Transitioning from teaching whole number operations to teaching fraction operations can prove difficult, even for the seasoned mathematics teacher. However, with effective literacy practices, teachers can seamlessly shift their students to learning the rules for fractions. The implications can be a mastery of mathematical language used to describe…

In this paper, we have tried to clearly explain the meaning of fractions and operations with fractions. Also, we have tried to illustrate with some examples how to apply the rules of operations with fractional numbers, giving different practical techniques through different figures, visualization methods, and concretizing problems. The paper…

Teaching fraction operations for conceptual understanding is a challenging task. For the topic of fraction division especially, teachers need support because teachers find this difficult to teach and elementary and middle school students struggle to learn this concept. Well-structured professional development can assist teachers in exploring their…

Despite the research regarding the importance of peer review and feedback in pre-service special education teachers, there exists a gap in teaching complex mathematical concepts such as fractional operations. This study sought to address this gap by investigating how pre-service teachers can effectively appraise and revise peer-generated teaching…

Learning progressions can reflect students' continuous in-depth thinking development paths, and their establishment is an iterative process from the construction of hypothetical learning progressions to the verification of that hypotheses. Considering the limitations of the existing verification method of learning progressions based on a rule…

In a previous study, we validated the fractions schemes and operations trajectory (Norton and Wilkins 2012; Steffe in J Math Behav 20(3): 267-307, 2002; Steffe and Olive Children's fractional knowledge. Springer, New York, 2010; Wilkins and Norton 2011) with PreK-8 prospective teachers and explored PreK-8 prospective teachers' understanding of…

Using memorized rules and algorithms without coherence and understanding is a perennial problem for teachers and students especially in the teaching and learning of fraction operations. I present data in which prospective middle school teachers explain a commonly used rule for fraction division--keep-change-flip. I argue that using both strip…

Although fraction operations are procedurally straightforward, they are complex, because they require learners to conceptualize different units and view quantities in multiple ways. Prospective secondary school teachers sometimes provide an algebraic explanation for inverting and multiplying when dividing fractions. That authors of this article…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as:…

The data used for the qualitative analysis reported here were generated as part of a larger study to understand and characterize teacher practice related to engaging students in algorithmic thinking associated with the fraction operations of addition, subtraction, multiplication and division. This paper presents ways in which teachers used…

The purpose of this research was to determine if recognizable error types exist in the work of preservice teachers required to create story problems for specific fraction operations. Students were given a particular single-operation fraction expression and asked to do the calculation and then create a story problem that would require the use of…

This article provides an example of how one sixth-grade classroom teacher and an instructional coach built a bridge for students in a grade 6 self-contained classroom to support their conceptual understanding and procedural fluency with dividing fractions. Baseline data showed that most of the students in this class had mastered only the…

I explore the impact of ambiguous referral to the unit on understanding of decimal and fraction operations during episodes in two different mathematics courses for pre-service teachers (PSTs). In one classroom, the instructor introduces a rectangular area diagram to help the PSTs visualize decimal multiplication. A transcript from this classroom…

This paper reports an exploration into Indonesian fourth graders' difficulties in fractions and their relation to the opportunity to learn fractions students got at schools. The concept of "opportunity to learn" is often considered as a framework to investigate possible reasons for students' difficulties. The data for this study was…