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Amanda L. Cullen

In 2018, NCTM published the first of three books in their Catalyzing Change series. Across the three texts, they call for the dismantling of all forms of inequitable grouping structures from early childhood and elementary school (NCTM 2020a) to middle school (NCTM 2020b) and high school (NCTM 2018). NCTM (2020a) asserted—

Any ability grouping in mathematics education is an inequitable structure that perpetuates privilege for a few and marginality for others. Ability grouping practices often occur with good intentions; we want to understand children’s learning needs and then tailor the content,

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Amanda L. Cullen and Rick Anderson

Regardless of your teaching context, we do not know of a single teacher who did not need to—at some point during 2020—abruptly change their practice. And those changes were not small. For some of us, it was a sudden transition from in-person learning to remote learning. For others, it was a disruption to normal with COVID-19 safety protocols (e.g., teach in a mask, facilitate physically distanced group work, clean everything anyone may touch in between classes or subjects, no hugs). We know several teachers who felt like they were going through their first year of teaching all over again,

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Jenna R. O’Dell, Cynthia W. Langrall, and Amanda L. Cullen

An unsolved problem gets elementary and middle school students thinking and doing mathematics like mathematicians.

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Amanda L. Cullen, Carrie A. Lawton, Crystal S. Patterson, and Craig J. Cullen

In this lesson, third graders were asked how many degrees is a full rotation around a circle. After we gave students time and space to disagree, to make and test conjectures, and to explore, they reasoned about angle as turn and determined a full rotation is 360 degrees.

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Amanda L. Cullen, Cheryl L. Eames, Craig J. Cullen, Jeffrey E. Barrett, Julie Sarama, Douglas H. Clements, and Douglas W. Van Dine

We examine the effects of 3 interventions designed to support Grades 2–5 children's growth in measuring rectangular regions in different ways. We employed the microgenetic method to observe and describe conceptual transitions and investigate how they may have been prompted by the interventions. We compared the interventions with respect to children's learning and then examined patterns in observable behaviors before and after transitions to more sophisticated levels of thinking according to a learning trajectory for area measurement. Our findings indicate that creating a complete record of the structure of the 2-dimensional array—by drawing organized rows and columns of equal-sized unit squares—best supported children in conceptualizing how units were built, organized, and coordinated, leading to improved performance.