The Complexity of Mental Integer Addition

@article{Buijsman2020TheCO,
  title={The Complexity of Mental Integer Addition},
  author={Stefan Buijsman and Markus Pantsar},
  journal={J. Numer. Cogn.},
  year={2020},
  volume={6},
  pages={148-163}
}
An important paradigm in modeling the complexity of mathematical tasks relies on computational complexity theory, in which complexity is measured through the resources (time, space) taken by a Turing machine to carry out the task. These complexity measures, however, are asymptotic and as such potentially a problematic fit when descriptively modeling mathematical tasks that involve small inputs. In this paper, we argue that empirical data on human arithmetical cognition implies that a more fine… Expand
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References

SHOWING 1-10 OF 51 REFERENCES
Tractability and the computational mind
TLDR
This work overviews logical and computational explanations of the notion of tractability as applied in cognitive science and surveys how complexity can be used to study computational plausibility of cognitive theories. Expand
Storage and retrieval of addition facts: The role of number comparison
TLDR
It is argued that the COMP model of addition fact retrieval fits not only the adult RT data better than do alternatives, but also the evidence from development of additional skills. Expand
Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving
TLDR
It is argued that human cognizers use heuristic and didactic tools and thus engage in cognitive processes that make their problem solving algorithms computationally suboptimal, in contrast with the optimal algorithms studied in the computational approach. Expand
A fresh look at research strategies in computational cognitive science: The case of enculturated mathematical problem solving
Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-usedExpand
The role of short-term working memory in mental arithmetic
  • G. Hitch
  • Mathematics
  • Cognitive Psychology
  • 1978
Abstract A series of experiments explored the role of information storage in working memory in performing mental arithmetic. Experiment 1 assessed the strategies people report for solving auditorilyExpand
Is adding 48 + 25 and 45 + 28 the same? How addend compatibility influences the strategy execution in mental addition
A recent study revealed that adults frequently start to add two two-digit numbers from the larger one, suggesting that addend magnitudes are compared at an early stage of processing. However, severalExpand
The Tractable Cognition Thesis
TLDR
How and why the P-Cognition thesis may be overly restrictive is explained, risking the exclusion of veridical computational-level theories from scientific investigation, and an argument is made to replace the Tractable Cognition thesis by the FPT-Cognitive thesis as an alternative formalization. Expand
The tractable cognition thesis.
TLDR
How and why the P-Cognition thesis may be overly restrictive is explained, risking the exclusion of veridical computational-level theories from scientific investigation, and an argument is made to replace the Tractable Cognition thesis by the FPT-Cognitive thesis as an alternative formalization. Expand
The Whorfian hypothesis and numerical cognition: is `twenty-four' processed in the same way as `four-and-twenty'?
TLDR
The possibility of a Whorfian effect in numerical cognition is examined by making use of the fact that in the Dutch number naming system the order of tens and units is reversed, and the idea that mathematical operations are based on verbal processes is questioned. Expand
Representing and using numerical information.
Issues of mental representation are central to cognitive psychology and indeed to psychology in general. This article synthesizes recent theoretical and empirical research concerning cognitiveExpand
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4
5
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