title: Operator priming and generalization of practice in adults' simple arithmetic.
abstract: There is a renewed debate about whether educated adults solve simple addition problems (e.g., 2 + 3) by direct fact retrieval or by fast, automatic counting-based procedures. Recent research testing adults' simple addition and multiplication showed that a 150-ms preview of the operator (+ or ×) facilitated addition, but not multiplication, suggesting that a general addition procedure was primed by the + sign. In Experiment 1 (n = 36), we applied this operator-priming paradigm to rule-based problems (0 + N = N, 1 × N = N, 0 × N = 0) and 1 + N problems with N ranging from 0 to 9. For the rule-based problems, we found both operator-preview facilitation and generalization of practice (e.g., practicing 0 + 3 sped up unpracticed 0 + 8), the latter being a signature of procedure use; however, we also found operator-preview facilitation for 1 + N in the absence of generalization, which implies the 1 + N problems were solved by fact retrieval but nonetheless were facilitated by an operator preview. Thus, the operator preview effect does not discriminate procedure use from fact retrieval. Experiment 2 (n = 36) investigated whether a population with advanced mathematical training-engineering and computer science students-would show generalization of practice for nonrule-based simple addition problems (e.g., 1 + 4, 4 + 7). The 0 + N problems again presented generalization, whereas no nonzero problem type did; but all nonzero problems sped up when the identical problems were retested, as predicted by item-specific fact retrieval. The results pose a strong challenge to the generality of the proposal that skilled adults' simple addition is based on fast procedural algorithms, and instead support a fact-retrieval model of fast addition performance.
authors.affiliation: Department of Psychology, University of Saskatchewan.
authors.forename: Yalin
authors.initials: Y
authors.lastname: Chen
authors.affiliation: Department of Psychology, University of Saskatchewan.
authors.forename: Jamie I D
authors.initials: JI
authors.lastname: Campbell
mesh_terms: D000328:Adult; D005260:Female; D005793:Generalization, Psychological; D006801:Humans; D007858:Learning; D008297:Male; D055641:Mathematical Concepts; D008960:Models, Psychological; D011340:Problem Solving; D011581:Psychological Tests; D011930:Reaction Time; D060865:Repetition Priming; D055815:Young Adult