The National Science Education Standards, Benchmarks for Science Literacy, and National Council of Teachers of Mathematics Standards are heavily laden with the philosophy of Jean Piaget, the late psychologist who developed the idea that young children go through a series of developmental stages that limit their ability to reason and develop number sense.
Educational famine sharpens the mind, apparently.
Young children often answered correctly that the two rows were the same, but if Piaget then changed the spacing of the objects in one of the rows to make it longer and repeated the question, the children answered incorrectly and said the longer row had more. Piaget could even add extra objects to one of the rows and the children would still be fooled by tighter spacing. This was taken as evidence that young children may have no number sense, even if they can count. A corollary is that children may have no sense of what addition and subtraction really are, even if they can add and subtract faster than Hewlett and Packard combined. In reviewing a series of research findings, Dehaene speculates that children are startled when an interviewer breaks the customs of polite conversation and repeats the exact same question about the two rows.