Students' opportunities to persevere in making sense of mathematical ideas have long been considered significant to learning. Building on existing literature and a case study of video-based teacher collaborative sensemaking, we propose a conceptual framework for bridging perseverance and sensemaking. This framework synthesizes dispositional,…

Learning to calculate the area of composite shapes is an important application of area measurement but evidence suggests that many middle school students struggle to calculate the area of even simple composite shapes. In this article, I report the findings of a classroom design study conducted to investigate the collective development of…

Little is known about the cognitive effort associated with algebraic activity in the elementary and middle school grades. However, this investigation is significant for sensitizing teachers and researchers to the mental demands of algebra learning. In this paper, we focus on the relationship between algebraic thinking and domain-general cognitive…

Although there is much research exploring students' covariational reasoning, there is less research exploring the ways students can leverage such reasoning to coordinate more than two quantities. In this paper, we describe a system of covariational relationships as a comprehensive image of how two varying quantities, having the same attribute…

This study aimed to investigate seventh-grade students' visuospatial thinking processes in an art studio environment, where students were engaged with geometrically rich artworks. The students were asked to observe minimalist artworks, then create and critique their own and others' artworks based on the Studio Thinking Framework. Data were…

In this study, the authors examined a group of related literatures that used the same large-scale nationally representative dataset with algebra achievement as the outcome to explore why results from the same dataset may differ across studies. More specially, the authors synthesized the extant research literature that utilized data from the High…

This paper describes the difficulties faced by a group of middle school students (13- to 15-year-olds) attempting to translate algebraic statements written in verbal language into symbolic language and vice versa. The data used were drawn from their replies to a written quiz and semi-structured interviews. In the former, students were confronted…

Though there is an extensive research literature on understanding and assessing individual modeling competencies, less attention has been given to characterizing the social context of the classroom in which modeling occurs. Yet a classroom's culture of modeling--its negotiated system of beliefs and values about the nature of modeling and what…

Students entering sixth grade operate with three different multiplicative concepts that influence their reasoning in many domains important for middle school. For example, students who are operating with the second multiplicative concept (MC2 students) can begin to construct fractions as lengths but do not construct improper fractions as numbers.…

Proving and refuting are fundamental aspects of mathematical practice that are intertwined in mathematical activity in which conjectures and proofs are often produced and improved through the back-and-forth transition between attempts to prove and disprove. One aspect underexplored in the education literature is the connection between this…

To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving…

Constructing multiplicative reasoning is critical for students' learning of mathematics, particularly throughout the middle grades and beyond. Tzur, Xin, Si, Kenney, and Guebert [American Educational Research Association, ERIC No. ED510991, (2010)] conclude that an assimilatory composite unit is a conceptual spring to multiplicative reasoning.…

Mathematics self-schemas are students' cognitive generalisations of their selves in learning mathematics (Ng in "Educational Psychology," 34(6), 730-762, 2014). These salient subject-based self-conceptions are conceptualised as a cognitive frame guiding students' coping responses when dealing with challenging mathematics tasks. In study…

It is widely assumed that teachers play a key role in providing high-quality learning opportunities to students and fostering students' learning. Yet it is still unclear how specific teacher knowledge facets as part of their professional competence contribute to classroom processes and learning outcomes. Focusing on mathematics education at the…

Exploring language provides us with one approach to better understanding the practices and beliefs of a community. With advances in technology--specifically, computational text processing and machine learning tools--we can now examine written language on a large scale. In this study, we investigate the language of mathematics teaching and learning…