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The principle ofinversion,thata + b − b mustequala, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya (2005). Hypothesis 1 is that greater calculational skill is related to greater use of inversion. Hypothesis 2 is that greater attentional skill is related to greater use of inversion. Hypothesis 3 is that the relation between attentional skill and the use of inversion is particularly strong among children with high skill in calculation. We found suggestive evidence for Hypothesis 2 and clear evidence for Hypothesis 3, indicating that for children who are strong at calculation, attentional flexibility is related to use of inversion. [ABSTRACT FROM PUBLISHER]

The goal of this project was to examine the profile of executive function (EF) deficits and age-related differences among children with FASD. Twenty-nine children with FASD (8 to 16 years of age) completed 8 tests from the Delis-Kaplan Executive Function System (D-KEFS). They had difficulty on many components of EF including cognitive flexibility, inhibition, some measures of verbal fluency, abstract thinking, deductive reasoning, hypothesis testing, problem solving, and concept formation. A distinctive profile emerged with performance being poorest on the card sorting test and relatively high on category fluency, design fluency, and the tower test, indicating relative strengths on some visual-spatial EF tasks. Older children with FASD showed more difficulty (relative to the norm) on some verbal tests of EF than younger children with FASD, suggesting that difficulty on some verbal EF tasks appears to become more pronounced with increasing age. [ABSTRACT FROM AUTHOR]

The principle of inversion, that a + b - b must equal a, is a fundamental property of conventional arithmetic. Exploring how children use and understand the principle of inversion can provide important insights about the development of mathematical thinking and about ways of optimizing instruction. Research on children's use and understanding of inversion has been focused primarily on whether they use inversion, with much less attention placed on what this understanding comprises and how it develops. To remedy this situation, we propose a framework in which understanding inversion is represented in terms of a matrix of possibilities. This framework is useful for highlighting the diverse ways in which children can show their understanding, for describing individual differences, for tracking changes in understanding, and for prompting investigations on the mechanisms that contribute to conceptual development. [ABSTRACT FROM AUTHOR]

The principle of inversion—that a + b - b must equal a—requires a sensitivity to the relation between addition and subtraction that is critical for understanding arithmetic. Use of inversion, albeit inconsistent, has been observed in school-age children, but when use of a computational shortcut based on inversion emerges and how awareness of the inversion principle relates to other mathematical or numerical skills remain unclear. Two possibilities were explored in 3-year-olds by adapting a method used previously with older children involving the addition and subtraction of blocks differing in length. These children were significantly more accurate on inversion than standard problems, this difference was observed even in children who did not count well, and performance did not differ between formats that afforded qualitative or quantitative solutions. Thus, 3-year-olds appear to develop an early sensitivity to quantitative inversion. [ABSTRACT FROM AUTHOR]

Evaluates students in grades three and six on measures of mathematics anxiety, school test anxiety and attitudes toward mathematics. Forms of mathematics anxiety; Increase of mathematics anxiety with age; Comparison between mathematics anxiety and school test anxiety.