As a part of the larger study, a case study of two seventh grade students, Peter and Willa, was conducted. To examine links between their fractional knowledge and algebraic reasoning, the students were interviewed twice, once for their fractional knowledge and once for their algebraic knowledge in writing linear equations that required explicit…

Competence with fractions is foundational to acquiring more advanced mathematical skills. However, achieving competency with fractions is challenging for many students, especially for those with mathematics learning difficulties who often lack foundational skill with whole numbers. Teaching fractions is also challenging for many teachers as they…

The study has two primary purposes. The first was to examine the efficacy of the "Super Solvers" Fractions Intervention (SSFI) for third-grade students at risk for mathematics learning disabilities (MLD). The second was to test the added value of embedding self-regulation instruction into the SSFI. Students were randomly assigned to a…

Previous research has shown knowledge, perceptions, and attitudes are essential factors during mathematics classroom instruction. The current study examined the effects of a 3-week fraction instructional unit using concrete models, problem-solving, and problem-posing to improve elementary preservice teachers' knowledge, perceptions and attitudes…

This study investigated 111 pre-service teachers' (PSTs') flexibility with referent units in solving a fraction division problem using a length model. Participants' written solutions to a measurement fraction division problem were analyzed in terms of strategies and types of errors, using an inductive content analysis approach. Findings suggest…

The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…

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…

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…

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…

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.

The narrative permeating higher education institutions globally is the assimilation of advancing information and communications technology into mainstream Mathematics Education. In this paper we report on a mixed mode case study which explored possible mathematical gaps that created barrier/s when engineering students (n=162) worked with the…

Adults use a variety of strategies to reason about fraction magnitudes, and this variability is adaptive. In two studies, we examined the relationships between mathematics anxiety, working memory, strategy variability and performance on two fraction tasks: fraction magnitude "comparison" and "estimation." Adults with higher…

In this study, we investigated how elementary pre-service teachers (PSTs) perceive using representations in teaching mathematics and what fractional representations (e.g., manipulatives or models) they suggest to guide students' incorrect use of representations in learning fractions. A written questionnaire was administrated to 151 PSTs at a large…

According to the design principle of progressive schematization, learning trajectories towards procedural rules can be organized as independent discoveries when the learning arrangement invites the students first to develop models for mathematical concepts and model-based informal strategies; then to explore the strategies and to discover pattern…