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Mark H. Ashcraft

Baroody (1985) suggests repeatedly that rules and procedures can provide the answers to the basic number combinations in simple arithmetic. My research with older children and adults indicates they do not, at least in the general case. After correcting Baroody's description of my network retrieval model, I indicate five weaknesses in his argument. The debate over fact retrieval versus rule- and procedure-generated answers is an empirical one. I invite Baroody to report data that buttress his position.

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Mark H. Ashcraft and Kelly S. Christy

We tabulated the frequency with which simple addition and multiplication facts occur in elementary school arithmetic texts for grades 1–6. The results indicated a strong “small-fact bias” in both addition and multiplication. “Large” facts, with operands larger than 5, occurred up to half as frequently as those with operands in the 2–5 range. As was also found in an earlier tabulation for grades K–3, facts with operands of 0 and 1 occurred relatively infrequently; the ostensible exceptions to this pattern, high frequencies for combinations like 1+2 and 1×3, were caused by the small-fact bias in multicolumn problems.