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Topic: parent's messages
Replies: 65   Last Post: Aug 29, 1998 10:45 AM

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Judith E. Jacobs

Posts: 168
Registered: 12/6/04
Re: parent's messages
Posted: Jan 27, 1997 12:55 PM
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Andre:

It has been so long since you referred to my stance on coin and digit
problems that I thought you had forgotten me. I am deligted that you still
remember what I said.

I do wish, though, that when you extrapolate from my statements, you
carefully indicate that it is your extrapoation or your conclusion based on
your reading of what I said. In your latest restatement you said:

>Remember how Prof. Jacobs argued against coin and digit problems:
>"This has nothing to do with solving a problem. This is understanding
>numeration. Why make-up a situation that is never faced in life to
>demonstrate to students that mathematics is useful. If solving problems
>is a reason to know mathematics and you present me with problems in which
>1) you know the answer if you know the data or 2) relate to mathematics
>as an abstract science, and neither of these concern me, then why would
>I want to learn mathematics."


That's fine up to here. You then go on to say:
>
>Pay attention that Prof. Jacobs is against relating to
>mathematics as an abstract science! This does not concerns her!


This is not what I said; it is not what I believe. I do not have the same
view of mathematics that most k-12 students have.

I do want students to relate to mathematics as an abstract system. I want
them to appreciate the fact that when it is impossible to do an operation
on two number, for there is no number in a set that represents the answer
or (forgive me Andre for this example) there is no number that describes
the solution to a real world problem, like owing money or how three people
can share two cookies), we simply invent new numbers. And, when we combine
the new numbers with the old numbers (until we get to the complex numbers),
we do not lose one single property that held for the original set and gain
some new ones in the superset. I also want them to realize that these
structures in mathematics do not apply just to numbers. Looking at what
happens in geometry, we find that we get a commutative group with rotations
(turns) but when we include reflections (flips) we lose commutativity.

I want students to explain why the divisisbilty rules that they intuitvely
figure out for 2, 5 and 10 work. Then I want them to examine the way we
write numbers and how our numeration/place value system works so that they
can figure out what other divisibilty rules can be developed. I am not
interested in the ones for 7 and 11, but the one for 12 is powerful. This
requires them to look at mathematics as an abstract sytem.

Andre, I am an algebraist and have done some work in number theory. Once I
get started on these topics I could go on forever. I do recognize that
those in applied mathematics or analysis see this stuff as mind games and
of little real value. Similarly, many students do not find the above
intrinsically interesting. When I am able to relate these excursions to
something that interests them or might make doing mathematics easier, I
stand a better chance of keeping them engaged in looking at mathematics as
an abstract system. No Andre, coin and digit problems just do not do it for
me. And, you can quote me on that.

Judith

======================= CEEMaST ==================
Judith E. Jacobs, Director
Center for Education and Equity in Mathematics, Science, and Technology
California State Polytechnic University, Pomona
3801 West Temple Ave.
Pomona, CA 91768
phone: 909-869-3473 fax: 909-869-4616 email: jejacobs@csupomona.edu





Date Subject Author
1/24/97
Read parent's messages
Andre TOOM
1/25/97
Read Re: parent's messages
Lou Talman
1/25/97
Read Re: parent's messages
Andre TOOM
1/25/97
Read Re: parent's messages
Tad Watanabe
1/25/97
Read Re: parent's messages
Andre TOOM
1/25/97
Read Presidential commission
ramserj@ten-nash.ten.k12.tn.us
1/25/97
Read Re: Presidential commission
Andre TOOM
1/25/97
Read Re: Presidential commission
Michael Paul Goldenberg
1/25/97
Read Re: Presidential commission
Andre TOOM
1/26/97
Read Re: Presidential commission
Michael Paul Goldenberg
1/26/97
Read Re: Presidential commission
Gary A. Wirsing
1/26/97
Read Re: Presidential commission
Gary A. Wirsing
1/26/97
Read Re: Presidential commission
Lutemann@aol.com
1/26/97
Read Re: Presidential commission
Francis M. Fennell
1/26/97
Read Re: Presidential commission
CHAPMAN@APSICC.APS.EDU
1/26/97
Read Re: parent's messages
Tad Watanabe
1/26/97
Read Re: parent's messages
Andre TOOM
1/26/97
Read Re: parent's messages
Michael Paul Goldenberg
1/26/97
Read Re: parent's messages
Tad Watanabe
1/26/97
Read Re: parent's messages
Andre TOOM
1/27/97
Read Re: parent's messages
Tad Watanabe
1/27/97
Read Re: parent's messages
Andre TOOM
1/27/97
Read Re: parent's messages
Tad Watanabe
1/27/97
Read Re: parent's messages
Andre TOOM
1/28/97
Read Re: parent's messages
Richard Fouchaux
1/28/97
Read Re: parent's messages
Andre TOOM
1/30/97
Read Re: parent's messages
Richard Fouchaux
1/30/97
Read Re: parent's messages
Andre TOOM
1/30/97
Read Re: parent's messages
Tad Watanabe
1/30/97
Read Re: parent's messages
Andre TOOM
1/28/97
Read Re: parent's messages
Tad Watanabe
1/28/97
Read Re: parent's messages
Jack Roach
1/28/97
Read Re: parent's messages
Tad Watanabe
1/28/97
Read Proofs and mathematical structure
Jack Roach
1/28/97
Read Re: Proofs and mathematical structure
Tad Watanabe
8/27/98
Read math proofs
lavalle watson
8/29/98
Read product=lcm x gcd
harry sedinger
1/29/97
Read Re: Proofs and mathematical structure
Tad Watanabe
1/29/97
Read Re: Proofs and mathematical structure
Jack Roach
1/29/97
Read Re: Proofs and mathematical structure
Ed Dickey
1/29/97
Read Re: Proofs and mathematical structure
Jack Roach
1/29/97
Read Re: Proofs and mathematical structure
Tad Watanabe
1/30/97
Read Re: Proofs and mathematical structure
Jack Roach
1/30/97
Read Re: Proofs and mathematical structure
W Gary Martin
1/29/97
Read Re: Proofs and mathematical structure
Tad Watanabe
1/28/97
Read Andre's interpretation of my words.
Judith E. Jacobs
1/28/97
Read Re: Andre's interpretation of my words.
Andre TOOM
1/28/97
Read Re: Andre's interpretation of my words.
Ed Wall
1/28/97
Read Re: Andre's interpretation of my words.
W Gary Martin
2/1/97
Read Re: parent's messages
scott powell
2/1/97
Read Re: parent's messages
Andre TOOM
2/1/97
Read Re: parent's messages
scott powell
2/1/97
Read Re: parent's messages
Andre TOOM
2/2/97
Read Re: parent's messages
Howard L. Hansen
2/2/97
Read Re: parent's messages
Andre TOOM
2/1/97
Read Re: parent's messages
scott powell
1/27/97
Read Re: parent's messages
Judith E. Jacobs
1/27/97
Read Re: parent's messages
Andre TOOM
1/27/97
Read Re: parent's messages
Judith E. Jacobs
1/27/97
Read Re: parent's messages
Michael Paul Goldenberg
1/26/97
Read Re: parent's messages
Ralph A. Raimi
1/27/97
Read Re: parent's messages
Tad Watanabe
1/25/97
Read Re: parent's messages
Michael Paul Goldenberg
1/26/97
Read Re: parent's messages
rgdbcd@summit.net
1/26/97
Read Re: parent's messages
rgdbcd@summit.net
1/28/97
Read Re: parent's messages
Mary K. Hannigan

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