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From: Tim Norfolk on 4 Oct 2009 20:30
On Aug 26, 12:37�pm, hru...(a)odds.stat.purdue.edu (Herman Rubin) wrote:
<snip>
>
> This was not the situation in Chicago, and I do not
> believe in Illinois.
<snip>

Herman;

I consider myself a skeptic, and even I believe in Illinois.
From: pubkeybreaker on 8 Oct 2009 11:59
On Sep 3, 4:07 pm, hru...(a)odds.stat.purdue.edu (Herman Rubin) wrote:
> In article <NdOdnRDiLZOjYQPXRVn_...(a)comporium.net>,
> Larry Hewitt  <larryh...(a)comporium.net> wrote:

>
> As I said before, what experts?  How many recognized researchers
> in mathematics, NOT "mathematics education", have been consulted?
>
> A head of a high school mathematics department said he used to
> ask his candidated for faculty positions to prove that 2+2=4.
> Not only could they not prove it, but they could not understand
> why such a question could be raised.  Anyone who understands
> the counting numbers can understand it, and should be able to
> come up with a proof;

Uh huh. And how many pages did Whitehead & Russell take to prove
1+1 = 2???

The underlying question is: what axioms am I allowed to use in such a
proof? Peano Arithmetic? or: May it be assumed that the integers are
well-ordered
or must this be proved? (equivalent to assuming axiom of induction).
etc.

OTOH, I would expect that a high school teacher would know the Peano
axioms.
From: Gerry Myerson on 8 Oct 2009 22:03
In article
<3fb1bc8f-73c3-41ff-b2d7-1b7d371f26f8(a)a6g2000vbp.googlegroups.com>,
pubkeybreaker <pubkeybreaker(a)aol.com> wrote:

> OTOH, I would expect that a high school teacher would know the Peano
> axioms.

I'd be very surprised if any of my high school (math) teachers knew
the Peano axioms (and I went to a good high school).

--
Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
From: Herman Rubin on 9 Oct 2009 15:34
In article <gerry-1BAEBD.13035509102009(a)feeder.eternal-september.org>,
Gerry Myerson <gerry(a)maths.mq.edi.ai.i2u4email> wrote:
>In article
><3fb1bc8f-73c3-41ff-b2d7-1b7d371f26f8(a)a6g2000vbp.googlegroups.com>,
> pubkeybreaker <pubkeybreaker(a)aol.com> wrote:

>> OTOH, I would expect that a high school teacher would know the Peano
>> axioms.

>I'd be very surprised if any of my high school (math) teachers knew
>the Peano axioms (and I went to a good high school).

You may be both partly right. SOME high school math
teachers do learn the Peano axioms, but probably most
do not.
--
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(a)stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
From: Tim Norfolk on 12 Oct 2009 21:47
On Oct 9, 3:34�pm, hru...(a)odds.stat.purdue.edu (Herman Rubin) wrote:
> In article <gerry-1BAEBD.13035509102...(a)feeder.eternal-september.org>,
> Gerry Myerson �<ge...(a)maths.mq.edi.ai.i2u4email> wrote:
>
> >In article
> ><3fb1bc8f-73c3-41ff-b2d7-1b7d371f2...(a)a6g2000vbp.googlegroups.com>,
> > pubkeybreaker <pubkeybrea...(a)aol.com> wrote:
> >> OTOH, �I would expect that a high school teacher would know the Peano
> >> axioms.
> >I'd be very surprised if any of my high school (math) teachers knew
> >the Peano axioms (and I went to a good high school).
>
> You may be both partly right. �SOME high school math
> teachers do learn the Peano axioms, but probably most
> do not.
> --
> 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
> hru...(a)stat.purdue.edu � � � � Phone: (765)494-6054 � FAX: (765)494-0558

The ones that we graduate here have seen them, and done some small
problems. Whether they remember and understand is something else. On a
related note, I have to disagree with your contention that the 'good',
but not excellent, student can learn analysis before the calculus. I
am teaching a complex analysis course right now, and the homework that
I am grading suggests that the students cannot easily 'see' that 2(3x)
= 6x, because their manipulative skills are so weak. How can they
follow a good proof?
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