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Topic: Set notation
Replies: 4   Last Post: Oct 29, 2007 12:01 PM

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Bob Burn

Posts: 48
Registered: 12/3/04
Re: Set notation
Posted: Oct 19, 2007 4:39 PM
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Ed Dubinsky cannot get his messages read by MATHEDU, so here is the response he wanted to make.

Bob Burn
Research Fellow, Exeter University
Sunnyside
Barrack Road
Exeter EX2 6AB
01392-430028



-----Original Message-----
From: Ed Dubinsky [mailto:edd@math.kent.edu]
Sent: Wed 17/10/2007 13:06
To: Burn, Robert
Cc: MATHEDU@jiscmail.ac.uk
Subject: Re: Set notation

See below for responses.

On Wed, 17 Oct 2007, Burn, Robert wrote:

> Just two thoughts.
> 1. To regard the empty set as a thing, is quite a step. I dont think it
> rates as a thing from the perspective of Euclid's Elements.


I agree completely.

> 2. Some autobiography might be illuminating: at what point did readers
> of this list recognise the distinction between the empty set and {the
> empty set}? I think for me it was at the construction of the natural

numbers.

I don't know about myself, but I can tell you what works really well
(that means, a high percentage of students get it): Having students write
computer programs that construct sets (including the empty set) and
perform actions on them such as checking their cardinality, forming
unions, intersections, etc.

Ed


> Bob Burn
> Research Fellow, Exeter University
> Sunnyside
> Barrack Road
> Exeter EX2 6AB
> 01392-430028
>
>
>
> -----Original Message-----
> From: Post-calculus mathematics education on behalf of Smith, Alexander J.
> Sent: Sun 07/10/2007 23:50
> To: MATHEDU@JISCMAIL.AC.UK
> Subject: Re: Set notation
>
> Let us not forget the following word of Feynman.
>
> (My humble experience is that it is a happy event when an undergraduate mathematics major can intuitively distinguish between the empty set and the set which contains only the empty set.)
>
> Feynman's words:
>
> The power of instruction is seldom of much efficacy except in
> those happy dispositions where it is almost superfluous.
>
> There isn't any solution to this problem of education other than
> to realize that the best teaching can be done only when there
> is a direct individual relationship between a student and a good
> teacher--a situation in which the student discusses the ideas,
> thinks about the things, and talks about the things. It's impossible to learn very much by simply sitting in a lecture, or even by simply doing problems that are assigned.
>
>
> ___________________________________
> From: Post-calculus mathematics education [MATHEDU@JISCMAIL.AC.UK] On Behalf Of Ralph A. Raimi [rarm@MATH.ROCHESTER.EDU]
> Sent: Sunday, October 07, 2007 5:17 PM
> To: MATHEDU@JISCMAIL.AC.UK
> Subject: Re: Set notation
>
> On Sun, 7 Oct 2007, Murray Eisenberg wrote:
>

>> I just experienced this phenomenon (again!) in the first exam in our proofs
>> course, where the question was to list the elements of the power set of
>> {1,2,3}.
>>
>> Several students gave the answer as
>>
>> {Ø}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}
>>
>> or as ... but to wonder what theory can overcome general linguistic
>> insensitivity. The relevant research might involve much earlier stages of
>> mental and linguistic development.

>
> An anecdote from the days of "the new math" in America, when
> elementary school teachers were instructed to tell the kiddies about sets,
> unions and such:
>
> The teacher, having seemingly absorbed the idea of distinguishing
> between a set and its members, and bent on transferring the lesson to her
> class, asks "the set of all boys to stand up", and then, "the set of all
> girls to stand up".
>
> (Excuse me: I meant "bent on transferring the lesson to the
> members of her class". The class cannot absorb a lesson any more than
> the set of all boys can stand up.)
>
> Which is to say that we (even mathematicians) are accustomed
> to conflating the set with its members in daily speech, and have really no
> reason to be pedantic about it until careful reasoning in mathematics
> requires it of us. I see little reason to try to teach such things before
> university mathematics begins to consider theorems regarding which, and
> regarding whose proofs, this distinction has some application. As we all
> have seen, the lesson simply won't go over, except for some few who don't
> need it anyhow, not even if they aspire to careers in science or
> mathematics, for they will learn it easily enough when the time comes.
>
> Ralph A. Raimi Tel. 585 275 4429 or (home) 585 244 9368
> Dept. of Mathematics, Univ.of Rochester, Rochester, NY 14627
> <http://www.math.rochester.edu/people/faculty/rarm/>
>
> "Algebra is conducive to symbolic reasoning." ....PSSM, p.345
>
>


--
**********************************
* !!!!!!!!!!!!!!!!!!!!!!!!!! *
* PLEASE NOTE NEW EMAIL ADDRESS *
* !!!!!!!!!!!!!!!!!!!!!!!!!! *
**********************************

I am going to move to a new internet access system, but the change will be a
long process. For the foreseeable future, I will use two systems
simultaneously and at some later date, I will drop one of them.

So, until further notice, please send all messages for me to both of the
following addresses:

edd@math.kent.edu
eddub@mindspring.com

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Internet:

Ed Dubinsky
edd@math.kent.edu
eddub@mindspring.com
http://www.math.kent.edu/~edd/

Home Address year-round (but see exceptions below).

265 North Woods Rd.
Hermon, NY 13652
Tel: (315) 386-2787
FAX: To send me a fax, contact me first by phone and email so I can switch
my phone to fax.


Occasionally to found at:

211 Carlton Dr.
N. Syracuse, NY 13212
Tel: (315) 451-0327



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Date Subject Author
10/19/07
Read Re: Set notation
Bob Burn
10/29/07
Read Re: Set notation
Bob Burn
10/29/07
Read Re: Set notation
Murray Eisenberg

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