Abstract
The present study investigated how elementary-school children solve two-digit addition problems (e.g., 34+68). To achieve this end, we examined age-related differences in children’s strategy use and strategy performance. Results showed that (a) both third and fifth graders used a set of 9 strategies, (b) fifth-grade individuals used more strategies than third-grade individuals, (c) age-related differences in the size of strategy repertoire was partially explained by age-related differences in basic arithmetic fluency, (d) how often children used each available strategy changed with problem difficulty and children’s age, as younger children tended to focus more on one or two strategies and older children used a wider range of strategies, (e) increased arithmetic performance with age varied with problem difficulty both when overall performance was analyzed and when analyses of performance was restricted to children’s favorite strategy. The present findings have important implications for our understanding of how complex arithmetic performance changes with children’s age and change mechanisms underlying improved performance with age in complex arithmetic.
Highlights
The present study investigated how elementary-school children solve two-digit addition problems (e.g., 34+68)
Results are reported in three main parts, each examining effects of age and problem difficulty on strategy repertoire, on strategy selection, and on performance
Previous works in arithmetic showed that children as young as 7 year-old solve two-digit arithmetic problems with several strategies and that their performance depend on which strategies are used (e.g., Beishuizen, 1993; Beishuizen et al, 1997; Fuson et al, 1997; Geary, Hoard, Byrd-Craven, & DeSoto, 2004; Kilpatrick et al, 2001; Lemaire & Calliès, 2009; Lucangeli et al, 2003; Verschaffel et al, 2007)
Summary
The present study investigated how elementary-school children solve two-digit addition problems (e.g., 34+68) To achieve this end, we examined age-related differences in children’s strategy use and strategy performance. We ignore whether some important previous findings (e.g., strategy variability) are specific to simple arithmetic and multi-digit subtraction problems, or generalize to all types of arithmetic problems (including two-digit addition problems investigated here) Knowing such empirical constraints may prove crucial for elaborating formal models of complex arithmetic and its development in children. No detailed analyses of strategies used by children to solve two-digit addition problems have yet been undertaken, and most of these previous studies tested small numbers of problems, and did not investigate systematically how problem features (like problem difficulty) influence children’s strategies and performance, as well as how such effects change with children’s age
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