A cognitive analysis of number-series problems: Sources of individual differences in performance

Two experiments were conducted to identify the roles of three hypothesized procedures in the solution of simple number-series problems and to determine whether individual differences in these solution procedures are related to performance on a number-series subtest from a standardized test of intelligence. The three procedures are recognition of memorized series, calculation, and checking. Subjects verified whether number sequences formed rule-based series. True series included both memorized counting series (e.g., “5 10 1520”) and unfamiliar noncounting series (e.g., “14 710”). False series could not be described by simple rules. The results of Experiment 1 indicated that (1) counting series were verified more quickly than were noncounting series, and (2) partial counting information in false series facilitated rejection. In Experiment 2, reliable differences in recognition of memorized sequences and calculational efficiency were found between individuals who scored well on a standardized test of number-series completion and those who scored poorly. The results provide a basis for understanding how individual differences in knowledge influence performance on problems often used to assess inductive reasoning skill.