While testing was done on 5- or 6-year-old children, it would be interesting to see if this intuitive skill persists after these students are exposed to standard mathematical instruction in the higher grades. I suspect that the answer will be no, as students restricted to a method of learning math will be deprived of this original ability.

Nelson Marans
Silver Spring, Md.

The pictorial examples presented suggest a possible problem with the design of the study or the need for a reinterpretation of the results. In both examples, the correct answer corresponds to the picture of Sarah, who has two bags above her image. Two bags would correspond to “more” in most kids’ minds, regardless of the numerical labeling and mathematical operation depicted and whether or not the kids can understand numerical and mathematical representation. I am suspicious of the results of the study.

Keith Propp
Colorado Springs, Colo.

Having been an early childhood educator for a number of years, I have a concern after reviewing the examples you gave. My experience working with young children has been that they will say whichever example has the most objects is worth “more.” Example: When learning about money, the students would often say that a child with three pennies has “more” money than a child with one nickel.

Dale Fishel
Indianapolis, Ind.