Phases of learning: How skill acquisition impacts cognitive processing
Open accessAbstract
This fMRI study examines the changes in participants' information processing as they repeatedly solve the same mathematical problem. We show that the majority of practice-related speedup is produced by discrete changes in cognitive processing. Because the points at which these changes take place vary from problem to problem, and the underlying information processing steps vary in duration, the existence of such discrete changes can be hard to detect. Using two converging approaches, we establish the existence of three learning phases. When solving a problem in one of these learning phases, participants can go through three cognitive stages: Encoding, Solving, and Responding. Each cognitive stage is associated with a unique brain signature. Using a bottom-up approach combining multi-voxel pattern analysis and hidden semi-Markov modeling, we identify the duration of that stage on any particular trial from participants brain activation patterns. For our top-down approach we developed an ACT-R model of these cognitive stages and simulated how they change over the course of learning. The Solving stage of the first learning phase is long and involves a sequence of arithmetic computations. Participants transition to the second learning phase when they can retrieve the answer, thereby drastically reducing the duration of the Solving stage. With continued practice, participants then transition to the third learning phase when they recognize the problem as a single unit and produce the…
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These findings provided converging evidence that skill acquisition of the pyramid problem is a three-stage process and that the cognitive processes involved in the three stages are consistent with ACT-R predictions.
“These findings, combined with the results of the HMM analysis, provided converging evidence that skill acquisition (at least of the pyramid problem) is a three-stage process and that the cognitive processes involved in the three stages are consistent with the predictions from ACT-R.”
From Testing the three-stage model of second language skill acquisition (2025) · cites this paper as Tenison & Anderson, 2016
Tenison and Anderson's neural results showed that regions known to subserve calculation, effortful retrieval, and automatic reflex were highly activated in the corresponding stages.
“The results showed that the regions known to subserve the hypothesized cognitive processings (i.e., calculation, effortful retrieval, and automatic reflex) were indeed highly activated in the corresponding stages.”
From Testing the three-stage model of second language skill acquisition (2025) · cites this paper as Tenison & Anderson, 2016
Tenison and Anderson (2016) found that the three-state model showed the best fit, while one- and two-state models provided substantially poorer fits, and four- and five-state models did not improve on the three-state model.
“They found that the three-state model showed the best fit, while the one-and two-state models provided substantially poorer fits, and the four-and fivestate models did not improve on the three-state model.”
From Testing the three-stage model of second language skill acquisition (2025) · cites this paper as Tenison & Anderson, 2016
A key assumption in the ACT-R learning mechanism is that most performance improvements occur through stage transitions or qualitative shifts in the underlying cognitive mechanism.
“A key assumption in the ACT-R learning mechanism is that most performance improvements occur through stage transitions or qualitative shifts in the underlying cognitive mechanism (Anderson, 2005;Tenison & Anderson, 2016).”
From Testing the three-stage model of second language skill acquisition (2025) · cites this paper as Tenison & Anderson, 2016
The equal contribution of within-stage and between-stage changes contrasts with previous findings on cognitive skill acquisition.
“which contrasts with previous findings on cognitive skill acquisition (Tenison & Anderson, 2016).”
From Testing the three-stage model of second language skill acquisition (2025) · cites this paper as Tenison & Anderson, 2016
Cites
Acquisition of cognitive skill
Anderson, J. R. (1982) · Psychological Review · doi:10.1037/0033-295x.89.4.369 · Cited by 3,663 · see citing works
Self-citationToward an explanation of the power law artifact: Insights from response surface analysis
Myung, I. J., Kim, C., & Pitt, M. A. (2000) · Memory & Cognition · doi:10.3758/bf03198418 · Cited by 126 · see citing works
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Mangaroska, K., Sharma, K., Gašević, D., & Giannakos, M. (2022) · Journal of Computer Assisted Learning · doi:10.1111/jcal.12590 · Cited by 100 · see citing works
Testing the three-stage model of second language skill acquisition
Maie, R., & Godfroid, A. (2025) · Studies in Second Language Acquisition · doi:10.1017/s027226312500021x · Cited by 5 · see citing works
“As a case in point, Tenison et al. (2016) examined how changes in learning stages in mathematical problem-solving (e.g., solving 5$3 as 5 + 4 + 3 = 12) impacted stages of cognitive processing happening within a single trial (problem encoding, problem solving, and producing a response).”
- Authors
- Tenison, C., Fincham, J. M., & Anderson, J. R.
- Affiliations
- Carnegie Mellon University (US)
- Corresponding author
- Tenison, Caitlin
- Venue
- Cognitive Psychology
- Publisher
- Elsevier BV
- Published
- 2016-06
- Volume
- 87
- Pages
- 1-28
- ISSN
- 0010-0285 (ISSN-L)
- OpenAlex
- W2307375722
- Cited by
- 67
- References
- 2
- Citations by year
- 2026: 9 · 2025: 4 · 2024: 6 · 2023: 10 · 2022: 2 · 2021: 3 · 2020: 8 · 2019: 10 · 2018: 6 · 2017: 7 · 2016: 2
- FWCI
- 8.44
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Cognitive Psychology (acceptedVersion)
- PubMed (publishedVersion)
- Funders
- Carnegie Mellon University
- National Science Foundation (DRL-1420008)
- U.S. Department of Education (R305B090023)
- James S. McDonnell Foundation
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Cognitive and developmental aspects of mathematical skills
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory Processes and Influences
- Keywords
- skill acquisition, learning stages, mathematical problem solving, arithmetic computation, cognitive development stages, encoding, problem solving, responding, automaticity, multi-voxel pattern analysis, brain activation patterns
- MeSH terms
- Adult, Brain, Brain Mapping, Female, Humans, Learning, Magnetic Resonance Imaging, Male, Practice, Psychological, Problem Solving, Mathematical Concepts, Young Adult
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