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While applauding the work on infant recognition of numbers and arithmetic, it seems prudent that allowance be made for clues in the environment. For example, Arabic numbers themselves contain numbers of end points that can be used to count that many items. I personally used that method in kindergarten when we were made to stop counting on our fingers. The numeral 4 has four points, and 2 has two ends. By the time you get to 7, 8, and 9, you’ve memorized them. Even when I won a gold medal in math in high school, I noticed I still used my old counting method for adding and subtracting small numbers.

Rick Merrill
Bolton, Mass.

The research shows that babies perceive quantity, not that they counted. My work shows that young children can learn to recognize quantity without counting. They easily learn quantities 1 to 4 as similar to showing fingers, while 5 is distinguished from 4 because 5 has a middle and 4 does not. They learn quantities 6 to 10 as 5 plus 1 to 5, similar to fingers or the Roman numeral VIII as 8.

Joan A. Cotter
Hutchinson, Minn.