Restructuring And Performing Operations With Fractions In The Classroom

Truly understanding fractions and performing operations with fractions can often be difficult for many children and even adults. According to N. Krasa and S. Shunkwiler (2009), “Learning fractions is like stepping into the upside-down world beyond Alice’s looking glass. No wonder children are confused!” (p. 115). Discovering fractions in a way that enhances a student’s number sense is extremely important before the student begins operations with fractions. The Common Core State Standards for Mathematics in Oregon explain what a child in a certain grade must know concerning number sense and fractions. For example, standards 4.NF.1 and 4.NF.2 state that students in the fourth grade must be able to find, identify, and explain why two fractions

The NCTM (2002) says that there are two phases of development when learning fractions: finding the meaning of fractions in regards to the link between division and divided quantities and discovering the strange properties of fractions (p. 7). Since developing a number sense of fractions is so important, teachers need to pick their students brains to decipher their thinking. According to the NCTM (2007), “Because getting the right answer is not always enough, teachers should implement classroom strategies to gather information on how students obtained the right answer (or wrong answer)” (p. 218). Problems that encourage students to explain their thinking can help the teacher discover how the students are processing the problem: either conceptually or procedurally. According to Krasa and Shunkwiler (2009), China’s education system implements the learning of fraction number sense in this specific order: the concept of fractions, decimals as special fractions with denominators of 10, decimal operations, multiples, factors, prime factors, improper fractions, mixed numbers, reducing fractions, common denominators, and finally, operations with fractions (p. 116). China’s approach is very logical and could be useful in the classroom. According to A. M. Klein (2003), the best learning environment for conceptual understanding is one that allows time for exploration, provides tools and models, and encourages children with a nurturing presence from the teacher (p.17). The authors of Helping children learn mathematics (2004) stress that teachers should “start with the simplest meaning and model” (p. 288). It is up to the teachers to create an environment where learning fractions is an exploration based on reasoning not a