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Amy Lucenta and Grace Kelemanik

Teaching students to apply structural thinking instead of automatically following procedures and algorithms can result in efficient, elegant strategies and fewer errors.

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Lara Jasien and Ilana Horn

We build on mathematicians’ descriptions of their work and conceptualize mathematics as an aesthetic endeavor. Invoking the anthropological meaning of practice, we claim that mathematical aesthetic practices shape meanings of and appreciation (or distaste) for particular manifestations of mathematics. To see learners’ spontaneous mathematical aesthetic practices, we situate our study in an informal context featuring design-centered play with mathematical objects. Drawing from video data that support inferences about children’s perspectives, we use interaction analysis to examine one child’s mathematical aesthetic practices, highlighting the emergence of aesthetic problems whose resolution required engagement in mathematics sense making. As mathematics educators seek to broaden access, our empirical findings challenge commonsense understandings about what and where mathematics is, opening possibilities for designs for learning.

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Richard A. Andrusiak and Antonella Perucca

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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Blair Izard

Thu author asks readers to pause and reflect on the progress made in instructional practice over the last decade and reminds teachers and educators that the power to make change is in their hands.

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

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Caleb Goff

This article describes how using music and the TikTok platform can help students recall mathematical definitions in a whimsical and relatable way.

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The Math Learning Center Content Development Team and J. Michael Shaughnessy

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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WenYen (Jason) Huang

The author discusses “synthesizing" teaching practice, which encourages students to explore patterns and its underlying mathematics structure through technology.

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Keith Weber, Juan Pablo Mejía-Ramos, and Tyler Volpe

Many mathematics educators believe a goal of instruction is for students to obtain conviction and certainty in mathematical statements using the same types of evidence that mathematicians do. However, few empirical studies have examined how mathematicians use proofs to obtain conviction and certainty. We report on a study in which 16 advanced mathematics doctoral students were given a task-based interview in which they were presented with various sources of evidence in support of a specific mathematical claim and were asked how convinced they were that the claim was true after reviewing this evidence. In particular, we explore why our participants retained doubts about our claim after reading its proof and how they used empirical evidence to reduce those doubts.