The teaching of fractions is often identified as the point in primary school instruction when the "wheels tend to fall off". While there could be many reasons for this, the overuse of one 'preferred' resource at the expense of a range of representations will often create gaps in understanding at best, and misconceptions at its worst. In…

This qualitative, multiple case study provided comprehensive descriptions of the conceptual difficulties and learning experiences of in-service teachers as they improved their ability to effectively model fraction division with pictorial diagrams. Video data were collected on eight teachers as they individually progressed through a professional…

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…

In this research, a new test for understanding simple fractions has been developed for students at the beginning of lower secondary education. In many countries, mathematics education in Grade 5 builds on elementary students' developing concepts of fractions. Understanding fractions causes many difficulties for students, and research on mental…

In grade 3, students are expected to be able to represent a fraction on a number line by first identifying the interval from 0 to 1 as the unit and by partitioning the unit as needed on the basis of the denominator. This task extends these grade 3 fraction goals stated in the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010)…

During lesson study teachers collaborate to design, teach, observe, and reflect on a lesson with the overarching goals of improving instruction and increasing student learning. This article examines how a 6th grade mathematics lesson study project challenged teachers' ideas and assumptions about their students' understanding of fraction concepts.…

Number lines and area models are both used pervasively in teaching fractions. Prior studies found that second and third graders demonstrated better magnitude knowledge of proper fractions after a 15-minute training using the number line as compared to using the area model. The current study aimed to extend these findings to improper fractions. We…

In this article the authors overview how the recently revised (version 9) Australian Curriculum (Australian Curriculum Assessment and Reporting Authority, 2022) and student difficulties with fractions relate to five developmental Fraction Schemes developed from multiple research projects in the literature. The article shares research findings from…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

To make complex mathematics concepts accessible to students, teachers often rely on visual representations. Because no single representation can depict all aspects of a mathematics concept, instruction typically uses multiple representations. Much research shows that multiple representations can have immense benefits for students' learning.…

The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties (N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was…

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…

The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties (N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was…

In these two companion papers, a learning activity is introduced that teaches students how mathematics works through the visual aid of picture grids. The picture grids are composed of 60 different acrylic stained-glass window overlays. Each fractional part is represented by a different color: fifths are green, quarters are yellow, etc. The square…

Describes three classroom techniques involving bulletin boards for the mathematics classroom; a visual representation of fractions in which the school day is broken up into parts by hour; and methods to test and review mathematical concepts while students work cooperatively. (MDH)