Academic journal article International Electronic Journal of Elementary Education

Sixth Grade Students' Skills of Using Multiple Representations in Addition and Subtraction Operations in Fractions *

Academic journal article International Electronic Journal of Elementary Education

Sixth Grade Students' Skills of Using Multiple Representations in Addition and Subtraction Operations in Fractions *

Article excerpt

Introduction

Most people define mathematics as a field consisting of abstract concepts, algorithms, and symbols without any connection with real world (e.g. Cramer, 2003). For this reason, researchers emphasize the necessity of teaching mathematics as an integrated concept and processing system based on certain patterns and associations that exist in the real world (Nair & Pool, 1991; Resnick & Ford, 1981). This necessity causes long debates in the need for using appropriate representations in teaching and learning of mathematics in terms of having complete understandings of mathematical concepts, expressing mathematical ideas and relationship between concepts (Duval, 2006; Goldin & Shteingold, 2001). Moreover, taking advantage of different representations in the teaching of a mathematical concept and making transitions between different forms of representations are critical in terms of a complete internalization of mathematics. (Kaput, Blanton, & Moreno, 2008; Lesh, 1999; National Council of Teachers of Mathematics [NCTM], 2000). Hence, the use of representations has been a crucial topic in learning of mathematics over the past three decades in standards of school mathematics for developing students' abilities to use appropriate representations and to make correct and robust translations among them (Ministry of National Education [MoNE, 2013]; National Council of Teachers of Mathematics [NCTM], 2000; Van de Walle, Karp, & Bay-Williams, 2010). However, studies focusing on students' abilities in use of representations indicate that middle school students have inadequate knowledge and ability to construct appropriate representations and to transform from one representation to the others (Gagatsis & Elia, 2004; Neria & Amit, 2004).

Multiple representations can be defined as a process of visualizing and concretizing abstract concepts or symbols in everyday life in general terms, as well as the definition of the relationship between objects or symbols in mathematics (Kaput, 1989). The theory of multiple representations in mathematics education has begun to gain importance with the studies of Dienes. Influenced by Piaget's theories and made studies with Bruner, Dienes called the concept of multiple representations as "Perceptual Diversity Principle." According to this principle, presenting a conceptual structure in multiple forms as perceptually identical as possible will make it easier for the student to have the mathematical significance of abstracting (Dienes, 1960). In this context, concepts should be able to be presented in different forms. Multiple representations and the learning relationship point to a learning environment with a particular focus on conceptual learning (Dufour-Janvier, Berdnarz, & Belanger, 1987). In this context, mathematics teachers need to consider and effectively use multiple representations of information in verbal, numerical, visual graphical or numerical forms, with the support of developing technology, rather than using only intensive verbal and mathematical language.

Research on multiple representations in mathematics teaching has shown that using multiple representations helps students better understand and improve their problem solving performances (Ainsworth, Bibby, & Wood, 1997; Akkuş-Çıkla, 2004; Moseley & Brenner, 1997; Sert, 2007). If it is not possible to switch between different representations, it can be said that the mathematics cannot be understood at the conceptual level (Ainsworth, 1999; Van der Meij & De Jong, 2006), When studies focusing on multiple representations are examined, it has been shown that the efforts of the students to determine the ability to switch between different representations are based on problem solving (Corter & Zahrer, 2004; İpek & Okumuş, 2012; Lesh, Landau, & Hamilton, 1983), algebraic expressions (Sert, 2007) and function (Baştürk, 2010). Moreover, some studies focused on the ability of students' and teachers' preferences for multiple representations (Ainsworth, 1999; Akkuş-Çıkla, 2004; Sert, 2007). …

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