> > >Maybe it depends on how the counting is done. Does the child actually >count something (blocks, beans, etc.) while doing the oral counting? Being >able to orally count by 2s to twenty could be rote, but might be considered >less rote if the child has to move two items for each verbalization. I >believe that rote counting could be considered a benchmark for this grade >level IF done in the context of a meaningful situation. This also adheres >to the Communication Standard which talks about "opportunities to >communicate so that the students can model situations using oral, written, >concrete, pictoral, graphical, and algebraic methods," and "appreciating >the value of mathematical notation and its role in the development of >mathematical ideas," (p. 78). I would say there was a role of numerical >language development in rote counting as well. > >Dawn Hoyt Kidd
There's a really serious issue here, and that's the question of whether moving away from concrete representations necessarily represents a loss of understanding.
The interplay between physical and quasi-physical representations and mathematical understandings is very complex.
==================================== Judy Roitman, Mathematics Department Univ. of Kansas, Lawrence, KS 66049 firstname.lastname@example.org =====================================