grade levels who used calculators together with traditional instruction maintained their computational skills. For average-ability students, a small negative effect at fourth grade suggested that sustained use of calculators at that grade might hamper the acquisition of basic skills. On the other hand, use of calculators enhanced basic skills acquisition by average-ability students at all other grade levels, so the negative effect at fourth grade might have been an artifact of conditions specific to those studies that included fourth graders. For all ability groups at all grades, problem solving was improved by the use of calculators. The positive effects were found when calculator use was permitted in testing; the effects were weak or absent, but never negative, when testing was conducted without calculators. Students using calculators were also found to possess a better attitude toward mathematics and a better self-concept in mathematics. This meta-analysis of calculator use has been widely cited to support efforts to introduce calculators into mathematics instruction in grades K to 8. Meta-analysis as a procedure for synthesizing research results, however, has not been without its critics.64 Studies included in such metaanalyses often vary in quality and use a variety of different treatments labeled with a single term, in this case “calculator use.”

Long-term studies of calculator use, however, support the findings of the meta-analysis. A study in Sweden found that students in grades 4–6 who used calculators improved in conceptual understanding, the ability to choose the correct operation, and proficiency with estimation and mental arithmetic but did not lose skill in pencil-and-paper calculations when compared with students in traditional classes.65 The students in the experimental classes continued to study algorithms, but they spent relatively less time on algorithms and more on problem solving than students in the traditional classes. In an Australian project involving over 60 teachers and 1,000 students, students who had been given unrestricted access to a calculator beginning in kindergarten were familiar with a wider range of numbers, were better with mental calculations and estimation, and were better able to tackle real-world problems than students who had not had access to calculators. Their pattern of use of standard algorithms, left-to-right algorithms, and invented methods did not vary greatly from that of the children who did not have access to calculators. Further, they did not become reliant on calculators at the expense of other methods of calculations. In sum, no detrimental effects of calculator use were observed.66 These findings are consistent with those from England in which six-year-olds in a calculator awareness project, compared with children in a regular program, demonstrated knowledge of a wider range of numbers, including decimals and negative numbers. Project children also performed

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