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…

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…

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,…

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.…

Finding ways for students to use manipulatives in a safe, yet collaborative, manner is a challenge the 2020-2021 school year introduced. Teachers scrambled to create a set of manipulatives for individual use on a budget so students could learn from home, in hybrid environments, or in socially distanced classrooms. This article presents a…

In this study, we present a mathematical analysis distinguishing two conceptions of equivalence: "proportional equivalence" and "unit equivalence." These two conceptions have distinct meanings in relation to equivalent fractions: one is grounded in proportionality, while the other is grounded in equal wholes. We argue that (a)…

The teaching of fractions is often identified as the point in primary school instruction when the "wheels tend to fall off". While there could be many reasons for this, the overuse of one 'preferred' resource at the expense of a range of representations will often create gaps in understanding at best, and misconceptions at its worst. In…

Getting the right answers in maths is only half the problem. Understanding why what you're doing works is the part that often stumps students and teachers alike. The essential guide for mathematics teachers and those training to teach, "Yes, but Why?" answers all your questions, and sheds light on the hidden connections between…

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…