Individual differences in the development of skill in mental addition: Internal and external validation of chronometric models

Keith F. Widaman, Todd D. Little, David C. Geary, Pierre Cormier

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29 Scopus citations


Two studies were undertaken to investigate the development of skill in mental addition. In Study 1, a sample of 123 second-, fourth-, and sixthgraders were administered 140 simple addition problems in a true-false reaction time (RT) format; scores on eight subtests of the Stanford Achievement Test were also available on these subjects. In Study 2, the sample consisted of 63 second-, fourth-, and sixth-graders and 100 college students. The RT tasks used in Study 2 comprised 80 simple addition problems and 80 complex addition problems, and a set of six paper-and-pencil tests for Numerical Facility and Perceptual Speed was also administered to the subjects. The results of the two studies support several conclusions. First, there are substantial individual differences in the age at which the transition from counting to retrieval strategies occurs. A large proportion of students in second grade already rely primarily on retrieval to respond to addition problems, yet a sizeable minority of sixth graders and even college students still apparently rely heavily on counting processes to solve addition problems. Second, there are different rates of automatization for the several processes that underlie skill in mental addition, processes of encoding of digits, recomputing or retrieving the correct sum, and carrying to the next column. Third, individual differences in efficiency in mental addition, indexed by retrieval speed for retrieval subjects and incrementing speed for digital subjects, exhibited strong relationships with achievement and ability measures. The results of these two studies demonstrated (a) the internal and external validity of the component processes in the proposed model of mental addition performance and (b) the need to use individual-level data to characterize properly the development of the cognitive skills underlying mental addition.

Original languageEnglish
Pages (from-to)167-213
Number of pages47
JournalLearning and Individual Differences
Issue number3
StatePublished - 1992


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