Alack of fractional understanding is a well-documented obstacle to student achievement in upper elementary and middle school math (National Center for Educational Statistics {NCES] 1999; Lamon 1999; National Research Council [NRC] 2001)
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Lamon (1999) notes that one major conceptual hurdle that students must overcome is the idea that fractions are numbers in and of themselves, not a composition of two, distinct, whole numbers. Further, it is likely that students fail to recognize fractions as discrete numbers because much of school mathematics focuses on understanding fractions as parts of wholes or parts of sets. To a great extent, children's earliest experiences with fractions are situated in part-whole contexts where both the part and the whole are whole numbers. Many of these experiences involve partitioning items like brownies or pizzas into equal regions. These are worthwhile endeavors for young children, but at some point, students must transition to thinking about fractions in ways that are more sophisticated.
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