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Sources of individual differences in fraction skills

Sources of individual differences in fraction skills,10.1016/j.jecp.2003.08.003,Journal of Experimental Child Psychology,Steven A Hecht,Linda Close,Mi

Sources of individual differences in fraction skills   (Citations: 16)
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The purpose of this investigation was to evaluate a conceptual model of relations between two kinds of mathematical knowledge (simple arithmetic and conceptual knowledge), two kinds of child characteristics (working memory and on-task related classroom behavior), and individual differences in three kinds of fraction outcomes (fraction computation, estimation, and word problems) in 105 fifth grade students. Structural equation modeling provided consistent evidence that conceptual knowledge independently contributes to individual differences in the three fraction outcomes. Simple arithmetic knowledge was uniquely related only to variability in fraction computation skills. Mathematical knowledge was found to mediate some of the contributions of both working memory and classroom behavior on variability in fraction outcomes. These supported mediating processes extend the current literature by explication of the pathways via which characteristics of children may affect individual differences in fraction outcomes.
Journal: Journal of Experimental Child Psychology - J EXP CHILD PSYCHOL , vol. 86, no. 4, pp. 277-302, 2003
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    • ...Hecht, Close and Santisi (2003) studied the unique contribution of students' conceptual knowledge of fractions and simple arithmetic skills for predicting variance in fraction computation, estimation and word problem solving skills for 105 grade 5 students, while controlling for working memory and classroom behavior...

    Leanne R. Ketterlin-Gelleret al. Algebra readiness for students with learning difficulties in grades 4–...

    • ...This work has attempted to measure and in a few cases account for individual differences in children's arithmetic performance (Hecht, Close, & Santisi, 2003; Swanson & Kim, 2007), conceptual understanding (Canobi, 2004, 2005; Canobi, Reeve, & Pattison, 1998; Dowker, 1998) and strategy use (Imbo & Vandierendonck, 2007; Kerkman & Siegler, 1997)...

    Camilla K. Gilmoreet al. Patterns of Individual Differences in Conceptual Understanding and Ari...

    • ...Fractions are difficult to learn because they require deep conceptual knowledge of part-whole (how much of an object or set is represented by the fraction symbol), measurement (fractions are made up of numbers that can be ordered on a number line), and ratios (Hecht, Close, & Santisi, 2003)...

    John A. Rosset al. Student achievement effects of technology-supported remediation of und...

    • ...Variation among children in working memory functioning (Geary, Hoard, Nugent, & Byrd-Craven, 2007; Hecht, Close, & Santisi, 2003), arithmetic fact retrieval (Geary & Hoard, 2005; Jordan et al. 2003), strategy execution and counting (Jordan, 2007), and other capabilities are also influential...

    Elida V. Laskiet al. Is 27 a Big Number? Correlational and Causal Connections Among Numeric...

    • ...However, there is converging evidence that a substantial number of undergraduates actually use strategies that are slower and more error prone than retrieval to solve some simple arithmetic problems (see, e.g., Campbell & Xue, 2001; Hecht, 1999, 2003; LeFevre, Sadesky, & Bisanz, 1996)...
    • ...Working memory refers to how well a person can maintain and simultaneously process information in his or her focus of attention (Baddeley, 1992; Hecht, 2003)...
    • ...These results are consistent with the idea that the speed of searching and accessing answers from long-term memory is an automatic process (Hecht, 2003) that reaches asymptote in adulthood (Geary & Wiley, 1991; Kail, 1988; Kaye, deWinstanley, Chen, & Bonnefil, 1989; Widaman et al., 1992)...
    • ...The present intercept differences between ability groups reflect differences in the speed of executing controlled attention-demanding processes, such as encoding and verbal production routines needed to utter the answer (Geary, Frensch, & Wiley, 1993; Geary & Wiley, 1991; Hecht, 2003)...

    Steven A. Hecht. Group differences in adult simple arithmetic: Good retrievers, not-so-...

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