Retrieval-induced forgetting of arithmetic facts across cultures

Abstract

Retrieving a single-digit multiplication fact (3×4 =12) can slow response time (RT) for the corresponding addition fact (3+4=7). The present experiment investigated effects of problem type (i.e., tie addition problems such as 3+3 vs. non-ties such as 3+4) and cultural background on this retrieval-induced forgetting (RIF) phenomenon in young adults. Canadians answering in English (n=36), Chinese adults answering in English (n=36), and Chinese answering in Chinese (n=36) received four blocks of multiplication practice and then two blocks of the addition counterparts and control additions. Tie addition problems presented a robust RIF effect that did not differ between groups, but only the Canadian group showed RIF for non-ties and only for small non-ties with sum≤10 (3+4). The Chinese groups' RIF effect for addition ties, but not small non-ties, converges with recent evidence that ties are solved by direct memory retrieval whereas small non-ties may be solved by highly efficient procedural processes in skilled performers.

Keywords:

• Arithmetic
• Culture
• Retrieval-induced forgetting

This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada. We thank Emily Yan for assistance with data collection.

Notes

¹ The experiment was conducted in two phases. A first group of 54 participants (18 per group) were tested in the autumn and winter of 2011/2012. Subsequently, to increase power and precision, a second group of 54 participants was tested in winter 2013. In the interval, the issue of different processes for ties and non-ties emerged (Barrouillet & Thevenot, 2013; Fayol & Thevenot, 2012) and we extended the theoretical framework and analytic approach to apply the experiment to this issue.

² Confidence intervals and effect size values were calculated using MorePower 6.0 (Campbell & Thompson, 2012a). MorePower 6.0 is freely available at https://wiki.usask.ca/pages/viewpageattachments.action?pageId=420413544

³ Comparisons between problem types should be interpreted cautiously because the median RTs for ties and small non-ties were based on different numbers of trials, which can bias comparisons of median RT (Miller, 1988). If the bias is constant across other experimental factors, however, interaction effects with problem type would be bias free.

⁴ We did not include the second addition test block from Campbell and Thompson (2012b) because a block of multiplication intervened between the addition blocks.