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The representation of multiplication and division facts in memory evidence for cross-operation transfer without mediation

Jolien De Brauwer (UGent) and Wim Fias (UGent)
(2011) EXPERIMENTAL PSYCHOLOGY. 58(4). p.312-323
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The integrative neuroscience of behavioral control (Neuroscience)
Abstract
Recently, using a training paradigm, Campbell and Agnew (2009) observed cross-operation response time savings with nonidentical elements (e. g., practice 3 + 2, test 5 - 2) for addition and subtraction, showing that a single memory representation underlies addition and subtraction performance. Evidence for cross-operation savings between multiplication and division have been described frequently (e. g., Campbell, Fuchs-Lacelle, & Phenix, 2006) but they have always been attributed to a mediation strategy (reformulating a division problem as a multiplication problem, e. g., Campbell et al., 2006). Campbell and Agnew (2009) therefore concluded that there exists a fundamental difference between addition and subtraction on the one hand and multiplication and division on the other hand. However, our results suggest that retrieval savings between inverse multiplication and division problems can be observed. Even for small problems (solved by direct retrieval) practicing a division problem facilitated the corresponding multiplication problem and vice versa. These findings indicate that shared memory representations underlie multiplication and division retrieval. Hence, memory and learning processes do not seem to differ fundamentally between addition-subtraction and multiplication-division.
Keywords
IDENTICAL ELEMENTS MODEL, BASIC ARITHMETIC SKILLS, CUED-RECALL, SUBTRACTION, arithmetic fact retrieval, simple multiplication, simple division

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Citation

Please use this url to cite or link to this publication:

Chicago
De Brauwer, Jolien, and Wim Fias. 2011. “The Representation of Multiplication and Division Facts in Memory Evidence for Cross-operation Transfer Without Mediation.” Experimental Psychology 58 (4): 312–323.
APA
De Brauwer, Jolien, & Fias, W. (2011). The representation of multiplication and division facts in memory evidence for cross-operation transfer without mediation. EXPERIMENTAL PSYCHOLOGY, 58(4), 312–323.
Vancouver
1.
De Brauwer J, Fias W. The representation of multiplication and division facts in memory evidence for cross-operation transfer without mediation. EXPERIMENTAL PSYCHOLOGY. 2011;58(4):312–23.
MLA
De Brauwer, Jolien, and Wim Fias. “The Representation of Multiplication and Division Facts in Memory Evidence for Cross-operation Transfer Without Mediation.” EXPERIMENTAL PSYCHOLOGY 58.4 (2011): 312–323. Print.
@article{2064542,
  abstract     = {Recently, using a training paradigm, Campbell and Agnew (2009) observed cross-operation response time savings with nonidentical elements (e. g., practice 3 + 2, test 5 - 2) for addition and subtraction, showing that a single memory representation underlies addition and subtraction performance. Evidence for cross-operation savings between multiplication and division have been described frequently (e. g., Campbell, Fuchs-Lacelle, \& Phenix, 2006) but they have always been attributed to a mediation strategy (reformulating a division problem as a multiplication problem, e. g., Campbell et al., 2006). Campbell and Agnew (2009) therefore concluded that there exists a fundamental difference between addition and subtraction on the one hand and multiplication and division on the other hand. However, our results suggest that retrieval savings between inverse multiplication and division problems can be observed. Even for small problems (solved by direct retrieval) practicing a division problem facilitated the corresponding multiplication problem and vice versa. These findings indicate that shared memory representations underlie multiplication and division retrieval. Hence, memory and learning processes do not seem to differ fundamentally between addition-subtraction and multiplication-division.},
  author       = {De Brauwer, Jolien and Fias, Wim},
  issn         = {1618-3169},
  journal      = {EXPERIMENTAL PSYCHOLOGY},
  keyword      = {IDENTICAL ELEMENTS MODEL,BASIC ARITHMETIC SKILLS,CUED-RECALL,SUBTRACTION,arithmetic fact retrieval,simple multiplication,simple division},
  language     = {eng},
  number       = {4},
  pages        = {312--323},
  title        = {The representation of multiplication and division facts in memory evidence for cross-operation transfer without mediation},
  url          = {http://dx.doi.org/10.1027/1618-3169/a000098},
  volume       = {58},
  year         = {2011},
}

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