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Jeffrey M. Choppin, Cynthia H. Callard, and Jennifer S. Kruger

Student-generated algorithms, despite being inelegant and cumbersome, can nevertheless highlight a Common Core standard on rational number subtraction to show flexibility and understanding.

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Teri N. Johnson and Stephen I. Tucker

During the past thirty years, various forms of technology have facilitated teaching and learning. Recently, touchscreen tablets are among the devices growing in popularity. Many mathematics apps are available; however, they vary in their usefulness for different users. Monitoring students' interactions with selected apps is important for teachers to do to ensure that earners are benefiting from technology integration. The Modification of Attributes, Affordances, Abilities, and Distance (MAAAD) for Learning Framework (see fig. 1) emerged from evaluations of students' interactions with educational technology (Tucker 2016). Teachers can use this framework to select apps for use in the classroom, formatively assess student understanding, and evaluate the appropriateness of tasks presented by apps.

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Victor Mateas

Teachers can benefit from productive and manageable suggestions to align instruction to the intention of the Common Core's Standards for Mathematical Practice.

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Lisa L. Lamb, Jessica Pierson Bishop, Randolph A. Philipp, Bonnie P. Schappelle, Ian Whitacre, and Mindy Lewis

Research on how students make sense of and use the minus sign indicates that students struggle to understand the multiple meanings of this symbol. Teachers can support students in developing a robust understanding of each interpretation.

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Jae Ki Lee, Kyong Mi Choi, and Melissa McAninch

The L-shaped 2-5-3-7 algorithm, combining efficient Singaporean and Korean procedures with divisibility rules of primes 2, 3, 5, and 7, helps students identify LCMs and GCFs.

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Debra I. Johanning

Research on how students add and subtract fractions indicates that students struggle to understand various algorithms.

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Juli K. Dixon and Jennifer M. Tobias

Anticipate and address errors that arise when fractions are placed in context and illustrated with models.

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Jessica Pierson Bishop, Lisa L. Lamb, Randolph A. Philipp, Ian Whitacre, and Bonnie P. Schappelle

Reasoning about integers provides students with rich opportunities to look for and make use of structure.

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James Metz

Students analyze football plays.

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Hoyun Cho

Real-life questions are asked about the fare charged by the New York Metropolitan Transit Authority.