You can decide which I belong to. As my favorite, math is to make difficult thing easier, math is starting from counting, and because we want to make thing easier to deal with, we invent "addition" then "substraction" then "multiplication" ...... It is building block. When student can count well, showing them why the addition can make their life easier will to easy.
I have a mentor/friend, John Marshall, who has worked closely with Sir Wilfred Cockcroft in England on the Maths for Schools elementary curriculum. His strongly worded message to me over the years is that this is the very issue on which we in the states "mess up" our early instruction. He would argue that counting is NOT the first step. He believes (and the English curriculum supports) that children need to develop an understanding of "2" and "4" by setting up sets in 1-1 correspondence, then using that work to inform the placement of number posters on the wall. The work for "4" goes to the right of "2" because the sets involve numbers beyond 2. When the young students return to develop the concept of "3", the major question becomes how that work with "3" compares to the work with "2" and "4". Number work develops from these early discussions about relationships and 1-1 correspondence. John's observations of our early curriculum work in this country reinforce his opinions that we assume counting will lay the foundations for these early understandings and comparisons of number...assumptions we are mistaken in making.
Anne Bartel Project Manager, SciMathMN 647 Capitol Square Building 550 Cedar Street St. Paul, MN 55101 W: 612-282-3707 FAX: 612-296-3348 firstname.lastname@example.org