This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…

Algebra as a study of quantitative relationship is one of four conceptions of school algebra which serves as a foundation for the concept of function. However, there is still a lack of attention to this particular relationship, especially in early algebraic reasoning. This study aims to investigate how the aspect of quantitative relationship in…

When students are working together, some off-task conversations actually smooth the way to working together more effectively. While many assume that off-task talk is unproductive, our study revealed that students used off-task talk predominantly for productive purposes. We found that off-task talk supported student access to collaboration, and…

Integrating multiple theoretical frameworks, the authors examined rising first- to fourth-grade students' mathematics utility conceptions--their knowledge and beliefs about the usefulness of mathematics, home-based mathematics engagement, and grade-level differences in mathematics utility conceptions and home engagement. Most children viewed…

The importance of ratio and proportional reasoning is regularly emphasised, however, the teaching and learning of these concepts continues to present challenges. In this article the authors explore a hands-on task, designed to encourage student visualisation of the concept of ratio. Teacher perceptions of this task were positive, indicating the…

This study aims to investigate how set model can help students' understanding of addition of integers in fourth grade. The study has been carried out to 23 students and a teacher of IVC SD Iba Palembang in January 2015. This study is a design research that also promotes PMRI as the underlying design context and activity. Results showed that the…

The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents--for example, the Common Core State Standards for Mathematics (CCSSI 2010) and "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics [NCTM] 2000). However, the…

Identity is an important tool for understanding students' participation in mathematics lessons. Researchers usually examine identity at a macro-scale: across typical classroom activity and in students' self-reports. However, learning occurs on a micro-scale: in moments during a lesson. To capture identity in these moments, I used positioning…

Researchers have linked teachers' use of mathematical tasks and questions to students' achievement in mathematics, and also have documented that the types of tasks and questions posed might change throughout the year in grades that include high-stakes tests of student achievement. This qualitative research study explored 3 elementary school…

Research shows that children of different backgrounds and cultures learn and perform differently in mathematics despite similar intelligence levels and mathematics instruction (Alvarez & Bali, 2004). Ethnomathematics strives to explore and explain such phenomena in terms of the complex role culture plays in one's background experiences and…

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, "TinkerPlots." Initial responses indicated that the students were aware of…

This book provides targeted mathematics instruction for every child. This book combines formative assessment with practical activities to differentiate the elementary classroom. The formative assessments include student work samples at varying levels. The authors: (1) Illustrate the distinction between a "traditional" assessment and an "enhanced"…

Recent reform efforts in mathematics education have stimulated a focus on learning trajectories. At the same time, a global increase in high-stakes testing has influenced instructional practices. This study investigated how four fourth grade teachers within a school planned and enacted lessons to understand what mediated their planning and…

"Bars, Lines, & Pies" is a dynamic math program designed to build graphing skills in students, while also showing them the relevance of math in their lives. Developed by The Actuarial Foundation along with Scholastic, the graphing lessons and activities involve engaging, real-world examples about the environment and recycling. In these lessons,…