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Chris Harrow and Justin Gregory Johns

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.

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Alice Aspinall

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.

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Mindy Kalchman

Process-oriented, question-asking techniques provide a framework for approaching modern challenges, including modality pivots and student agency.

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Enrique Ortiz

This article presents an example of discovering an idea through creative play. After some trial and error, I drew a wonderful image, which I later learned was a two-dimensional view of a four-dimensional shape called tesseract.

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Ruthmae Sears

As mathematics teachers, we establish several norms, expectations, rules, and daily routines that result in culture building. Hence, in my classes, I decided to center the norms and culture building around five Rs: (1) rigor, (2) relevance, (3) responsiveness, (4) relationship, and (5) responsibility. Using these five Rs provided a norm to engage in our mathematical activities and reflections and established the expectation that everyone would contribute to mathematics teaching and learning (Boyce et al. 2021). Thus, this reflection describes how articles published this year (2021) in Mathematics Teacher: Learning and Teaching PK–12 (MTLT

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Min Wang, Candace Walkington, and Koshi Dhingra

An example of an after-school club activity gives educators some tools and suggestions to implement such an approach in their schools.

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Deanna Pecaski McLennan

For the Love of Mathematics

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Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

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Joanne Caniglia and Michelle Meadows

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

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Atara Shriki and Dorit Patkin

Success in STEM fields depends largely on robust spatial skills, in particular on the ability to perform a mental rotation. Given that this ability can be nurtured, this article includes examples of diverse relevant tasks appropriate for grades 6–8 students.