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Lidia Gonzalez

This method using the area of regular polygons inscribed in circles to approximate a value for pi is similar to the method used by Archimedes using circumferences.

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Sam Rhodes, Alesia Mickle Moldavan, Montana Smithey, and Allison DePiro

Interrogate deficit-based thinking and suggest asset-based language to develop mathematical identities, understandings, and consciousness.

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Christian Rüede, Sog Yee Mok, and Fritz C. Staub

This article shows that enabling teachers to integrate comparing solution strategies into their teaching fosters student flexibility in algebra. We designed two professional development (PD) programs that either focused exclusively on comparing solution strategies, or additionally introduced the accountable talk approach to guiding productive classroom discussions. The effects of both PD programs were investigated in an experimental field study (N = 39 teachers, 739 students). In both experimental groups, student posttest gains in strategy flexibility and procedural knowledge were greater than in the control group. The accountable talk group also increased conceptual knowledge. Significant effects in strategy flexibility were still observed 2.5 months later. We discuss recommendations for PD programs to foster flexibility in algebra using comparing.

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Nicole R. Rigelman and Introduction by: Sam Rhodes

From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the MTLT Journal Club.

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Daniel K. Siebert and Monica G. McCleod

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

In our editorial last January, echoed a question often raised by reviewers of manuscripts: What is this manuscript's contribution to our research field? In that first elaboration on how manuscripts may contribute to the field of research in mathematics education, we discussed the contributions of basic research. In this editorial, motivated by the illustrations provided by the articles included in this issue, we do a similar exercise with applied research.

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Douglas H. Clements, Julie Sarama, Carolyn Layzer, and Fatih Unlu

A follow-up of a cluster-randomized trial evaluated the long-term impacts of a scale-up model composed of 10 research-based guidelines grounded in learning trajectories. Two treatment groups received the intervention during the prekindergarten year, and one of these groups received follow-through support in kindergarten and first grade. Business-as-usual curricula were used in all other cases, including all years for the control group. Early effects on mathematics achievement decreased through fourth grade but reemerged at fifth grade. These results support both a latent trait hypothesis, whereby stable characteristics of students explain differences in achievement, and a latent foundation hypothesis, whereby early mathematical knowledge and skills provide a foundation for competence in mathematics in later years, especially those that involve challenging mathematics.