2577 words - 10 pages

Mine is not to reason why, I just invert and multiply.There is ample evidence that children find the learning of fractions a major difficulty (Behr, Harel, Post, & Lesh,1992; Davydov & Tsvetkovich,1991; Hiebert & Behr,1988; Kieren,1976; Mack,1990; McLellan & Dewey, 1908: Cited in Tzur, 1999: Van de Walle, 1990: Behr, Harel, Post, & Lesh; Hunting, Davis, & Pearn, 1996; Mack, 1995: Cited by Thompson, & Saldanha, 2003). Students have many misconceptions about fractions including the belief that the fraction having the larger denominator is always larger, two fractions that are almost equal are equivalent (Johnson, 1998; Mack, 1990), fractions are parts of shapes, fractions are never bigger than 1 and that fractions are not numbers in their own right (Mack, 1990). Many students have trouble interpreting mixed numbers (Kouba, 1988a; cited by Van de Walle, 2007: Ball, 1990; As cited in Tsao, 2005) and suffer confusion with the meaning of operations and rules learnt (Mack, 1995: Ball, 1990; As cited by Tsao, 2005). Research also shows that although some students may be fairly capable of working with fractional computations they dont really understand what fractions are (Kouba, Zawojewski, and Strutchens, 1997).Often children come into the classroom with a basic understanding of fractions through sharing (Mack, 1990), particularly when performing operations on fractions using real-life situations (Gunderson & Gunderson, 1957; Leinhardt, 1988: as cited by Mack, 1990). This gives a strong base for teachers to help students construct the idea of fractional parts of a whole and the outcome of sharing in equal parts through the acting out of story based problems such as sharing lollies or biscuits among a varying number of students (Van de Walle, 2007). It is very important to introduce the vocabulary of fractional language which can be done quite casually using terms such as fourths, thirds etc (Van de Walle, 2007). From here a teacher might begin to point out the two components of fractional parts, the number of parts and the equality of the parts. Fractions are simply an easy way of writing how many of what; the top number counts and the bottom number is what is being counted (Van de Walle, 2007).There is evidence to suggest that the use of models benefit students understanding of fractional sizes as experienced by Mack (1995) who asked students which fraction of a pizza would be larger, 1/8 or 1/6. All subjects said 1/6, yet when the question used no concrete examples, upon being asked which was larger, the majority replied 1/8 was bigger, suggesting they were applying their understandings of whole number operations. This may argue well for the use of the pizza pie models to assist students in constructing knowledge of area or region as they are models students can relate to and allowing students to make use of their informal knowledge. Pizza pie models can...

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