We examined the development of numerical magnitude representations of fractions and decimals from fourth to 12th grade. In Experiment 1, we assessed the rational number magnitude knowledge of 200 Chinese fourth, fifth, sixth, eighth, and 12th graders (92 girls and 108 boys) by presenting fraction and decimal magnitude comparison tasks as well as…

This study's first purpose was to investigate effects of a fourth- and fifth-grade "next-generation" fraction intervention, which included six enhancements over a previously validated fraction intervention, designed to address career- and college-readiness standards. The study's second purpose was to assess effects of the next-generation…

This study used traditional and holographic video, along with eye-tracking technology, to examine how preservice teachers' physical act of looking is associated with how they attend to and assess students' fraction reasoning. Findings revealed that, although viewing of holograms may have influenced more focus on students' work area, there was…

Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers' attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using…

Despite receiving increasing attention from mathematics education scholars, there has not yet been any overall understanding of the current state of realistic mathematics education (RME). To address this gap, this study aims to provide a review of 288 studies on realistic mathematics education from the Scopus database between 1972 and 2019. Using…

The purpose of the systematic review of mathematics intervention syntheses was to identify patterns and gaps in content areas, instructional strategies, effect sizes, and definitions of learning disabilities (LD), mathematics LD (MLD), and mathematics difficulty (MD). Using rigorous inclusion criteria, we evaluated 36 syntheses that included 836…

The purpose of this study is to examine the effect of using concrete and virtual manipulatives relevant fractions subject to 3rd grade students' understanding of fractions and motivation towards mathematics lessons. The study group consists of 61 students studying in three different classes at the 3rd grade level of a private primary school in…

Given its pedagogical appeal, the number line is a commonly used representation in the teaching and learning of fractions. However, behind its apparent simplicity, this mathematical object may involve layers of complexity when looked at from the perspective of affordances as is the case in this study. In particular, this in situ exploration…

The aim of the current study is to investigate the effects of digital teaching materials on 4th graders' academic achievement on fractions subject and attitudes towards mathematics and computers. The study was planned with a pretest and posttest control group design. The participants of the study were 60 students studying in a public elementary…

We analyzed item responses provided by a nationwide sample of 990 in-service U.S. middle grades mathematics teachers to a novel survey focused on fraction arithmetic. The survey targeted four components of reasoning in terms of measured quantities: "Referent units," "Reversibility," "Partitioning and iterating," and…

Background: Within the ambit of the Fourth Industrial Revolution (4IR), the use of technology-based tools within teaching and learning is advancing rapidly at education institutions globally, including the teaching and learning of mathematics. Learners and teachers have challenges with teaching and learning fractions in mathematics. A learner's…

This study investigated relations between the distribution of practice problems in textbooks and students' learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal…

The mathematical domain of fraction division continues to be an area of great difficulty for many teachers and preservice teachers (Lo and Luo, Journal for Mathematics Teacher Education 15:481-500, 2012; Newton, American Educational Research Journal 45:1080-1110, 2008; Rizvi and Lawson, International Education Journal 8(2):377-392, 2007; Young and…

This study was conducted with the aim of investigating the current knowledge of Primary Teachers and Primary Pre-service Teachers on the misconceptions of primary school students about the subject of fractions. The qualitative research method of case study was used to conduct the research. The data were collected with semi-structured forms that…

The book synergizes research on number across two disciplines--mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children's activity, including mental and physical actions. Subsequent chapters are organized into sections that…