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The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions related to enrichment and differentiation in the elementary grades, equivalent equations in the middle grades, and assessment retakes in high school.

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Jerome A. White

Inspired by the “Batman Equation” of 2011, this article presents a challenging and engaging process for graphing complicated designs from just a single parametric equation pair. Reinforces numerous analytic geometry skills. Works in popular graphing software such as Desmos or GeoGebra, or even graphing calculators.

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Crystal Kalinec-Craig and Rose Ann Robles

The article describes how one fifth-grade teacher helped her students to exercise their Rights of the Learner (e.g., to be confused; to claim a mistake; to speak, listen, and be heard; and to write, do, and represent what makes sense) as they learned to graph and interpret non-linear data.

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Kimberly A. Conner

By having students practice constructing diagrams for geometric theorems, teachers can develop students' understanding of mathematical claims, vocabulary, and notation methods. This practice can also strengthen students' ability to interpret mathematical diagrams and recognize their limitations.

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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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Clayton M. Edwards and Rebecca R. Robichaux-Davis

This manuscript will highlight MTLT's digital first philosophy, which is not just an add-on to the mathematics, but a partner, working hand in hand with the mathematics to enhance the experience.

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Stephanie Casey and Joel Amidon

Developing expertise in professional noticing of students’ mathematical thinking takes time and meaningful learning experiences. We used the LessonSketch platform to create a learning experience for secondary preservice teachers (PSTs) involving an approximation of teaching practice to formatively assess PSTs’ noticing skills of students’ mathematical thinking. Our study showed that approximations of teaching practice embedded within platforms like LessonSketch can enable mathematics teacher educators (MTEs) to carry out effective formative assessment of PSTs’ professional noticing of students’ mathematical thinking that is meaningful for both PSTs and MTEs. The experience itself as well as its design features and framework used with the assessment can be applied in the work of MTEs who develop teachers’ professional noticing skills of students’ mathematical thinking.

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Samuel Otten, Wenmin Zhao, Zandra de Araujo and Milan Sherman

Teachers who are flipping instruction face the challenging task of selecting or creating high-quality videos for their students. This article presents a framework for evaluating videos and describes the benefits of including interactive features and considering options beyond lecture videos.

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Amber G. Candela and Zandra de Araujo

In this growing problem solvers article, readers explore their impact on the environment with their use of straws through measurement and geometry. The sequence of tasks spans grades P-12 and we invite readers to explore real world contexts with mathematics.

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John Rowe

The Hook-Line-Sinker eBook aims to utilise rich tasks as the core learning in mathematics rather than a selection of “one-hit-wonders”. The featured resources intend to provide teachers with a starting point for sparking student curiosity, developing the need to learn, and consolidating learning in multiple ways.