The aim of this longitudinal study was to examine the differences between high- and low-performing students' development of fraction proficiency over a school year and to investigate how those differences were related to instruction in fractions versus instruction in other mathematics topics. The data for this study were drawn from a group of (n =…

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…

Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often, conceptual knowledge by means of exploratory tasks. However, both types of knowledge are needed for complete domain knowledge that persists over time and supports subsequent learning. We investigated in two…

Research suggests teachers have positive motivational and emotional orientations regarding statistics but little statistical knowledge. How does this fit together? Since teachers' professional competence in statistics has not been well explored, we asked 88 in-service mathematics teachers about their orientations regarding teaching statistics and…

This research aimed to develop a valid and reliable test to be used to detect sixth grade students' misconceptions and errors regarding the subject of fractions. A misconception diagnostic test has been developed that includes the concept of fractions, different representations of fractions, ordering and comparing fractions, equivalence of…

The main purpose of this study is to assess pre-service and public elementary mathematics school teachers' conceptual understanding and computational abilities of fractions. 20 pre-service mathematics teachers and 24 in-service mathematics teachers participated in this study. In-service teachers were divided into two categories; one for teachers…

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…

This study examines the different ways in which fractions are dealt with in two elementary mathematics textbook series: Kang Hsuan (KH) in Taiwan and Laskutaito in Finland. The results showed that the total number of fraction questions in Laskutaito is higher than that in KH and that Laskutaito highlights the basic definition of fractions to help…

This study analyzed the methods used to teach the multiplication of fractions in Turkish and American textbooks. Two Turkish textbooks and two American textbooks, "Everyday Mathematics" (EM) and "Connected Mathematics 3" (CM), were analyzed. The analyses focused on the content and the nature of the mathematical problems…

We report on mixed methods research that explored pre-service teachers' pedagogical content knowledge in basic musical methods for teaching and learning of basic fractions within the framework of Vygotsky's Theory of Scaffolding. Vygotsky's use of scaffolding opines that knowledge, skills and prior experiences, create the foundation for potential…

We report on mixed methods research that explored pre-service teachers' pedagogical content knowledge in basic musical methods for teaching and learning of basic fractions within the framework of Vygotsky's Theory of Scaffolding. Vygotsky's use of scaffolding opines that knowledge, skills and prior experiences, create the foundation for potential…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

Teaching simulations such as scriptwriting tasks offer a novel way to support pre-service teachers in gaining diagnostic competencies and in guiding students to work through difficulties. We first report on the theory-driven development of a scriptwriting task, specifically the theoretically-founded language- and accompanying content-related…

A deep understanding of fraction concepts and operations is necessary if pre-service teachers (PSTs) are to present the concepts in multiple forms to learners. Such an understanding needs to be grounded in rich conceptual knowledge. In the present study, we explore the development of this understanding by supporting a cohort of 103 PSTs, who had…

The contribution investigates opportunities that an educational tool called Concept Cartoons can offer in future teachers' education, namely in comparison with word problems in standard written tests. The referred empirical study was conducted in two separated consecutive stages, with two groups of future primary school teachers (the first one…