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Steve Ingrassia and Molly Rawding

These are the March 2020 P2P problems from Steve Ingrassia and Molly Rawding.

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Emilie Wiesner, Aaron Weinberg, Ellie Fitts Fulmer and John Barr

Textbooks are a standard component of undergraduate mathematics courses, but research shows that students often do not view textbooks as productive resources to support learning. This article seeks to understand the factors affecting how individuals engage in reading a calculus textbook excerpt and what they learn from reading. To better understand the separate roles of background knowledge and other reading practices, we compare 2 readers: a 2nd-semester calculus student and a nonmathematics STEM professor. We employ the concepts of sense making and the implied reader to analyze each reader’s experience and a disciplinary literacy perspective to explain the similarities and differences we find between the 2 readers. We propose the concept of didactical disciplinary literacy—an adaptation of disciplinary literacy applied to didactical texts—to describe the ways that the professor drew on his identity as a teacher to shape his reading practices.

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Dan D. Meyer

Students use computers outside and inside of math classes and they enjoy them immeasurably more outside of math class. That's because, outside of class, they use their computers in ways that are creative and social. The same can and must be true about computers inside of math class.

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Erin E. Baldinger, Matthew P. Campbell and Foster Graif

Students need opportunities to construct definitions in mathematics. We describe a sorting activity that can help students construct and refine definitions through discussion and argumentation. We include examples from our own work of planning and implementing this sorting activity to support constructing a definition of linear function.

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Rebecca Vinsonhaler and Alison G. Lynch

This article focuses on students use and understanding of counterexamples and is part of a research project on the role of examples in proving. We share student interviews and offer suggestions for how teachers can support student reasoning and thinking and promote productive struggle by incorporating counterexamples into the classroom.

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Krista L. Strand and Katie Bailey

K-5 teachers deepen their understanding of the Common Core content standards by engaging in collaborative drawing activities during professional development workshops.

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Teruni Lamberg, Linda Gillette-Koyen and Diana Moss

Formative assessment helps teachers make effective instructional decisions to support students to learn mathematics. Yet, many teachers struggle to effectively use formative assessment to support student learning. Therefore, teacher educators must find ways to support teachers to use formative assessment to inform instruction. This case study documents shifts in teachers’ views and reported use of formative assessment that took place as they engaged in professional development (PD). The PD design considered the formative assessment cycle (Otero, 2006; Popham, 2008) and embedded it within a pedagogical framework (Lamberg, 2013, in press) that took into account the process of mathematics planning and teaching while supporting teachers to learn math content. Teachers restructured their definition of student understanding, which influenced how they interpreted student work and made instructional decisions. Teachers’ pre-PD instructional decisions focused on looking for right and wrong answers to determine mastery and focused on pacing decisions. Their post-PD decisions focused on student thinking and adapting teaching to support student thinking and learning. Implications for PD to support teachers to use formative assessment and research are discussed.

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Bilge Yurekli, Mary Kay Stein, Richard Correnti and Zahid Kisa

A major influence on mathematics teachers’ instruction is their beliefs. However, teachers’ instructional practices do not always neatly align with their beliefs because of factors perceived as constraints. The purpose of this article is to introduce a new approach for examining the relationship between teachers’ beliefs and practices, an approach that focuses on specific instructional practices that support the development of students’ conceptual understanding and on mismatches that occur between what teachers believe to be important and what they report actually doing in the classroom. We also examine the relationship between teachers’ self-reported constraints and mismatches between teachers’ beliefs and practices.

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Over the past 100 years, technology has evolved in unprecedented fashion. Calculators, computers, and smart phones have become ubiquitous, yet school mathematics experiences for many children still remain without many powerful technological tools for the exploration of mathematics. We consider the evolution of some tools as we imagine a future.

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M. Kathleen Heid

Technological tools for mathematics instruction have evolved over the past fifty years. Some of these tools have opened the door to explorations of new mathematics. Features of others have made access to curricular mathematics more convenient. Thoughts on this evolution are shared.