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Clayton Edwards and Rebecca Robichaux-Davis

Common computational algorithms have largely been accepted as important to teach over the years, as evidenced by specific Common Core State Standards for Mathematics requiring such algorithms to be mastered in grades 4–6 (NGA Center and CCSSO 2010). This is likely because of the characteristics of such “standard” algorithms: certainty, reliability, efficiency, and generalizability (Fan and Bokhove 2014). Multidigit addition and subtraction are introduced in grades 1–3, whereas multidigit multiplication and division are experienced in grades 3–5. Some of these standard algorithms can align closely to student-invented strategies, which are typically characterized by conceptual approaches

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Blake Peterson

Examining the covariation of triangle dimensions and area offers a geometric context that makes analyzing a piecewise function easier for students.

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Jessica Pierson Bishop, Lisa L. Lamb, Ian Whitacre, Randolph A. Philipp, and Bonnie P. Schappelle

Are your students negative about integers? Help them experience positivity and joy doing integer arithmetic!

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Sandra Crespo, Patricio Herbst, Erin K. Lichtenstein, Percival G. Matthews, and Daniel Chazan

In this editorial, we focus on the movement within our field to attend more explicitly to issues of equity in mathematics education research. When Beatriz D’Ambrosio et al. (2013) introduced a JRME special issue on equity in mathematics education, 1 they seemed to suggest that the journal was lagging in the extent to which it covered the equity-focused research being done in mathematics education. Hence, a goal of that special issue was to broaden and deepen our collective understanding of equity-focused research. In the intervening 8 years, out of the 233 articles JRME has

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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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Andrew Brantlinger

This article presents a philosophical and pragmatic critique of critical mathematics (CM) and current vocational mathematics (VM) in the United States. I argue that, despite differences, CM and VM advocates share the view that the inauthentic contextualization of secondary mathematics does particular harm to students from historically marginalized groups and that the subject therefore should be recontextualized to address their lived experiences and apparent futures. Drawing on sociological theory, I argue that, in being responsive to so-called authentic real-world concerns, CM and VM fail to be responsive to the self-referential principles and specialized discourses necessary for future study of mathematics and, as such, may further disempower the very students that CM and VM advocates seek to empower.

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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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Katherine Ariemma Marin and Natasha E. Gerstenschlager

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.