Article
Groen GJ, Parkman JM. A chronometric analysis of simple addition
Psychological Review (Impact Factor: 7.97). 06/1972; 79(4):329343. DOI: 10.1037/h0032950
ABSTRACT
Considers a number of models that specify how children and adults solve singledigit addition problems. It is shown that the most adequate of these for children's response latencies is a model that assumes the existence of a counter with 2 operations: setting and incrementing. The child adds 2 digits, m and n, by setting this counter to max (m,n) and then incrementing it min (m,n) times. This model also accounts for adults' latencies, though with a drastically reduced incrementing time. Some theoretical issues raised by this reduced time are considered, and an alternative model is suggested which assumes that adults usually use a memory lookup process with homogeneous retrieval times, but occasionally revert back to the counting process used by children. (2l ref.) (PsycINFO Database Record (c) 2012 APA, all rights reserved)

 "Contrary to most past seminal studies (e.g., Ashcraft & Fierman, 1982), we used a production task wherein children were asked to give oral responses to the problems rather than a verification task, which, due to the possible use of plausibility judgments , might not reflect the real mental processes that individuals use to solve problems (Campbell & Tarling, 1996; Lemaire & Fayol, 1995; Zbrodoff & Logan, 1990). A production task in which solution times are precisely measured through voice key activation is also more ecologically valid than asking children to press a key corresponding to the answer (Groen & Parkman, 1972) or asking the experimenter to press a key when the child gives his or her response (Svenson, 1975; Svenson & Broquist, 1975). Moreover, in order to increase the reliability of our conclusions, and again contrary to original studies, a substantial number of data was collected . "
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ABSTRACT: For more than 30 years, it has been admitted that individuals from the age of 10 mainly retrieve the answer of simple additions from longterm memory, at least when the sum does not exceed 10. Nevertheless, recent studies challenge this assumption and suggest that expert adults use fast, compacted and unconscious procedures in order to solve very simple problems such as 3 + 2. If this is true, automated procedures should be rooted in earlier strategies and therefore observable in their noncompacted form in children. Thus, contrary to the dominant theoretical position, children's behaviors should not reflect retrieval. This is precisely what we observed in analyzing the responses times of a sample of 42 10yearold children who solved additions with operands from 1 to 9. Our results converge towards the conclusion that 10yearold children still use counting procedures in order to solve nontie problems involving operands from 2 to 4. Moreover, these counting procedures are revealed whatever the expertise of children, who differ only in their speed of execution. Therefore and contrary to the dominant position in the literature according to which children's strategies evolve from counting to retrieval, the key change in development of mental addition solving appears to be a shift from slow to quick counting procedures. 
 "Based on these measures, a variety of studies have suggested that strategy selection and strategy efficiency depend on the problem size, the arithmetic operation, and the level of arithmetic ability. The problemsize effect has been widely reported and refers to the fact that response time and errors increase as the size of the operands increases (Groen & Parkman, 1972; Zbrodoff & Logan, 2005). Campbell and Xue (2001) proposed three sources of the problemsize effect related to strategy selection and strategy efficiency. "
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ABSTRACT: The aim of this study was to examine whether differences in strategy selection and/or strategy efficiency can explain the modulation of the problemsize effect by arithmetic skill. More specifically, we wondered whether arithmetic skill increases the use of retrieval strategy in large problems, and/or enhances the efficiency of either retrieval or procedural strategies. The performance of highlyskilled (HS) and less highlyskilled (LS) individuals on a subtraction verification task was analyzed according to problem size and to the strategy reported on a trialbytrial basis after each problem. The problem size effect was larger for LS individuals than for their HS peers, both in response time and in hit rate. Nevertheless, groups did not differ regarding the strategy reported for each subtraction size. As expected, problems in which retrieval strategy was reported were solved more quickly and more accurately than problems solved by procedural strategies. Responses using retrieval strategy were equally fast in the two groups, but HS individuals performed better than LS when using procedural strategies. The results therefore suggest that the differences in behavioral measures between groups might specifically be due to differences in the efficiency of procedural strategies. 
 "001 . This difference might produce a problem size effect ( Ashcraft , 1992 ; Groen & Parkman , 1972 ) , which consists in longer reaction times and more errors when solving additions with large problem size relative to problems with small problem size . Hence , we report first the results obtained in the first trial ( Related 1 condition vs . "
Article: Simple arithmetic development in school age: The coactivation and selection of arithmetic facts
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ABSTRACT: We evaluated the possible inhibitory mechanism responsible for selecting arithmetic facts in children from 8 or 9years to 12 or 13years of age. To this end, we used an adapted version of the negative priming paradigm (NP paradigm) in which children received additions and they decided whether they were correct or not. When an addition was incorrect but the result was that of multiplying the operands (e.g., 2+4=8), only children from 10 or 11years of age onward took more time to respond compared with control additions with unrelated results, suggesting that they coactivated arithmetic knowledge of multiplications even when it was irrelevant to perform the task. Furthermore, children from 10 or 11years of age onward were slower to respond when the result of multiplying the operands was presented again in a correct addition problem (e.g., 2+6=8). This result showed the development of an inhibitory mechanism involved in the selection of arithmetic facts through formal education. Copyright © 2015 Elsevier Inc. All rights reserved.
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