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Pacific Bloom, Terri L. Kurz and H. Bahadir Yanik

Sickle cell disease is a very common disease throughout the world. We used it to contextualize probability for upper elementary school students. Using Punnett squares, activities guide students' evaluation of inheritance using theoretical probability. Then, students perform trials using tools to compare theoretical and experimental probabilities.

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Kwaku Adu-Gyamfi, Michael. J. Bossé, Ronald Preston and Derek A. Williams

The notion or expectation of simplifying final mathematical results remains problematic in that it is ill-defined, tied more closely to algorithmic versus conceptual understanding, and decontextualized from the content, purpose, and application of the mathematics in question. Through examples, we propose that simplification needs to be contextualized.

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Susie Katt, Megan Korponic and Cathy A. Martin

Problems to ponder

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Jason Knight Belnap and Amy Parrott

Technology is used effectively when it enables students to engage in authentic mathematical activity. Using four mathematical tasks, we discuss how technology, carefully designed tasks, and orchestrated discussions can both reveal our students' mathematical practices and provide opportunities to shape those practices.

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Jane-Jane Lo and Nina White

In this article, we discuss issues to consider when using learning goals to strategically select applets from a large public database and some pitfalls to avoid, namely being aware of error-prone applets.

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Jennifer M. Bay-Williams

Transparencies were commonplace in the 1980s when the first NCTM Standards were released. This article reflects on how the use of an overhead projector and transparencies helped to enact the Process Standards - and make the real purpose of learning mathematics more transparent to students.

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Kari N. Jurgenson and Ashley R. Delaney

The Three Little Pigs launched a lesson in which kindergarten students were challenged with designing a house out of materials such as marshmallows and toothpicks that could withstand the Big Bad Wolf. Students engaged in the engineering design process and geometry standards while building and testing their models.

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Amy J. Hackenberg, Robin Jones and Rebecca Borowski

We tiered instruction for a class of seventh grade students during a proportional reasoning unit by providing the same problem with different numbers to different groups of students. We explain why we tiered, show students' work, describe what students learned, and give recommendations about differentiating instruction.

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Debra Monson, Kathleen Cramer and Sue Ahrendt

We share the impact different models have on students' fraction thinking. We have come to understand, through several teaching experiments, how fraction circles, paper folding and number lines support students' learning about key fraction ideas including the role of the unit, partitioning, and fraction order.

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Angela T. Barlow

These comments provide potential authors with insights to support the writing process.