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Topic: Intro to Number; counting and all that
Replies: 67   Last Post: Nov 28, 1995 6:07 PM

 Messages: [ Previous | Next ]
 Bartel, Anne Posts: 7 Registered: 12/6/04
Intro to Number; counting and all that
Posted: Nov 6, 1995 12:18 PM

My friend, Harold Fletcher, wrote some words to the hymn "Onward Christian
Soldiers" which went something like......

SORTING, PATTERN, MATCHING
THIS IS HOW WE START
THEN WE MOVE TO NUMBER
ETCH IT ON YOUR HEART ................................etc

Thank you for involving me in the "starting from counting" debate. I will try
and join the list in due course.

I have a number of concerns with what I see as "starting from counting" in
the schools I have visited, the materials I have read and the equipment I
have seen in USA catalogues. I think it is all about what we mean when we
talk of children understanding

1. How does counting "ONE-TWO-THREE-.....etc." (forget the 1-1 matching for a
minute) represent an "UNDERSTANDING OF NUMBER"? My question is how do the
children know that the number name "two" exists to use as part of the
counting process? Where is "two" taught? Who tells the children? There is a
difference in the children's eyes between 2 objects (alone) and the single
object they touch as they count a series of objects. What actually happens
when the advocates of counting work with young children? I can imagine a
collection of objects displayed on the table but what is said then?

2. How does all this counting (first) relate to that paragraph on page 33 of
your STANDARDS book which says (see below figure 4.1) "....young children
need to make the connection between seven toy cars, seven counters, seven
tally marks and the symbol 7" (I do wish the authors had included the word
"seven" as well!!!!) How does "counting first" fit in with our friend
Prof Tom Post, of the University of Minnesota, when he said in his book "A
Review of Manipulative Materials in the Teaching of Mathematics" ....." no one
has ever seen a number and no one ever will; Number is an abstraction
......... the squiggle 2 of itself is not "2" but the representation of "2".
(You must forgive me if I misquote or have the wrong book title but my
references are in my study 5000 miles away,) How does counting first fit in
with the STANDARDS (or for that matter the English National Curriculum) when
it says on page 38 "Children must understand number if they are to make sense
of the ways numbers are used in their everyday world."

3. It may surprise you to know that I don't object to people "starting from
counting." After all we are looking for solutions to difficult problems. What
I do find hard to accept is that the advocates of "starting from couting"
claim to be teaching for understanding, or rather be following the STANDARDS.
It is my view that this approach represents rote learning and as such is a
long way from understanding. (I know of two U.S. gurus, whose work you have
sent me to read, speak of rote counting!!!!)

I think that once numbers have been invented by the children and put in order
we can count to our hearts delight. I could outline my approach if people on the
list are interested. Meanwhile, I am counting the days to when children not
only understand number but mathematics itself.

John Marshall
1225 Clays Trail
Oldsmar, FL
USA 34677
Tel/FAX: (813) 786-8152

Trentham, Stoke on Trent,
Staffordshire ST4 8LP
England
Tel/FAX: 01782 641818

Date Subject Author
11/6/95 Bartel, Anne
11/6/95 Susan L. Addington
11/6/95 Tom Johnson
11/6/95 Bill Juraschek
11/7/95 Francis Fennell
11/7/95 Judith E. Jacobs
11/7/95 Lou Talman
11/8/95 W Gary Martin
11/8/95 Sheryl Cox
11/9/95 Bill Juraschek
11/13/95 Chi-Tien Hsu
11/9/95 roitman@oberon.math.ukans.edu
11/11/95 DORSDUNHAM@aol.com
11/12/95 Arthur Howard
11/12/95 roitman@oberon.math.ukans.edu
11/14/95 Arthur Howard
11/14/95 Andre TOOM
11/14/95 Arthur Howard
11/15/95 Andre TOOM
11/16/95 Arthur Howard
11/14/95 roitman@oberon.math.ukans.edu
11/15/95 Chi-Tien Hsu
11/14/95 roitman@oberon.math.ukans.edu
11/14/95 Arthur Howard
11/15/95 David K. Pugalee
11/16/95 Arthur Howard
11/14/95 Sheryl Cox
11/15/95 Tom Johnson
11/16/95 Eileen Abrahamson
11/16/95 Jack Roach
11/16/95 Joan Reinthaler
11/16/95 Chi-Tien Hsu
11/16/95 lummusms@PLU.edu
11/16/95 Lou Talman
11/16/95 Lutemann@aol.com
11/17/95 dief@fast.net
11/17/95 Susan L. Addington
11/19/95 David K. Pugalee
11/17/95 Sam Evers
11/17/95 Andre TOOM
11/17/95 Lou Talman
11/17/95 Andre TOOM
11/17/95 Chi-Tien Hsu
11/17/95 Andre TOOM
11/17/95 Lutemann@aol.com
11/17/95 Lutemann@aol.com
11/17/95 Lutemann@aol.com
11/17/95 Lou Talman
11/17/95 Andre TOOM
11/17/95 Lutemann@aol.com
11/17/95 Andre TOOM
11/17/95 Lou Talman
11/17/95 Andre TOOM
11/17/95 Lou Talman
11/17/95 Lou Talman
11/18/95 Andre TOOM
11/18/95 Lou Talman
11/18/95 Lutemann@aol.com
11/18/95 Lou Talman
11/28/95 Chi-Tien Hsu
11/16/95 Francis Fennell
11/19/95 David K. Pugalee
11/16/95 DORSDUNHAM@aol.com
11/19/95 roitman@oberon.math.ukans.edu