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# The Frequency of Arithmetic Facts in Elementary Texts: Addition and Multiplication in Grades 1-6

Mark H. Ashcraft and Kelly S. Christy
Journal for Research in Mathematics Education
Vol. 26, No. 5 (Nov., 1995), pp. 396-421
DOI: 10.2307/749430
Stable URL: http://www.jstor.org/stable/749430
Page Count: 26
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## Abstract

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. The small-fact bias in the presentation of basic arithmetic, at least to the degree observed here, probably works against a basic pedagogical goal, mastery of simple arithmetic. It may also provide a partial explanation of the widely reported problem size or problem difficulty effect, that children's and adults' responses to larger basic facts are both slower and more error prone than their solutions to smaller facts. Theoretical and practical implications of the small-fact bias are discussed briefly.

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