Cognitive arithmetic: Evidence for obligatory activation of arithmetic facts

In two experiments, obligatory activation of arithmetic facts resulted in interference on a simple number-matching task. Subjects were required to verify the presence of a probe number (e.g., 5) in a previously presented pair (e.g., 5+1). Items for which the probe was the sum of the initial pair (e.g., 5+1 and 6) were rejected more slowly than items for which the probe was not the sum (e.g., 5+1 and 3), and this effect was largest at stimulus onset asynchronies of less than 180 msec between the number pair and the probe. The results are consistent with the notion that arithmetic knowledge is represented in an associative network and accessed by means of spreading activation.

[1]  J. LeFevre,et al.  A cognitive analysis of number-series problems: Sources of individual differences in performance , 1986, Memory & cognition.

[2]  K. Denise Muth,et al.  Solving Arithmetic Word Problems: Role of Reading and Computational Skills , 1984 .

[3]  Janet A. Schmidt,et al.  Associative confusions in mental arithmetic , 1974 .

[4]  ROBERT S. MOYER,et al.  Time required for Judgements of Numerical Inequality , 1967, Nature.

[5]  D. Kahneman,et al.  Tests of the automaticity of reading: dilution of Stroop effects by color-irrelevant stimuli. , 1983, Journal of experimental psychology. Human perception and performance.

[6]  G. Logan.  Skill and automaticity: Relations, implications, and future directions. , 1985 .

[7]  Thomas K. Landauer,et al.  Determinants of reaction time for digit inequality judgments , 1973 .

[8]  M. Ashcraft,et al.  Menatal addition: A test of three verification models , 1981, Memory & cognition.

[9]  A. Newell.  You can't play 20 questions with nature and win : projective comments on the papers of this symposium , 1973 .

[10]  Jamie I. D. Campbell.  Network interference and mental multiplication. , 1987 .

[11]  G D Logan,et al.  Constraints on strategy construction in a speeded discrimination task. , 1982, Journal of experimental psychology. Human perception and performance.

[12]  Mark H. Ashcraft,et al.  A network approach to mental multiplication. , 1982 .

[13]  Mark H. Ashcraft,et al.  Simulating Network Retrieval of Arithmetic Facts. , 1983 .

[14]  F N Dyer,et al.  The Stroop phenomenon and its use in the stlldy of perceptual, cognitive, and response processes , 1973, Memory & cognition.

[15]  Mark H. Ashcraft,et al.  Children’s Knowledge of Simple Arithmetic: A Developmental Model and Simulation , 1987 .

[16]  Mark H. Ashcraft,et al.  Evidence for retrieval and decision processes in mental addition , 1978 .

[17]  I. Fischler.  Semantic facilitation without association in a lexical decision task , 1977, Memory & cognition.

[18]  N. Segalowitz,et al.  Automatic and controlled processes in the first- and second-language reading of fluent bilinguals , 1983, Memory & cognition.

[19]  Jamie I. D. Campbell,et al.  Mental multiplication skill: Structure, process, and acquisition. , 1985 .

[20]  G. Logan.  Attention and automaticity in Stroop and priming tasks: Theory and data , 1980, Cognitive Psychology.

[21]  G D Logan,et al.  On the autonomy of mental processes: a case study of arithmetic. , 1986, Journal of experimental psychology. General.

[22]  Mark H. Ashcraft,et al.  Mental addition in third, fourth, and sixth graders , 1982 .

[23]  M. Perlmutter,et al.  Cognitive arithmetic: comparison of operations. , 1984, Journal of experimental psychology. Learning, memory, and cognition.

[24]  Gary L. Dannenbring,et al.  Strategic factors in a lexical-decision task: Evidence for automatic and attention-driven processes , 1983, Memory & cognition.

[25]  Mark H. Ashcraft,et al.  Simple and complex mental addition across development , 1985 .

[26]  Mark H. Ashcraft,et al.  The development of mental arithmetic: A chronometric approach☆ , 1982 .

[27]  John R. Anderson.  The Architecture of Cognition , 1983 .

[28]  Allan Collins,et al.  A spreading-activation theory of semantic processing , 1975 .

[29]  J. H. Neely.  Semantic priming and retrieval from lexical memory: Roles of inhibitionless spreading activation and limited-capacity attention. , 1977 .

[30]  J. H. Neely.  Semantic priming and retrieval from lexical memory: Evidence for facilitatory and inhibitory processes , 1976, Memory & cognition.