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

Abstract

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 col-

Individual differences in the obligatory activation of addition facts

“…Although models of arithmetic solution in children allow for nonretrieval processing (i.e., Siegler & Shrager, 1984), models of arithmetic processing in adults have not been elaborated in this direction (e.g., Ashcraft, 1982). The present results, in combination with recent findings that many adults use counting or other reconstructive strategies on a substantial number of problems (Bisanz, 1992;Geary, Frensch, & Wiley, 1993;Geary & Wiley, 1991;LeFevre, Sadesky, & Bisanz, 1994;Svenson, 1985;Widaman et al, 1992), suggest that models of adults' arithmetic processing may require elaboration and revision. Reconstructive strategies could be fast and automatic (Baroody, 1983(Baroody, , 1985, but they would not produce obligatory activation of the sort measured by the number-matching task.…”

“…Most theorists assume that adults have achieved asymptotic performance on the retrieval of basic facts (Ashcraft, 1987;Siegler, 1988). The large individual differences that exist in arithmetic performance even among adults suggest, however, that not all adults have automatic retrieval processes (Widaman et al, 1992). For example, Geary and Copyright 1994 Psychonomic Society, Inc. Widaman (1987) found that performance on a multidigit arithmetic test was related to speed of memory retrieval and speed of performing the carry procedure on a chronometric arithmetic task.…”

“…First, adults and older children retrieve facts faster and more accurately than younger children do (see, e.g., Ashcraft & Fierman, 1982;Groen & Parkman, 1972;Hamann & Ashcraft, 1985;Miller & Paredes, 1990;Stazyk, Ashcraft, & Hamann, 1982;Widaman, Little, Geary, & Cormier, 1992). Second, adults show evidence for obligatory (unintentional) activation of arithmetic knowledge (LeFevre, Bisanz, & Mrkonjic, 1988;LeFevre, Kulak, & Bisanz, 1991;Stazyk et al, 1982;Winkelman & Schmidt, 1974;Zbrodoff & Logan, 1986).…”

Group differences in adult simple arithmetic: Good retrievers, not-so-good retrievers, and perfectionists

“…An alternative prediction would be equivalent rates of fact-retrieval processes in the three adult subgroups. Memory retrieval in simple arithmetic appears to be at, or very close to, asymptote by high school in students schooled in North America (Geary & Wiley, 1991;Kail, 1988;Widaman, Little, Geary, & Cormier, 1992). Indeed, even extended practice does not appear to increase the speed with which memory-search and -access processes in simple arithmetic occur in adults .…”

Standardized Assessment of Strategy Use and Working Memory in Early Mental Arithmetic Performance

“…For instance, if problems are solved by means of counting, then RT should be linearly related to the magnitude of the counted addend and the corresponding raw regression coefficient should be consistent with independent estimates of speed of implicit counting Groen & Parkman, 1972;Svenson, 1985;Widaman, Little, Geary, & Cormier, 1992). For retrieval, the best predictor of RTs should be a variable that models the underlying structure of the long-term memory organization of addition facts (Ashcraft & Battaglia, 1978).…”