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…

This scoping review describes mathematics intervention studies that include initial skill moderation analyses. Sixteen studies were included that focused on students with or at risk for mathematics difficulties (MD). The results revealed that mathematics intervention studies with initial skill moderation analyses focused on students in…

This research aims to 1) develop an effective Active Learning plan combined with skill practice according to the 70/70 criterion, 2) study the learning achievement index through Active Learning combined with skill practice, and 3) investigate the satisfaction towards Active Learning combined with skill practice. The sample group consisted of 27…

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…

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…

Determining the most effective ways to support student-to-student talk requires some negotiating from a responsive teacher. This paper reports on a case study of two emergent multilingual students in Grade 3 (seven to eight-year-olds) who explained their strategies to each other. The transcript of their conversation was analysed using Chan and…

Peer-mediated instructional strategies (e.g., peer tutoring) have been effective at teaching academic responses in previous research. This study extended the literature by programming for inference-making, or derived relations. Across two experiments, researchers investigated the use of peer tutoring and inference-making to teach…

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…

Learning fractions is essential for academic and daily life success. A critical first step in acquiring fractions is learning to transcode them (e.g., writing ½ when hearing "one half"). However, little is known about how students master fraction transcoding. We addressed this gap by assessing fraction writing in two groups of Brazilian…

Young children have informal knowledge of fractions before learning about fraction symbols in school. In the current study, we followed 103 children in the Mid-Atlantic United States from the fall to the spring of first grade to characterize the development of individual differences in early informal fraction knowledge, as well as its relation to…

This paper reports an intervention study in the teaching of fraction concepts at a village school in Hong Kong. The classes consisted of 60 Grade three students with different cultural backgrounds, including African, Chinese, Filipino, Korean, Nepalese, and Pakistani. The study represents one of the relatively few studies that investigate the…

Teachers across the United States struggle with meeting students' needs in their classrooms amidst the growing diversity of children in their classrooms and the amplification of standardized testing. Time and again, teaching with the heart and action of inclusivity is placed on the back burner as teachers feel the pressure for students to perform…

This study contributes to efforts to characterize teaching that is responsive to children's mathematical ideas and linguistic repertoire. Building on translanguaging, defined in this article as a pedagogical practice that facilitates students' expression of their understanding using their own language practices, and on the literature surrounding…

Lesson study, especially when conducted with support from targeted resources, is often identified as a potentially effective means to support teacher learning. In this study, 80 school-based teams of educators, representing 80 classrooms of third- or fourth-grade students in the US, were randomly assigned to one of four conditions: lesson study…