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The Mathematics of Sewing

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The Search for Perfect Donuts

We define and investigate the concept of perfect donuts—rectangular donuts with a uniform width that is a natural number. Our investigation leads us to an interesting connection between the area of perfect donuts and the area of Pythagorean-triple triangles. We also provide ideas for further investigation.

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Bodies in Motion: Exploring Dynamic Angles

The authors describe a fourth-grade lesson that promotes understanding of angle as a dynamic figure through use of a real-world tool used by physical therapists to measure joint motion.

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GPS: The Dog Leash Problem

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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Developing Preservice Teachers’ Understanding of Area Through a Units Intervention

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.