Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014),…

Developing an understanding of fractions is critical as a significant predictor for the learning progression of advanced domains; however, students face significant challenges in learning fractions because of their unique properties. To systematically approach remediation, this study examined the common error patterns committed by middle-school…

The current study aims to show the transition skills of sixth grade students between the representations (numerical, model, number line and verbal) given in addition-subtraction operations in fractions and to analyse the ability of the students to construct each representation type. In this research, case study method was used in terms of the…

The goal of this study was to describe fraction-calculation errors among fourth-grade students and to determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low-, average-, or high-achieving). We…

The goal of the present study was to describe fraction-calculation errors among 4th-grade students and determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low- vs. average- vs. high-achieving). We…

Addition of fractions is an important foundation for students to experience success in mathematics. This mixed-methods study was conducted to measure the effectiveness of robotics as a mathematics manipulative with seventh grade students. Two groups of students were established: control and treatment. The control group received teacher-centered…

Mathematical knowledge in classrooms is mediated through the use of both technical and informal language. This paper is a report of a study of the language use of teachers as they examine students' work and discuss teaching for the topic of fraction operations. This provides a window on their pedagogical content knowledge and also on the way in…

The contributions of domain-general abilities and domain-specific knowledge to subsequent mathematics achievement were longitudinally assessed (n = 167) through 8th grade. First grade intelligence and working memory and prior grade reading achievement indexed domain-general effects, and domain-specific effects were indexed by prior grade…

Large-scale numeracy assessments are intended to facilitate the improvement of educational outcomes; however, it is not clear exactly how this is to be achieved. To move towards the goal of numeracy for all, it is necessary to systematically address issues that are known to be difficult, pervasive and persistent. This paper includes an analysis of…

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

This research study, carried out in South Africa and the United States of America, investigated issues that may hamper prospective primary school teachers from writing acceptable problem posing scenarios involving the addition of fractions. Pre-service teachers (n=44) were asked to compose real life problems involving the addition of two fractions…

This study examined various misconceptions committed by junior high school students in fraction addition and subtraction problems. Almost 600 subjects were administered two tests, addition and subtraction, and their performances were analyzed by several computer programs, including two programs (FBUG and SPBUG) which are so flexible to any items…

Four sequential Basic Skill Levels (levels G, H, HA, and I) of a self-paced, individualized mathematics program designed to improve the achievement of junior high school students are presented in this student workbook. Each level includes a pretest, four to seven lessons, quizzes (checkpoints) after each fourth lesson, a posttest, and a level…