# The Principles Of Knowledge For Manipulating Fractions And Decimals

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Fractions Constructs in fractions extend many of the principles encountered in multiplicative thinking. It has been observed language and a variety of models improve understanding of these constructs (Reys et al, 2012). Therefore, these models should be scaffolded to develop student skills and knowledge for manipulating fractions with operations. The underpinning principle is the part-whole construct (Charalambous & Pitta-Pantazi, 2005). The subconstructs for fractions that build on this construct are quotient, ratio, measure and operator (Charalamous & Pitta-Pantazi, 2005; Clarke, Roche & Mitchell, 2008). As with multiplicative thinking there is a loose sequence to learning these constructs which overlaps. Their instruction during the primary years is important because a fifth-grader’s fractional knowledge can predict later outcomes in mathematics (Dooren & Vershaffel, 2015). There are both universal and distinct aspects to fractions and decimals. Universally, they need to be discussed in class, including discussion of individual answers (Reys et al., 2012). Learner interaction is consistent with Vygotsky’s belief social negotiation develops higher cognitive processes (Woolfolk & Margetts, 2013). Students must talk and listen to each other (Woolfolk & Margetts, 2013). This is not unique to fractions of course, as it also applies to every big idea in mathematics. However, the order of acquisition is a point of difference between fractions and decimals. Reys et al (2012)