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Joanne Lobato, Charles Hohensee, and Bohdan Rhodehamel

Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats noticing as a complex phenomenon that is distributed across individual cognition, social interactions, material resources, and normed practices. Specifically, this research demonstrates that different centers of focus emerged in two middle grades mathematics classes addressing the same content goals, which, in turn, were related conceptually to differences in student reasoning on subsequent interview tasks. Furthermore, differences in the discourse practices, features of the mathematical tasks, and the nature of the mathematical activity in the two classrooms were related to the different mathematical features that students appeared to notice.

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AnnaMarie Conner and Laura Marie Singletary

Supporting students in making mathematical arguments is an important part of discourse practices in mathematics classrooms. Differences in teachers’ support for collective argumentation have been observed and documented, and the importance of the teacher’s role in supporting collective argumentation is well established. This article seeks to explain differences in teachers’ support for argumentation by examining two student teachers’ beliefs about mathematics, teaching, and proof to see which beliefs are visible in their support for argumentation. Assisted by a framework for argumentation and a commitment to teachers’ beliefs and actions as sensible systems, we found that teachers’ beliefs about the role of the teacher, particularly with respect to giving explanations, were more visible in their support for collective argumentation than other beliefs about mathematics or proof.

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Susanne Prediger, Kirstin Erath, Henrike Weinert, and Kim Quabeck

, engaging students in rich discourse practices, and using macroscaffolding (as used in several approaches, see overview in Erath et al., 2021 ), with one intervention additionally providing integrated vocabulary work. In the first section of the article

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Heather West, Emily Elrod, Karen Hollebrands,, and Valerie Faulkner

that focused on discourse; diversity, equity, and language; technology; and methods of research . Articles related to discourse explore classroom discourse and teachers’ discourse practices ( n = 15). For example, Webel and Conner (2017

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Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

the teacher (Han) and extra practice (Lenora), as helpful to their engagement. Opportunities for social engagement and student-centered discourse practices through defending a mathematical position with peers were also associated with positive

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Eric Cordero-Siy and Hala Ghousseini

representation” (p. 29). Literature on classroom mathematics discussions offers practices supporting students in making and strengthening connections across representations by focusing on underlying meanings. Among the various discourse practices available, we

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Matthew P. Campbell

, which include not just vocabulary but grammar, syntax, discourse practices, and representations ( Moschkovich 2012 , p. 17). To do this, teachers must engage students in the complexity of language and allow their reasoning to become central as opposed to

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Elizabeth Fleming and Dana L. Grosser‐Clarkson

or geometric patterns make for wonderful classroom tasks. They are easily accessible, allow for multiple solution strategies, and can be used to establish or further develop classroom discourse practices and norms ( Smith, Hillen, and Catania 2007

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Elizabeth A. van Es, Victoria Hand, Priyanka Agarwal, and Carlos Sandoval

. Marisol shifted into youth discourse practices when she said, “Yeah boi!" and Parker mirrored this shift by describing how she might be “kick[ed] back on my couch" when reviewing Marisol’s work. Although we do not know what Parker was noticing that

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Richard Barwell

discourse practices that arise within these speech events. In this article, therefore, I make a similar distinction. I refer to moments of significance in students’ socialization into mathematics and language as socialization events , and I refer to the