In this study, our team observed sixth-grade teachers as they taught fractions to students in their mathematics intervention classes to see whether they were including motivational-supportive messages within the framework of Situated Expectancy-Value Theory. Messages in the intervention lessons and teacher transcripts were explored and analyzed,…

This article analyzes Malaysian and Japanese educators' reactions to a mathematics lesson observed by a subset of researchers. The main aims are to reveal the cultural scripts about mathematical learning that are held by, but often invisible to, members of a culture; and to address educators' conceptions of teaching mathematics across cultures.…

The purpose of this research was to investigate students' mathematical understandings of fraction division with an ethnomathematics/STEM framework. A small group teaching study (Cobb et al., 2003) was conducted using design research methodology to examine how students interacted with the curriculum. The researcher served as interventionist and…

Manipulative-based instructional sequences have proven to be successful with students with disabilities. However, instruction must not only support the acquisition of conceptual and procedural knowledge but also build on students' strengths. This article describes how teachers can use manipulative-based instructional sequences to support the…

The number line is a powerful tool for supporting students' understanding of fraction magnitude. Fractions are a critical component of mathematics instruction in the elementary and intermediate grades. More specifically, understanding fraction magnitude is central to mathematical development. Yet, fractions are challenging for many students,…

This study's purpose was to examine the effects of the concrete-representational-abstract integrated (CRA-I) sequence on the performance of students who struggled with rational number concepts. Three students in southeastern U.S. fifth grade class participated in the study. The CRA-I intervention was grounded in the principles of explicit…

Education has always been and will continue to be the key that unlocks doors of opportunity and success for all. Our national test scores, over the last several decades, reveal that a majority of America's students are failing to meet academic benchmarks and standards, thus limiting the possibilities for opportunity. Mathematics, in particular,…

Preservice teachers commonly struggle with topics related to fractions, ratio, and proportion. The use of double number lines can facilitate the teaching in these areas and provide autonomy and flexibility in mathematical thinking. Moreover, double number lines support many topics in the curriculum, including unit rate, convenience scaling, and…

This study is an examination of 79 elementary prospective teachers' (PSTs') capacity for recognizing the core ideas involved in modeling fraction addition problems and their difficulties in solving and presenting the process of fraction addition using area, length, and set models. PSTs completed a written task in which they represented the process…

After years of noticing the challenge our students have with fraction operations, we decided to implement a scaffold approach that focuses on using benchmarks to better develop both students' understanding of a fraction as a quantity and their ability to think about fraction operations meaningfully. While we found this approach supported students…

Students are indeed weak when it comes to understanding fractions and decimals. In line with the national curriculum, whole numbers and fractions are taught first before students start to learn decimals. By the time the students approach decimals, they should have acquired sufficient knowledge of whole numbers but limited knowledge of fractions.…

In this theoretical paper, I use an empirically based example to illustrate particular design features of the Learning Through Activity (LTA) design framework and examine the impact of particular design principles. The LTA design framework is based on our elaboration of Piaget's construct of reflective abstraction. The example discussed here,…

This paper reports on a key representation, a triple number line, designed as part of the first author's doctoral study. The study sought ways to represent multiple constructs of fractions in the context of merging music and mathematics to support learners' understanding of fractions. A problem scenario was designed guided by Realistic Mathematics…

The algorithm for fraction multiplication is relatively easy to memorize and implement with accuracy. The simplicity of the algorithm masks the conceptual complexity involved in making sense of what fraction multiplication means in quantitative situations. One important interpretation of fraction multiplication involves fraction composition,…

Fractions are among the most problematic concepts that children encounter in their primary school years because of the many different conceptions of fractions. Textbook analyses have tried to provide insights into how fractions are introduced, focusing on the different concepts and representations of fractions. In this paper, we contribute to…