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Kyle T. Schultz and Stephen F. Bismarck

A geometric approach using exact square manipulatives can promote an understanding of the algorithm to dismantle radical expressions.

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Kristen Lew and Juan Pablo Mejía-Ramos

This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First, mathematicians believed that mathematical language should obey the conventions of academic language, whereas students were either unaware of these conventions or unaware that these conventions applied to proof writing. Second, students did not fully understand the nuances involved in how mathematicians introduce objects in proofs. Third, mathematicians focused on the context of the proof to decide how formal a proof should be, whereas students did not seem to be aware of the importance of this factor.

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Hagit Sela, Nicole Davis, and Jennifer Hulse

Teachers reflect on how three dialogue protocols can promote meaningful and efficient communication and learning through social interactions.

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David Rock and Joel Amidon

A monthly set of problems is aimed at a variety of ability levels.

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David Rock and Mary K. Porter

A monthly set of problems is aimed at a variety of ability levels.

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Jennifer M. Mayer, Mary Ann Huntley, Nicole L. Fonger, and Maria S. Terrell

In a recent Mathematics Teacher article, Fonger and her colleagues explain why teachers should engage in research studies: Researchers working alone lack the information needed to effectively address problems of practice that matter most-problems that are highly contextual and based on teachers' day-to-day experience. (2017, p. 462)

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Finding regular polygons, such as equilateral triangles, squares, hexagons, and even octagons, in art or architecture is not unusual, but seeing a nonagon, or nine-sided regular polygon, such as the Mongolian drum (see photograph 1) is less common. Perhaps 9 is a special number in Mongolia: Shamans have 99 tengri, or spirits, (55 benevolent ones and 44 “dark” ones) on their drums, although the drums are more often circular.

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