Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Benchmarks
Posted:
Mar 27, 1995 12:10 PM


I would tend to agree with your colleague who feels oral counting shouldn't be included as a benchmark. I would strongly suggest the works by Steffe and his colleagues on children's counting. What seems to be important is not whether or not children can count, but _what_ they are counting when they count. Ability to produce number words in correct sequence is necessary, but it does not necessarily tell you much about the child's number sense.
I've seen many children who can "count by 10's" to produce the sequence, "10, 20, 30, ..." who still have to count by 1 to answer what is 10 more than 13, for example. So, what does the children's ability to "count by 10's" tell us in this case?
Another example. Some time I ask children, with longs (10) from the base 10 blocks, and ask how many unit there are. I will put something like 6 longs and ask how many? Many children can answer that easily. Then I add one more and ask how many again. Again, relatively easy question. But, when I add one more after 100 (most children can answer 100 easily, too), a good number of kids say "200" instead of 110.
Anyway, although the ability to produce numer words in a correct sequence is important, I'm not sure if it is a "benchmark" of the child's mathematical development.
Tad Watanabe Towson State University Towson, MD 21204
On Mon, 27 Mar 1995 CHAPMAN@APSICC.APS.EDU wrote:
> A group of teachers is working in Albuquerque to develop appropriate > benchmarks for assessing children's mathematical understandings. We are > looking specifically at grade 2. In writing a developmental continuum we > have reached a small but significant disagreement. One of our colleagues > feels uncomformtable with the inclusion of benchmarks on oral counting > under numbers and numeration. (Specifically: in the "developing" category > counts orally to 100 by ones and tens, to 50 by fives, to twenty by 2s. > In the "independent" category : counts to 100 by 2s, 5s, and 10s.) Our > collegue feels oral counting is too rote. > > > and therefore shouldn't be included as a benchmark. > > The Standards say: "Counting skills, which are essential for ordering and com > paring numbers, are an important component of the development of number > ideas. Counting on, counting back, and skip counting mark advances in > children's development of number ideas. However, counting is only one > indicator of children's understanding of numbers" > > The developmental continuum being written contains many, many more > indicators of understanding of numbers. > > I have also seen research findings that show that children build their > number sense from counting. Frankly, I can't think of any other way > to learn to count than by rote and there are clear developmental aspects > to how children learn to count. > > What do you think? Do the Standards say that anything that must be done > by rote should not be considered a benchmark? (Remember, as I said, these > rote counting benchmarks are only a small part of the benchmarks being > written, but some of our colleagues consider them very important.) > Clearly, oral counting is part of the "decreased attention" category > as that pretty much WAS the curriculum for primary children if you added > writing numeralsbut is oral counting passe???? > > If this seems too dull for the list, please respond to me personally at > Chapman@apsicc.aps.edu THANKS! Cindy >



