The obligatory activation of practiced complex multiplication facts and what it tells us about models of arithmetic processing
Author(s) / Creator(s)
Tronsky, Loel Nicholas
Abstract / Description
Three experiments were conducted in which adults practiced complex multiplication problems (e.g., 4 x 17). In Experiments 1 and 2, after practice participants completed a number-matching task in which two digits (cues) were followed by a single digit (probe) and had to determine whether the probe matched either of the cues. In simple arithmetic (e.g., 4 x 3), when the probe is the product of the cues (12), participants are slower/more error prone when determining whether there is a match. Results of Experiment 1 extended this effect to complex multiplication. In Experiment 2, participants practiced problems with the larger operand first (e.g., 17 x 4) or with the smaller operand first (e.g., 4 x 17). The number-matching interference effect from Experiment 1 was replicated, and was equal across the two groups whether cues were presented in their practiced or non-practiced order. Experiment 3 was conducted to determine if two additional simple multiplication effects, consistency and relatedness, could be documented for complex multiplication. After practice, in a verification task (4 x 13 = 56?) it was found that when presented answers shared a digit with the decade digit of the correct answer (consistency) or were a correct answer to another practiced problem (relatedness), participants rejected answers more slowly and/or less accurately. Together, findings from the three experiments support arithmetic models that posit that commuted pairs are not represented in long-term memory independently and that posit representations of two-digit multiplication answers are decomposed into decades and units during arithmetic processing.
Keyword(s)
complex multiplication numerical cognition arithmetic number-matching practice obligatory activationPersistent Identifier
Date of first publication
2016-08-05
Journal title
Journal of Numerical Cognition
Volume
2
Issue
2
Page numbers
140–165
Publisher
PsychOpen GOLD
Publication status
publishedVersion
Review status
peerReviewed
Is version of
Citation
Tronsky, L. N. (2016). The obligatory activation of practiced complex multiplication facts and what it tells us about models of arithmetic processing. Journal of Numerical Cognition, 2(2), 140–165. https://doi.org/10.5964/jnc.v2i2.22
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Author(s) / Creator(s)Tronsky, Loel Nicholas
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PsychArchives acquisition timestamp2018-11-21T11:42:41Z
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Made available on2018-11-21T11:42:41Z
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Date of first publication2016-08-05
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Abstract / DescriptionThree experiments were conducted in which adults practiced complex multiplication problems (e.g., 4 x 17). In Experiments 1 and 2, after practice participants completed a number-matching task in which two digits (cues) were followed by a single digit (probe) and had to determine whether the probe matched either of the cues. In simple arithmetic (e.g., 4 x 3), when the probe is the product of the cues (12), participants are slower/more error prone when determining whether there is a match. Results of Experiment 1 extended this effect to complex multiplication. In Experiment 2, participants practiced problems with the larger operand first (e.g., 17 x 4) or with the smaller operand first (e.g., 4 x 17). The number-matching interference effect from Experiment 1 was replicated, and was equal across the two groups whether cues were presented in their practiced or non-practiced order. Experiment 3 was conducted to determine if two additional simple multiplication effects, consistency and relatedness, could be documented for complex multiplication. After practice, in a verification task (4 x 13 = 56?) it was found that when presented answers shared a digit with the decade digit of the correct answer (consistency) or were a correct answer to another practiced problem (relatedness), participants rejected answers more slowly and/or less accurately. Together, findings from the three experiments support arithmetic models that posit that commuted pairs are not represented in long-term memory independently and that posit representations of two-digit multiplication answers are decomposed into decades and units during arithmetic processing.en_US
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Publication statuspublishedVersion
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Review statuspeerReviewed
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CitationTronsky, L. N. (2016). The obligatory activation of practiced complex multiplication facts and what it tells us about models of arithmetic processing. Journal of Numerical Cognition, 2(2), 140–165. https://doi.org/10.5964/jnc.v2i2.22en_US
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ISSN2363-8761
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Persistent Identifierhttps://hdl.handle.net/20.500.12034/1239
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Persistent Identifierhttps://doi.org/10.23668/psycharchives.1431
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Language of contenteng
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PublisherPsychOpen GOLD
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Is version ofhttps://doi.org/10.5964/jnc.v2i2.22
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Keyword(s)complex multiplicationen_US
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Keyword(s)numerical cognitionen_US
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Keyword(s)arithmeticen_US
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Keyword(s)number-matchingen_US
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Keyword(s)practiceen_US
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Keyword(s)obligatory activationen_US
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Dewey Decimal Classification number(s)150
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TitleThe obligatory activation of practiced complex multiplication facts and what it tells us about models of arithmetic processingen_US
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DRO typearticle
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Issue2
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Journal titleJournal of Numerical Cognition
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Page numbers140–165
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Volume2
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Visible tag(s)Version of Record