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Using Microcomputers with Fourth-Grade Students to Reinforce Arithmetic Skills

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This paper presents a learning-research based argument for the integration of computer programming into the science and mathematics curricula in pre-college education as well as college. Students who generate solutions to science and mathematics problems develop a procedural understanding of the fundamental theories of these disciplines. Students should be taught to use programming languages for these solutions for the same reasons they are taught the universal tools of arithmetic and algebra, and because only a computer provides the means to describe solutions in explicit, correct, and executable form. Programming should be integrated into all mathematics and science teaching from the earliest years. In precollege education, programming should be taught over a period of eight to ten years, rather than as a 6-12 week separate topic, and should be matched to the level of complexity of the science and mathematics content.
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The effects of practicing computerized exercises in class by 59 learning disabled students who received an 8-hr. training program, 30 min. per week, were evaluated. Six exercises designed to facilitate basic cognitive skills development were used. Twelve subjects were assigned to a control group without any form of intervention. Covariance analysis (pretest scores used as covariates) showed a significant effect of training on mental arithmetic. These results suggest that practicing a computerized exercise of mental arithmetic can facilitate the automatization of basic arithmetic skills (addition, subtraction, and multiplication). The nature, progress, and evaluation of such types of intervention are discussed.
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Reviewers have consistently concluded that males perform better on mathematics tests than females do. To make a refined assessment of the magnitude of gender differences in mathematics performance, we performed a meta-analysis of 100 studies. They yielded 254 independent effect sizes, representing the testing of 3,175,188 Ss. Averaged over all effect sizes based on samples of the general population, d was -0.05, indicating that females outperformed males by only a negligible amount. For computation, d was -0.14 (the negative value indicating superior performance by females). For understanding of mathematical concepts, d was -0.03; for complex problem solving, d was 0.08. An examination of age trends indicated that girls showed a slight superiority in computation in elementary school and middle school. There were no gender differences in problem solving in elementary or middle school; differences favoring men emerged in high school (d = 0.29) and in college (d = 0.32). Gender differences were smallest and actually favored females in samples of the general population, grew larger with increasingly selective samples, and were largest for highly selected samples and samples of highly precocious persons. The magnitude of the gender difference has declined over the years; for studies published in 1973 or earlier d was 0.31, whereas it was 0.14 for studies published in 1974 or later. We conclude that gender differences in mathematics performance are small. Nonetheless, the lower performance of women in problem solving that is evident in high school requires attention.
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The author reviews the research on the effectiveness of graphics in instruction and then proposes a framework for developing a theory that accounts for the syntax, semantics, and pragmatics of graphics. His goal is to lay the groundwork for developing prescriptive guidelines for the design of effective graphics in training documents. He stresses that further research needs to be done in order that a theory of learning from graphics can be developed in sufficient detail for design prescriptions to be provided and that prescriptive theory for graphic design is necessary
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