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Students' Mathematical Noticing

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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Teacher Support for Argumentation: An Examination of Beliefs and Practice

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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Only for Multilingual Students at Risk? Cluster-Randomized Trial on Language-Responsive Mathematics Instruction

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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Teaching Is a Journey: Math Talks for Agency, Identity, and Ownership

Timothy L. Weekes

changed the trajectory of my journey as a mathematics educator in ways that benefited both me and my students. The project opened my eyes to some of the limitations of my classroom discourse practices and how some of the ways that I taught mathematics may

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Analyzing Eight Years of Mathematics Teacher Educator Articles: Where We Were, Where We Are, and Where We Are Going

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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Not Just Number: Representation Talks

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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Looking for Zebras: Unexpected Solutions to Pattern Tasks

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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Student Engagement with the “Into Math Graph" Tool

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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Supporting Understanding Using Representations

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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Enacting Co-Craft Questions Using Flexible Teaching Platforms

T. Royce Olarte and Sarah A. Roberts

students to consider their peers’ questions and to identify similarities and differences between the questions. This stage of the routine provides multiple opportunities to engage your multilingual learners in rich discourse practices, through discussing