Article Version of Record

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 activation

Persistent 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
  • Author(s) / Creator(s)
    Tronsky, Loel Nicholas
  • PsychArchives acquisition timestamp
    2018-11-21T11:42:41Z
  • Made available on
    2018-11-21T11:42:41Z
  • Date of first publication
    2016-08-05
  • 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.
    en_US
  • Publication status
    publishedVersion
  • Review status
    peerReviewed
  • 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
    en_US
  • ISSN
    2363-8761
  • Persistent Identifier
    https://hdl.handle.net/20.500.12034/1239
  • Persistent Identifier
    https://doi.org/10.23668/psycharchives.1431
  • Language of content
    eng
  • Publisher
    PsychOpen GOLD
  • Is version of
    https://doi.org/10.5964/jnc.v2i2.22
  • Keyword(s)
    complex multiplication
    en_US
  • Keyword(s)
    numerical cognition
    en_US
  • Keyword(s)
    arithmetic
    en_US
  • Keyword(s)
    number-matching
    en_US
  • Keyword(s)
    practice
    en_US
  • Keyword(s)
    obligatory activation
    en_US
  • Dewey Decimal Classification number(s)
    150
  • Title
    The obligatory activation of practiced complex multiplication facts and what it tells us about models of arithmetic processing
    en_US
  • DRO type
    article
  • Issue
    2
  • Journal title
    Journal of Numerical Cognition
  • Page numbers
    140–165
  • Volume
    2
  • Visible tag(s)
    Version of Record