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Procedural complexity underlies the efficiency advantage in abacus-based arithmetic development

Donlan, C; Wu, C; (2017) Procedural complexity underlies the efficiency advantage in abacus-based arithmetic development. Cognitive Development , 43 pp. 14-24. 10.1016/j.cogdev.2017.02.002. Green open access

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The abacus is a counting frame designed to facilitate the process of arithmetic calculation. This paper focusses particularly on the Japanese ‘soroban’ abacus, examining the role of complementary numbers in its operation. We propose that the combination of quinary (base five) and decimal (base ten) systems, and the consequent use of complementary numbers (CN) in calculation, are transferred from physical to mental procedures. The more CN steps involved in a calculation, the more time it should take for mental abacus users to complete. This hypothesis was tested in Experiment 1: 146 Taiwanese abacus users aged 3–15, identified as either abacus learners (n = 126) or abacus experts (n = 20), were given parallel sets of serial addition and subtraction problems, matched on conventional metrics of difficulty level, but differing in the number of CN steps entailed in abacus calculation. An effect of CN was found whereby response times were significantly greater for the condition involving double CN steps. Experts were significantly faster than learners, but the effect of CN did not differ between groups. In Experiment 2, in order to test the specificity of the CN effect, a group of British children (n = 20), with no experience of the abacus, was given the same mental calculation tasks. They achieved accuracy levels equivalent to the abacus experts, but their calculation speed was very much slower, and they showed no evidence of the CN effect. Our findings demonstrate the importance of complementary numbers in children’s mental abacus calculation. We found the CN effectto be equally strong in expert and non-expert users, and confirmed the specificity of the effect by showing it to be absent in participants not exposed to abacus use. We argue that the use of complementary numbers in mental abacus calculation provides learners, from the outset, with exposure to a dual-base system which, while procedurally complex, affords a representational advantage not enjoyed by learners working within the exclusively decimal system of Arabic numerals

Type: Article
Title: Procedural complexity underlies the efficiency advantage in abacus-based arithmetic development
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.cogdev.2017.02.002
Publisher version: http://doi.org/10.1016/j.cogdev.2017.02.002
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Abacus, Complementary number, Calculation
URI: http://discovery.ucl.ac.uk/id/eprint/10052259
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