Academic journal article Curriculum and Teaching Dialogue

Teaching and Learning of Fractions in Elementary Grades: Let the Dialogue Begin!

Academic journal article Curriculum and Teaching Dialogue

Teaching and Learning of Fractions in Elementary Grades: Let the Dialogue Begin!

Article excerpt

Fractions are a challenge, yet they form a critical conceptual base for proportional reasoning and other mathematical concepts. Hence, it is imperative to look deeply into the development of students' fractional thinking, especially in elementary grades where they are first exposed to fractions. The Common Core State Standard Initiative (2010) for mathematics does not address fractions in early grades but rather recommends the major introduction fractions in the third grade with very limited experiences in first and second grade. This study adopts a contrasting view by examining fractional understanding of students who had been exposed to fraction instruction from kindergarten to third grade. A multiple-case study approach is adopted to gain an in-depth insight into students' fractional understanding as a function of time. Results of the study urge mathematics educators, teachers, and community to re-evaluate the current position of fractions in Common Core State Standards and mark the beginning of an important dialogue.

LITERATURE REVIEW

For over three decades, fractions have been recognized as a challenge for teachers, students, and mathematics educators (Behr, Lesh, Post, & Silver, 1983; Bezuk & Cramer, 1989; Brizuela, 2005; Charalambous & Pitta-Pantazi, 2007; Cwikla, 2014; Kieren, 1976; Lamon, 2005; National Mathematics Advisory Panel, 2008; National Research Council, 2001; Petit, Laird, & Marsden, 2010; Siegler, Fazio, Bailey, & Zhou, 2013). The National Assessment of Educational Progress (NAEP) has shown that students have problems with fractions (Good et al., 2013). Additionally, according to Mazzocco and Devlin (2008) only 59% of the sixth graders with an IQ of 116 could correctly order a set of fractions. The National Mathematics Advisory Panel (2008) reports the percentage of middle school students that face difficulties with fractions as high as 40%. These examples point out that students have difficulties with fractions even in middle and high school and hence it becomes even more important to give due attention to the development of conceptual understanding of fractions in early elementary grades.

Fractions are the first experience that students have with rational numbers in the elementary grades. Students face difficulty with conceptualizing a fraction as a number in the form of a/b, where b is not zero. Moreover, fractions have their own set of well-defined and well-known operations such as the commutative and associative properties of addition and multiplication, identity operations, and others that require students to expand their realm of whole numbers and its knowledge. Carraher (1996) iterates that viewing a fraction simply as a number is "pedagogically naive as well as historically and psychological inaccurate" (p. 241). Understanding fractions requires students to understand the relationships between numbers and quantities and be able to express these relationships in diverse ways. For example, a fraction like "1/2" is a powerful mathematical idea that can present several different relationships. Lamon (2005) states that the relative size of "1/2" changes depending on the whole that requires students to think about fractions differently beyond cognitive structures of whole numbers, thus creating difficulties and confusions.

Motivated by providing early elementary students with rich experiences that would enable them to build conceptual understanding of fractions, this research study was designed to expose early elementary students to focused fraction instruction that incorporated use of manipulatives. According to Post (1981), manipulatives parallel the real-world and the models help students make conclusions and predictions about the real-world, thus gaining an insight into the mathematical concept. Providing concrete representations gives students a platform to be more successful with fractions and develop a strong understanding of fraction concepts (Bezuk & Cramer, 1989; Cramer & Wyberg, 2009; NCTM, 2014; Van de Walle, Karp, & Bay-Williams, 2010). …

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