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Allison W. McCulloch, Rachael H. Kenney, and Karen A. Keene

This article reports findings from a study on what students trust and why when checking their written work with a graphing calculator results in conflicting solutions. Based on these findings, suggestions for promoting good checking practices are provided.

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Allison W. McCulloch, Ashley Whitehead, Jennifer N. Lovett, and Blake Whitley

A task using trig functions helps students build an understanding of the importance of context in the modeling process.

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Allison W. McCulloch, Patricia L. Marshall, and Jessica T. DeCuir-Gunby

Youngsters' out-of-school knowledge influences their pictorial representations of number.

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Allison W. McCulloch, Nina G. Bailey, Kristen Fye,, and Gayle Scott

In this article, we examine the ways in which the creation of a third space can bridge the divide between coursework and practice for preservice secondary mathematics teachers (PSTs) taking a technology, pedagogy, and content course. A university-based instructor partnered with two high school teachers to create a space in which PSTs draw upon and use both academic and practitioner knowledge while creating technology-based tasks for high school students to use. Our results revealed increased focus on pedagogical decisions in areas such as technology-task design and questioning techniques. The data also indicate that the success of this collaboration was connected to fair distribution of work, feeling valued, and personal benefit and challenges centered on maintaining rejection of hierarchy.

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Lara K. Dick, Allison W. McCulloch, and Jennifer N. Lovett

A framework to guide teacher noticing when students are working in technology-mediated learning environments.

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Nina G. Bailey, Samuel D. Reed, Kristen Fye, Allison W. McCulloch,, and Jennifer N. Lovett

Dynamic representations situated within a “Which One Doesn’t Belong?” routine can extend students’ exploration of functions and can enable a focus on the variant and invariant characteristics of mathematical objects.

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Jennifer N. Lovett, Allison W. McCulloch, Lara K. Dick, and Charity Cayton

In this article, we present a set of design principles to guide the development of instructional materials aimed to support preservice secondary mathematics teachers (PSMTs) examining student practices in technology-mediated environments. To develop design principles, we drew on the literature related to technological pedagogical content knowledge (TPACK; ), video cases as learning objects (), and professional noticing (). After presenting the design principles, we share a task created using these design principles. Finally, we share PSMTs’ reflections about changes in their own understanding after examining students’ practices. Their responses provide insights into the usefulness of the design principles for deepening PSMTs’ mathematical knowledge and knowledge of students’ understanding, thinking, and learning with technology.

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Allison W. McCulloch, Keith R. Leatham, Jennifer N. Lovett, Nina Gabrielle Bailey, and Samuel D. Reed

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Nina G. Bailey, Demet Yalman Ozen, Jennifer N. Lovett, Allison W. McCulloch, and Charity Cayton

Three different technological activities to explore parameters of quadratic functions each has its own pros and cons.

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Jennifer N. Lovett, Allison W. McCulloch, Blain A. Patterson, and Patrick S. Martin

In this manuscript we describe a lesson that utilizes an applet we designed to help students develop a conceptual understanding of the concept of function. We describe how removing algebraic representations and focusing on a real world context can support students' development of these conceptual understandings of the function concept.