Considers a number of models that specify how children and adults solve single-digit 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 look-up 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 . "
[Show abstract][Hide abstract] 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 long-term memory, at least when the sum does not exceed 10. Nevertheless, recent studies challenge this assumption and suggest that expert adults use fast, com-pacted 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 non-compacted 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 10-year-old children who solved additions with operands from 1 to 9. Our results converge towards the conclusion that 10-year-old children still use counting procedures in order to solve non-tie 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 problem-size 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 problem-size effect related to strategy selection and strategy efficiency. "
[Show abstract][Hide abstract] ABSTRACT: The aim of this study was to examine whether differences in strategy selection and/or strategy efficiency can explain the modulation of the problem-size 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 highly-skilled (HS) and less highly-skilled (LS) individuals on a subtraction verification task was analyzed according to problem size and to the strategy reported on a trial-by-trial 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 . "
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