### MISTAKES TEACHERS MAKE

Based on previous research Moss and Case (1999) identified four major problems with current teaching methods in the area of fractions. The first is a syntactic rather than a semantic emphasis, which is to say that researchers have identified that teachers often emphasize technical procedures in doing fraction arithmetic at the expense of developing a strong sense in children of the meaning of rational numbers. The second problem identified is that teachers often take an adult-centered rather than a child-centered approach, emphasizing fully formed adult conceptions of rational numbers. As a result teachers often do not take advantage of students "prefractional knowledge" and their informal knowledge about fractions thus denying children a spontaneous "in" to their formal study of fractions. A third issue is the problem of teachers using representations in which rational and whole numbers are easily confused e.g. students count the number of shaded parts of a figure and the total number of parts so that each part is regarded as an independent entity or amount (Kieran cited in Moss & Case (1999). Finally, researchers have identified considerable problems in use of notation that can act as a hindrance to student development. These problems center around teachers' perceptions that the notation used for rational numbers is transparent while this has been shown not to be the case, especially with regard to decimal fractions (Hiebert, cited in Moss & Case (1999)). Tirosh (2000) conducted a study on teacher knowledge in teaching of fractions and concluded that teachers needed to pay considerably more to analysis of student errors.

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