This study investigated upper elementary teachers' framings of their students' mathematical thinking in written across the three component skills of noticing. Drawing on a situated perspective, the research examines the influences of teachers' culturalhistorical backgrounds, attitudes, dispositions, interactions with students, and other situated…

Competence with rational numbers is essential for mathematics proficiency in secondary mathematics. However, many students struggle with rational number concepts, and students with mathematics difficulties struggle even more. The purpose of this study was to examine the effects of an intervention that incorporated the use of explicit instruction…

Conceptual and procedural instruction order may affect students' learning and generalization of math skills. This study compared two instruction sequences, concepts-first and iterative, and their effect on fraction performance through a class-wide intervention. Fourth-grade students (N = 114) were randomly assigned to the concepts-first,…

This study used fraction number line estimation tasks to evaluate students' developmental patterns, and the relationship of such tasks with whole number bias was explored. In total, 189 fourth-grade students in a northern Taiwan elementary school were followed over 2 years. The results demonstrated that the students' fraction learning development…

This quasi-experimental study was designed to investigate the initial efficacy of a fraction-vocabulary intervention for Grade 4 students with mathematics difficulty (MD) and to explore its impact on relevant fraction competencies. Thirty-three students were assigned to either the intervention condition (n = 16) or a business-as-usual comparison…

Learning fractions poses a challenge for many elementary school students, including applying fraction knowledge in novel contexts. For instance, there are substantial individual differences in students' tendency of spontaneous focusing on quantitative relations (SFOR), which is related to the development of rational number knowledge. In this…

In this study, we examine students' mathematical reasoning within a technological environment designed to support understanding of relationships between quantities with adjustable measuring units. In particular, we provide a cross-sectional snapshot of how 30 elementary students (Grades 3-5) engaged in a series of fraction-as-measurement tasks…

Developing mathematics proficiency requires an understanding of mathematics vocabulary. Although previous research has developed several measures of mathematics vocabulary at different grade levels, no study focused solely on fraction vocabularies. We developed and tested a measure of fraction vocabulary for students in Grade 4 to determine the…

Understanding of fractions is difficult for Indonesian students. This often leads to misinterpretation in solving fractional problems. In this study, a task aiming at identifying students' struggles in understanding the basic concept of part-whole relationships in fractions was developed and tested with six 4th-grade students. The task uses…

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…

Students with mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000), the association between…

For students to develop adequate conceptual understanding about fractions, they require experiences that afford them opportunities to think flexibly about multiple interpretations of fractions. This article presents a sequence of lessons designed to offer such experiences for students in Years 3 and Year 4. The lessons adopt a challenging tasks…

The purpose of this study was to investigate the effects of the concrete-representational-abstract--integrated (CRA-I) sequence on students with learning disabilities' performance when learning fraction and decimal concepts. Three elementary-level students in Grades 4 and 6 participated in a single-case multiple probe across behaviors study. The…

The aim of this longitudinal study was to examine the differences between high- and low-performing students' development of fraction proficiency over a school year and to investigate how those differences were related to instruction in fractions versus instruction in other mathematics topics. The data for this study were drawn from a group of (n =…

Background/Context: The U.S has experienced years of lost progress in math because of the COVID-19 pandemic (NAEP, n.d.a). Fraction understanding is widely characterized as the gatekeeper to algebra (Booth et al., 2012; National Mathematics Advisory Panel, 2008) and can support success in middle and high school math (Bailey et al., 2012; Booth et…