Several researchers, including Booth (1984, 1988), Greeno (1982), Kieran (1988, 1992), Lins (1990), and Matz (1980), attributed many of the fundamental difficulties experienced by beginning algebra students to their failure to identify equivalent forms of an algebraic expression. According to Kieran (1988), structural knowledge means being able to identify ‘all the equivalent forms of the expression’. Linchevski and Vinner (1990)…

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In the paper Using intuition from everyday life in ‘filling’ the gap in children’s extension of their concept to include negative numbers, the authors reports an instructional method designed to address the cognitive gaps in children’s mathematical development where operational conceptions give rise to structural conceptions (such as when the subtraction process leads to the negative number concept). The…

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In this paper the authors examine the possibility of differentiating between two types of nonexamples. The first type, intuitive nonexamples, consists of nonexamples which are intuitively accepted as such. That is, children immediately identify them as nonexamples. The second type, non-intuitive nonexamples, consists of nonexamples that bear a significant similarity to valid examples of the concept,…

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