title: No generalization of practice for nonzero simple addition.
abstract: Several types of converging evidence have suggested recently that skilled adults solve very simple addition problems (e.g., 2 + 1, 4 + 2) using a fast, unconscious counting algorithm. These results stand in opposition to the long-held assumption in the cognitive arithmetic literature that such simple addition problems normally are solved by fact retrieval from declarative memory. Here we tested a large sample of diversely skilled and culturally diverse men and women at the University of Saskatchewan and examined multiple categories of simple (1 digit plus 1 digit) addition problems for evidence of generalization of practice, a signature of procedure use. The procedure-based 0 + N = N problems presented clear evidence of generalization (i.e., practicing a subset of 0 + N problems lead to speed-up for a different subset of 0 + N problems), but there was no evidence of such generalization of practice for the nonzero problems, although the experiment had good power to detect small effects. Given that generalization of practice is a basic marker of procedure-based processing, its absence for the nonzero addition problems casts doubt on the compacted counting theory.
authors.affiliation: Department of Psychology, University of Saskatchewan.
authors.forename: Jamie I D
authors.initials: JI
authors.lastname: Campbell
authors.affiliation: Department of Psychology, University of Saskatchewan.
authors.forename: Leah C
authors.initials: LC
authors.lastname: Beech
mesh_terms: D000328:Adult; D005260:Female; D006801:Humans; D008297:Male; D055641:Mathematical Concepts; D008568:Memory; D011340:Problem Solving; D011930:Reaction Time; D014163:Transfer, Psychology; D055815:Young Adult