The traditional technique for converting repeating decimals to common fractions can be found in nearly every algebra textbook that has been published, as well as in many precalculus texts. However, students generally encounter repeating decimal numerals earlier than high school when they study rational numbers in prealgebra classes. Therefore, how…

Designing a mathematically worthwhile task is critical for promoting students' reasoning. To improve task design skills, teachers often engage in collaborative lesson planning activities such as lesson study. However, to learn from the process of lesson study, it is important for teachers to notice productively the concepts, students' confusion…

Transitioning from teaching whole number operations to teaching fraction operations can prove difficult, even for the seasoned mathematics teacher. However, with effective literacy practices, teachers can seamlessly shift their students to learning the rules for fractions. The implications can be a mastery of mathematical language used to describe…

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.

National and state assessments show that English language learners (ELs) in elementary and secondary grades score lower in mathematics compared with their matched English proficient peers (EPs). To provide information on strategies for enhancing learning opportunities for ELs in language inclusive classrooms, we analyze the efficacy of…

In the current study we examined the effect of a self-regulated strategy development intervention on the fraction calculations of students with or at risk for disabilities using a multiple-baseline-across-sites, single-case design. Specifically, the intervention package addressed the following skills: adding and subtracting fractions with unlike…

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…

Inspired by the promise of new 3D technologies and the proposition that new tools make innovation possible, this article provides a case study of how a tool called Thirty6 was designed and used in classrooms by mathematics teachers in their own varied and invented ways. Unlike established manipulatives that are designed to support the learning of…

This study highlighted the characteristics and patterns of preservice teachers' informal formative assessment conversations woven into mathematics classrooms. Participants were four preservice teachers from an elementary mathematics methods course whose videotaped lessons were analyzed using an analytic framework based on Initiation, Response and…

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…

Using multiple representations and changing between them is at the heart of the mathematics classroom; unconnected changes can, however, be obstructive for students' learning. In order to support students' learning with multiple representations, teachers have to link observed situation aspects with relevant professional knowledge, a competence we…

It is important for pre-service teachers to know the conceptual difficulties they have experienced regarding the concepts of multiplication and division in fractions and problem posing is a way to learn these conceptual difficulties. Problem posing is a synthetic activity that fundamentally has multiple answers. The purpose of this study is to…

Pedagogical content knowledge forms the core of teachers' professional knowledge; it refers to knowledge about making subject matter accessible to students. Thus, the formation of pedagogical content knowledge constitutes a crucial issue for educational research and practice. We investigated the contributions of content knowledge and pedagogical…

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…

We present study findings that depict the natural and fractional number knowledge of one third grade student with learning disabilities (LDs) in seven experimental sessions. We utilize qualitative analysis methods to illustrate how this student evidenced her knowledge of natural number and fractions through her interactions with varied learning…