you are an
educational
> theorist who is reading this, go and look at ZimÂs page to get an
idea
> of what other scientist, mathematicians, etc. think your theories
> sound like. If you are a teacher, go visit his web page so that you
> can learn how not to be fooled by bad theories.
>
> My harshest criticism is to the educational theorist, Zim, not to
you.
> You have been blessed with curiosity and a willingness to think
about
> deep things. Even Einstein would have been proud of you. I suggest
> that you go back to school and take some graduate level classes in
> logic and mathematics (for people who don't know, he has a minor in
> mathematics which is a good start). You will find them very
> interesting and they help you to organize your thoughts and ideas in
a
> way that is accessible to other people. Who knows, with some more
> practice and training, you may be the person who will be able to
write
> down a full theory of information. Good Luck!
>
>
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