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Amber G. Candela, Melissa D. Boston, and Juli K. Dixon

We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.

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Dr. Geraldo Tobon and Ms. Marie Tejero Hughes

We share our experiences and those of culturally diverse families who participated in math workshops. We tie our experiences with the importance of family engagement, in particular, viewing families as a resource to be tapped into. We do so, in hopes that other school personnel take on a similar venture.

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Pi

Joe F. Allison

When I was in graduate school, my math professor, using a straightedge and a compass, marked off a unit distance and then halved it. He said he could halve the exact ½ again and exactly get ¼. He was leading up to infinite series.

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Kathleen Melhuish, Eva Thanheiser, and Joshua Fagan

In classrooms, students engage in argumentation through justifying and generalizing. However, these activities can be difficult for teachers to conceptualize and therefore promote in their classrooms. In this article, we present the Student Discourse Observation Tool (SDOT) developed to support teachers in noticing and promoting student justifying and generalizing. The SDOT serves the purpose of (a) focusing teacher noticing on student argumentation during classroom observations, and (b) promoting focused discussion of student discourse in teacher professional learning communities. We provide survey data illustrating that elementary-level teachers who participated in professional development leveraging the SDOT had richer conceptions of justifying and generalizing and greater ability to characterize students' justifying and generalizing when compared with a set of control teachers. We argue that the SDOT provides both an important focusing lens for teachers and a means to concretize the abstract mathematical activities of justifying and generalizing.

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Martin V. Bonsangue

In the absence of a decimal number system and representations for square roots, Archimedes estimated the value of pi using inscribed and circumscribed polygons to a circle.

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Taehoon Choi and Dae S. Hong

Using iPad's GeoGebra app with the Snell-Huygens method significantly improves Archimedes's process of approximating Pi.

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Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month, photographs of the Salvador Dali Museum in St. Petersburg, Florida, serve a generous helping of pi from the editors.

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Alessandra King

An analysis of Archimedes' contributions to the field of mathematics and the meaning behind C = pd are explored. Activity sheets are included.