Re: General knowledge for teachers in mathematics

In article <1135213743.424936.3680@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
anw@xxxxxxxxxxxxxxxx wrote:

>Guess who wrote:
>> On Tue, 20 Dec 2005 16:24:08 GMT, Gunnar G <debian@xxxxxxxxx> wrote:
>> >Todays topic: What can be considered to be "general knowledge" of
>> >mathematics?
>> But what you express below is not a general knowledge of mathematics,
>> but an interest in the history of mathematicians. They are separate
>> studies. Gauss studies mathematics, not Gauss.
>
> Different, not separate. I don't think you can *understand* [tho'
>you may be able to handle-churn enough to use] calculus [eg] without
>going through some of the struggles that Newton, Leibniz, Euler, ...
>went through in order to turn evanescent quantities and fluxions into
>infinitesimals and differentials and then into limits.

Even if so, the fact is that too few non-elite students can even
handle-churn calculus (etc.) proficiently. And the trend seems to be
away from the actual mathematical content of calculus (especially the
proofs) in favour of more time spent on handle-churning, since after all
that's what is mostly assessed.

IMO, far too little understanding occurs across the education system,
and mathematics is a particular victim of this.

>Similarly for
>the number systems that we have, and for geometry, and for
>mechanics, .... The notations that we use are derived from that
>history, for example.

Well, the notations are part of the current content of mathematics,
independently of its history. It could be said about *anything* that it
"derives from its history", but that alone is surely insufficient
grounds for diverting resources into explicitly teaching that history.

>> Cerainly introduce the student to the developers of the works they
>> are studying, but don't make it of paramount importance on an
>> examination for example. [...]
>
> Why not? OK, perhaps not for the *whole* exam, but why not for a
>question or two? Why should some of this stuff not be formally part of
>the syllabus?

Do you have any suggestions on what to *remove* from the mathematics
syllabus in order to make room for a history unit?

(BTW, I personally do like to understand the historical and other
contexts of things; but I wouldn't inflict that personal preference on
my students.)

--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum viditur.
| BBB aa a r bbb |
-----------------------------
.

Relevant Pages

  • Re: Monte Carlo computer go methods
    ... As for "historical" character in mathematics ... Sophie Germain was one of the great mathematicians ... history of mathematics. ... a brief introduction to "Sylver Coinage" in his game theory ...
    (rec.games.go)
  • Re: Polysign numbers Was: Give wedge products the wedgie they deserve
    ... Some interesting history: ... "In mathematics, quaternions are a non-commutative ... to add to the list with "polysign" numbers, ... algebraic system, to the menu. ...
    (sci.math)
  • Re: General knowledge for teachers in mathematics
    ... >independently of its history. ... dot/dash/subscript notations for derivatives were it not for the ... students should have a basic timeline ... >Do you have any suggestions on what to *remove* from the mathematics ...
    (uk.education.maths)
  • Review of Turchin
    ... Peter Turchin, Princeton University Press, 2003. ... Greaves asked me if I had ever thought about how the study of history ... itself might become an experimental science. ... History and sociology both rely on verbal arguments, not mathematics, ...
    (uk.philosophy.humanism)
  • Re: Lessons From The Cantor Transfinite Thread
    ... the importance of History including the History of mathematics, ... physics, engineering, psychology, biology, and the USA and the world. ... What seems to have struck the mathematics ... I think that it has to do with the Composition operation (composition ...
    (sci.physics)