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Susie Katt and Megan Korponic

Problems to Ponder provides 28 varied, classroom-ready mathematics problems that collectively span PK-12, arranged in order of grade level. Answers to the problems are available online.

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Allyson Hallman-Thrasher and Denise A. Spangler

We share ideas for preparing for and enacting high-cognitive demand tasks in ways that support students in articulating and justifying their ideas. We offer strategies for developing and posing several types of purposeful questions: (1) eliciting thinking, (2) generating ideas, (3) clarifying explanations, and (4) justifying claims.

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Natalie L. F. Hobson

A quilt design repeating the use of Pythagoras's Theorem provides a variety of questions we can begin to ponder.

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Shelli Casler-Failing

This article shares the learning experienced by my seventh-grade students during a lesson incorporating LEGO robotics into my mathematics class. I provide evidence of my students' learning, which represents how LEGO robotics can benefit students in the mathematics classroom to support engagement and development of understanding.

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Zalman Usiskin

This article briefly describes the timing of the first concentrated study of algebra over the 100 years of NCTM, from a 9th-grade course taken by only about 1/5 of students to a course taken by virtually all students, with almost half taking it in 8th grade.

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Randall E. Groth, Jennifer A. Bergner, Jathan W. Austin, Claudia R. Burgess and Veera Holdai

Undergraduate research is increasingly prevalent in many fields of study, but it is not yet widespread in mathematics education. We argue that expanding undergraduate research opportunities in mathematics education would be beneficial to the field. Such opportunities can be impactful as either extracurricular or course-embedded experiences. To help readers envision directions for undergraduate research experiences in mathematics education with prospective teachers, we describe a model built on a design-based research paradigm. The model engages pairs of prospective teachers in working with faculty mentors to design instructional sequences and test the extent to which they support children’s learning. Undergraduates learn about the nature of systematic mathematics education research and how careful analyses of classroom data can guide practice. Mentors gain opportunities to pursue their personal research interests while guiding undergraduate pairs. We explain how implementing the core cycle of the model, whether on a small or large scale, can help teachers make instructional decisions that are based on rich, qualitative classroom data.

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Robyn Ruttenberg-Rozen

Mathematical paradoxes often produce awe and wonder in the mathematics classroom. In this classroom episode, I share a paradoxical task, based on Simpson's Paradox, and its power as an intervention for a child diagnosed with ADHD. The Paradox leveraged his strengths to help him build understandings in proportional reasoning.

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Edward A. Silver

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How much do you know about presidents of NCTM? For each of the 50 past or present leaders of NCTM, try to match the timeframe of their leadership and the state from which they hailed.