A task-based written survey was administered to 69 pre-service teachers (PSTs) at a large Midwestern University in the USA to examine their recognition of examples/non-examples of [one-fourth] presented in various forms of the area model, their perceived mathematical key points in identifying examples/non-examples, and their instructional…

Our research with Grade 9 learners at a school in Soweto was conducted to explore learners' understanding of fundamental fraction concepts used in applications required at that level of schooling. The study was based on the theory of constructivism in a bid to understand whether learners' transition from whole numbers to rational numbers enabled…

Positioning teachers as designers of curricular resources invites opportunities for exploration at the intersection of content, pedagogy, and design. As researchers accepting greater responsibility for preparing teachers to maintain a commitment to their pedagogical vision in practice, this work seeks to cultivate the imagination of humanistic…

Research on fraction knowledge has revealed that prospective teachers' (PSTs) often lack fraction proficiency. The aim of this dissertation was to develop and test an intervention intended to increase PSTs' fraction proficiency by focusing on fraction comparison. I first adopted a five-dimensional framework to define PSTs' fraction proficiency. I…

This study evaluated the effects of the "Super Solvers" Tier II fraction intervention program on the algebra and fraction skills of secondary students with mathematics learning disabilities and consistent low achievement in mathematics. A quasi-experimental group design was used to evaluate the performance of the treatment and control…

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…

Mobile devices, and their applications, are becoming common-place around the world, and especially with adult-age college students in the United States. At the same time, community college students who are interested in becoming members of the trade workforce, such as auto mechanics, are continuing to need to learn basic mathematic concepts such…

This case study aims to describe the learning characteristics of a child and evaluate his preferences for using physical manipulatives (PM) and virtual manipulatives (VM) to solve fraction problems. The participant in this study was a fourth-grade child. The child was given similar problems to solve using PM and VM. Data sources were observations…

This paper describes the authors' journey in designing a linear representation that aligns mathematics and music to support fractional reasoning. The three authors, guided by the theoretical framing of realistic mathematics education, engaged in a task design process over a 12-month period to develop integrated resources. Data were collected in…

Context: The island of Malta is a former British colony, and to this day, education continues to be accessed bilingually. For mathematics education, Maltese and English are used for verbal interaction, with subject-specific words tending to be retained in English. Written mathematics texts are in English, including textbooks, worksheets, digital…

Promoting an understanding of multiplication of fractions has proved difficult for mathematics educators. I discuss a research study aimed at developing a concept of multiplication that supports both multiplication of whole numbers and multiplication of fractions. The study demonstrates how domain-specific theories grounded in two major…

This commentary raises and discusses questions based on some of the agreements, disagreements, and themes found in the four chapters on fractions. It considers (1) the importance of tasks that are based in perception and readily available activity in light of an emphasis on problem solving in mathematics education, and the role that theories about…

Purpose: This paper seeks to understand how teachers' mathematical knowledge for teaching (MKT) is developed during a lesson study regarded as a professional development process that places particular emphasis on teachers' knowledge of tasks, representations and students' learning. Design/methodology/approach: This study is based on the networking…

The current study examined lasting learning effects of communal contexts for 124 African American third and fourth-grade students using a mathematics fractions unit with students' regularly assigned teachers. Teachers in two experimental conditions received training on implementing communally or individually structured fractions curricula, and a…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction "x/y," children are often taught to use "partitioning": break the whole into "y" parts, and shade in "x" parts. Past research has shown that partitioning on number lines supports children's fraction…