In this study, it was aimed to reveal the explanatory strategies that preservice teachers use in the process of explaining the concept of divisibility by zero. It was investigated how the concept of divisibility by zero, which can be used in expressing the case where the denominator is present in the definition of important concepts of the…

This study examined the effects of two teaching treatments [multiple-representation instruction (MR) and traditional algorithmic instruction (TA)] on students' performance on mathematics problems that integrated fractions, decimals, and percent. Using a 2 × 2 crossover design, the effect of the teaching treatments and their sequences on student…

Students with mathematics learning disabilities (MLD) often require more intensive intervention in addition to quality core mathematics instruction. This research evaluates the effects of a point of view video modeling (POVM) intervention including virtual demonstrating of concrete mathematics manipulatives to teach simplifying fractions. Three…

In this article we present an overview of four studies investigating Greek secondary students' conceptual and procedural knowledge of fractions. We discuss the problem of defining conceptual and procedural knowledge, and the implications of adopting one particular definition over others. We draw on the studies and their results to discuss the…

The purposes of this study were twofold. The first was to test the efficacy of two versions of the "Super Solvers" (SS) intervention for fourth- and fifth-grade students at-risk for mathematics learning disabilities (MLD). The second was to test the value of adding an error analysis component to the SS intervention. Students were…

Students' sound knowledge of mathematical concepts is important for the development of their mathematical knowledge to support the more challenging application skills at higher levels of mathematics learning. Diverse classroom teaching strategies with appropriate teaching tools are crucial to ensure that students meaningfully achieved the set…

Teaching fraction operations for conceptual understanding is a challenging task. For the topic of fraction division especially, teachers need support because teachers find this difficult to teach and elementary and middle school students struggle to learn this concept. Well-structured professional development can assist teachers in exploring their…

In this paper, we present a design experiment in a "Teaching Mathematics" course for prospective elementary teachers where we sought to develop a "measurement approach" to fractions. We focus on the conceptualization of the mathematical content of the approach. We attribute our progress in the conceptualization to our efforts…

In this commentary, I examine some of the distinctive, foundational difficulties in learning fractions and other types of rational numbers encountered by students with a mathematical learning disability and how these differ from the struggles experienced by students classified as low achieving in math. I discuss evidence indicating that students…

This research examined the role of the teacher in supporting students to make sense of fraction multiplication when using a problem solving approach. Using a qualitative approach, the teaching of four skillful experienced sixth-grade teachers was examined as they implemented a problem-based unit on fraction multiplication. This paper will present…

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…

A formative pilot study of a fractions intervention was conducted to address the intervention's potential for improving fifth-grade struggling students' knowledge of fractions, and to identify any logistical or instructional design issues, before scaling up for a randomized control trial. In the first section, we provide details of the formative…

The main purpose of this study was to develop a scale for measuring content knowledge (CK) and pedagogy content knowledge (PCK) of in-service elementary teachers on mathematical fractions. Another aim of this study was to consider whether CK and PCK are separate from each other, or are in a single body. Therefore, a scale containing 22 items about…

We constructed and calibrated an instrument targeting conceptual and procedural fraction knowledge. We used this instrument in a quantitative study with 126 secondary students (7th and 9th graders), testing the hypothesis that there are individual differences in the way students combine the two types of knowledge. Cluster analysis revealed four…