This paper presents findings from a study that examined the strategies that children, who had only been taught the part-whole fraction sub-construct at school, used for finding the fraction associated with solving varied partitive quotient problems. A qualitative, microgenetic research design was used involving nine year 5 (aged 9-10) children…

There is a long tradition of teaching science through inquiry, with broad agreement about the form it should take. Students should investigate researchable questions; gather and analyse data; and develop and represent evidence-based claims. Authoritative teacher or textbook representations are generally used to guide this learning (Buckley &…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

This study investigates the use of manipulatives by elementary students working on a fraction task. Extending previous work on the role played by the manipulatives in students' activity, we aim at describing how the choices made for the task design disrupt students' activity, creating opportunities to learn. The theoretical underpinnings allow…

Mathematics teachers' identities profoundly influence how they interact with and position their students to learn mathematics. In this paper, we examine how a year-long teacher learning intervention supportive of student engagement in mathematics helped shift teachers' mathematics-related identities. We use an implied identity perspective as a…

This study applies a framework for mathematical cognition and learning (Bossé, et al., 2018a; Bossé et al., 2019; Bossé et al., 2018b) to examples of students' comprehension of geometric concepts related to angles. This framework utilizes key concepts from second language acquisition (SLA) to elucidate processes involved in mathematical learning.…

In this study, we analyzed the imprecise (i.e., less mathematically precise) responses that 148 third- to fifth-grade Chinese students made on selected-response problems that were part of a spontaneous mathematical focusing task, the Quantitative Relations Test for Chinese Children (QRTC[superscript 2]). The purpose for this analysis was to…

Many studies have shown that visual representations can enhance student understanding of STEM concepts. However, prior research suggests that visual representations alone are not necessarily effective across a broad range of students. To address this problem, we created a novel, scaffolded form of diagrammatic self-explanation in which students…

Background: Design thinking, with its emphasis on iterative prototyping and mantra of "fail early and often," stands in stark contrast to the typical one-and-done, failure-averse culture of the classroom. Iterative prototyping and fail-forward mindsets could promote valuable iterative practices and positive reactions to failure, but…

Calls for "mathematics for all" or "mathematics for social justice" bring light to the importance of equity issues within and through mathematics education. Employing the theoretical perspectives of equity and social justice for mathematics education, and the intersection of language, culture, and mathematics, this study…

The epistemic trust literature emphasizes that children's evaluations of informants' trustworthiness affects learning, but there is no evidence that epistemic trust affects learning in academic domains. The current study investigated how reliability affects decimal learning. Fourth and fifth graders (N = 122; M[subscript age] = 10.1 years)…

This study applies the Mathematics Acquisition Framework (MAF) (Bossé, Ringler, Bayaga, Fountain, & Young, 2018) to investigate fifth- through seventh-grade students' comprehension of fractions and decimals and examines how students build understanding of mathematical principles and concepts regarding fractions and decimals. Based on case…

Mathematical problem solving typically involves manipulating visual symbols (e.g., equations), and prior research suggests that those symbols serve as diagrammatic representations (e.g., Landy & Goldstone, 2010). The present work examines the ways that instructional design of student engagement with these diagrammatic representations may…

In this study, we examined how curricular resources supported three expert teachers in their enactment of progressions. Using a video-stimulated interview process, we documented the multiple types of progressions identified, described, and enacted by the teachers. Results indicate that the teachers used four different types of…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…