Modeling ancient and modern arithmetic practices : addition and multiplication with Arabic and Roman numerals

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Schlimm_283870.pdf
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2008
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Schlimm, Dirk
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COGNITIVE SCIENCE SOCIETY, , ed.. 30th annual conference of the Cognitive Science Society : CogSci 2008 ; July 23 - 26, 2008, Washington, D.C., USA. 4. Red Hook, NY: Curran, 2008, pp. 2097-2102. ISBN 978-1-60560-542-5
Zusammenfassung

To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar - a claim that is widely disputed. An analysis of our models' elementary processing steps reveals intricate trade-offs between problem representation, algorithm, and interactive resources. Our simulations allow for a more nuanced view of the received wisdom on Roman numerals. While symbolic computation with Roman numerals requires fewer internal resources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
150 Psychologie
Schlagwörter
Numeral systems, arithmetic algorithms, mathematical practice, immediate interactive behavior
Konferenz
CogSci, 23. Juli 2008 - 26. Juli 2008, Washington, D.C., USA
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Zitieren
ISO 690SCHLIMM, Dirk, Hansjörg NETH, 2008. Modeling ancient and modern arithmetic practices : addition and multiplication with Arabic and Roman numerals. CogSci. Washington, D.C., USA, 23. Juli 2008 - 26. Juli 2008. In: COGNITIVE SCIENCE SOCIETY, , ed.. 30th annual conference of the Cognitive Science Society : CogSci 2008 ; July 23 - 26, 2008, Washington, D.C., USA. 4. Red Hook, NY: Curran, 2008, pp. 2097-2102. ISBN 978-1-60560-542-5
BibTex
@inproceedings{Schlimm2008Model-28387,
  year={2008},
  title={Modeling ancient and modern arithmetic practices : addition and multiplication with Arabic and Roman numerals},
  isbn={978-1-60560-542-5},
  publisher={Curran},
  address={Red Hook, NY},
  booktitle={30th annual conference of the Cognitive Science Society : CogSci 2008 ; July 23 - 26, 2008, Washington, D.C., USA},
  pages={2097--2102},
  editor={Cognitive Science Society},
  author={Schlimm, Dirk and Neth, Hansjörg}
}
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