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Dr. Barbara Sarnecka, Assistant Professor of Cognitive Sciences at the University of California, Irvine, studies the relationship between young children's number word knowledge and how it predicts their performance on a numerical task without number words, i.e. What is the early meaning of counting "one", "two," and "three"? She has discovered that many children answer the question "how many" with the last word used in counting, despite not understanding how counting works. Only children who have mastered the cardinal principle, or are just short of doing so, understand that adding objects to a set means moving forward in the numeral list whereas subtracting objects mean going backward.

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