TY - JOUR
T1 - The development of skill in mental arithmetic
T2 - An individual differences perspective
AU - Widaman, Keith F.
AU - Little, Todd D.
N1 - Funding Information:
The present work was supported in part by grants HD-21056 and HD-22953 from the National Institute of Child Health and Human Development and by intramural grants from the Academic Senate of the University of California, Riverside to the first author, by grants GOO8530208 and H023C80072 from the U. S. Office of Education (Donald MacMillan, Principal Investigator), and by computing grants from Computing and Communications, University of California, Riverside to both authors. The insightful comments by Jamie Campbell to a previous version of this paper are gratefully acknowledged. Many thanks as well are extended to Chris Strand for her invaluable help in preparing the final draft of this chapter. Parts of this chapter were written while the first author was on sabbatical leave at the Department of Psychology, University of Trier, Trier, Germany; the support, in various ways, provided there by Professor Leo Montada, Maria Haas, and Manfred Schmitt is also gratefully acknowledged. Requests for reprints should be sent to Keith Widaman, Department of Psychology, University of California, Riverside, CA 92521, or to Todd Little, Max Planck Institute for Human Development and Education, Lentzeallee 94, loo0 Berlin 33, Germany.
PY - 1992/1
Y1 - 1992/1
N2 - In this chapter, we attempt first to describe the different emphases inherent in traditional experimental and individual differences approaches. Next, we discuss the types of cognitive models that have been proposed to account for mental arithmetic performance. In doing so, the nature of the basic theoretical propositions (e.g., underlying the retrieval of answers from a memory store) and the proper means of testing these propositions will be stressed. Then, we survey the findings of several studies, highlighting recently published findings on individual and developmental differences in the skills underlying proficiency in mental addition. One unique contribution of an individual differences approach is the external validation of proposed models specifying the elementary cognitive processes invoked during problem solution. External validation requires the fitting of statistical models to data from each individual, resulting in the estimation of parameters that reflect speed of executing each of various cognitive processes, or elementary cognitive components. Then, individual differences in these parameter estimates, or component scores, are related to individual differences on traditional measures of ability and achievement. Various implications of our findings for research on numerical facility and for applications in education are also discussed.
AB - In this chapter, we attempt first to describe the different emphases inherent in traditional experimental and individual differences approaches. Next, we discuss the types of cognitive models that have been proposed to account for mental arithmetic performance. In doing so, the nature of the basic theoretical propositions (e.g., underlying the retrieval of answers from a memory store) and the proper means of testing these propositions will be stressed. Then, we survey the findings of several studies, highlighting recently published findings on individual and developmental differences in the skills underlying proficiency in mental addition. One unique contribution of an individual differences approach is the external validation of proposed models specifying the elementary cognitive processes invoked during problem solution. External validation requires the fitting of statistical models to data from each individual, resulting in the estimation of parameters that reflect speed of executing each of various cognitive processes, or elementary cognitive components. Then, individual differences in these parameter estimates, or component scores, are related to individual differences on traditional measures of ability and achievement. Various implications of our findings for research on numerical facility and for applications in education are also discussed.
UR - http://www.scopus.com/inward/record.url?scp=77956757624&partnerID=8YFLogxK
U2 - 10.1016/S0166-4115(08)60888-2
DO - 10.1016/S0166-4115(08)60888-2
M3 - Article
AN - SCOPUS:77956757624
SN - 0166-4115
VL - 91
SP - 189
EP - 253
JO - Advances in Psychology
JF - Advances in Psychology
IS - C
ER -