Cited by 231Cognitive and developmental aspects of mathematical skillsMemory Processes and InfluencesCognitive Abilities and Testing

Bending the power law: A CMPL theory of strategy shifts and the automatization of cognitive skills.

Rickard, Timothy C.·1997·Journal of Experimental Psychology: General

Abstract

The shift with practice from use of generic, multistep problem-solving strategies to fast and relatively effortless memory-based strategies, was explored in 2 experiments using pseudoarithmetic tasks. A complete transition to the memory strategy occurred by about the 60th exposure to each problem. The power law of practice did not hold in the overall data for either the mean or the standard deviation of response latency, but it did hold within each strategy (algorithm or retrieval). Learning was highly specific to the practiced problems. These results constitute the 1st clear demonstration of a skill for which the power law does not apply overall. The results do not support the instance theory of automatization (G. D. Logan, 1988) but are consistent with an alternative component 12ower laws (CMPL) theory that assumes that because of intrinsic attentional limitations, only 1 strategy can be executed at a time. One of the fundamental processes of human skill acquisition is the strategy shift with practice from use of generic, multistep procedures to direct retrieval of answers from

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Crossref · 10.1037/0096-3445.126.3.288

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  • CMPL theory hypothesizes a two-stage model based on the transition from algorithmic processing to memory retrieval.

    “This is where CMPL theory differs from the race model by hypothesizing a two-stage model based on the transition between two different mechanisms.”

    From Testing the three-stage model of second language skill acquisition (2025) · cites this paper as Rickard, 1997

  • Competing theoretical models of L2 skill acquisition with fewer stages exist.

    “yet competing theoretical models with fewer stages also exist”

    From Testing the three-stage model of second language skill acquisition (2025) · cites this paper as Rickard, 1997

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Authors
Rickard, T. C.
Affiliations
University of California San Diego (US)
Corresponding author
Rickard, Timothy C.
Venue
Journal of Experimental Psychology: General
Published
1997-09
Volume
126
Issue
3
Pages
288-311
ISSN
  • 0096-3445 (ISSN-L)
  • 1939-2222
OpenAlex
W1977919377
Cited by
231
References
2
Citations by year
2026: 3 · 2025: 5 · 2024: 6 · 2023: 4 · 2022: 4 · 2021: 6 · 2020: 6 · 2019: 7 · 2018: 6 · 2017: 3 · 2016: 9 · 2015: 9 · 2014: 7 · 2013: 10 · 2012: 9
FWCI
6.37
Type
journal article
Language
en
Open access
closed
Locations
Journal of Experimental Psychology General (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Cognitive and developmental aspects of mathematical skills
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Memory Processes and Influences
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Cognitive Abilities and Testing
Keywords
strategy switching, power law of practice, algorithmic problem solving, response latency, attentional limitations, skill acquisition

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