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