Kognitionswissenschaft 8(1), pp. 5-19.
ISSN/ISBN: Not available at this time. DOI: 10.1007/BF03354932
Abstract: Cognitive arithmetic studies the mental representation of numbers and arithmetic facts and the processes that create, access, and manipulate them. The contradiction between the apparent straightforwardness of its exact formal structure and the difficulties that every child faces in mastering it provides an important window into human cognition. An ACT-R model is proposed which accounts for the central results of the field through a single simulation of a lifetime of arithmetic learning. The use of the architecture's Bayesian learning mechanisms explains how these effects arise from the statistics of the task. Because of the precise predictions of the simulation, a number of lessons are derived concerning the teaching of arithmetic and the ACT-R architecture itself. A formal analysis establishes that the simulation can be viewed as a dynamical system whose ultimate learning outcome is fundamentally dependent upon some architectural parameters. Finally, an empirical study of the sensitivity of the simulation to its parameters determines that the values that yield the best fit to the data also provide optimal performance. The implications of these findings for the fundamental adaptivity of human cognition are discussed.
Bibtex:
@article{,
title={The dynamics of cognition: An ACT-R model of cognitive arithmetic},
author={Lebiere, Christian},
journal={Kognitionswissenschaft},
volume={8},
number={1},
pages={5--19},
year={1999},
publisher={Springer},
DOI={@article{,
title={The dynamics of cognition: An ACT-R model of cognitive arithmetic},
author={Lebiere, Christian},
journal={Kognitionswissenschaft},
volume={8},
number={1},
pages={5--19},
year={1999},
publisher={Springer},
DOI={10.1016/j.spl.2009.09.015},
}
Reference Type: Journal Article
Subject Area(s): Psychology