This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.
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S. Asli Özgün-Koca and Monica G. McLeod
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.
Chris Harrow and Justin Gregory Johns
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.
Chunlian Jiang and Eunmi Joung
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.
Daniel Frischemeier
Bar graphs are fundamental to display distributions of categorical variables in primary school. Here is an approach using TinkerPlots™ to create bar graphs on different representation levels in small and large data sets.
Surani Joshua, James Drimalla, Dru Horne, Heather Lavender, Alexandra Yon, Cameron Byerley, Hyunkyoung Yoon, and Kevin Moore
The Relative Risk Tool web app allows students to compare risks relating to COVID-19 with other more familiar risks, to make multiplicative comparisons, and to interpret them.
Mindy Kalchman
Process-oriented, question-asking techniques provide a framework for approaching modern challenges, including modality pivots and student agency.
José N. Contreras
Megan H. Wickstrom
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.
Hyunyi Jung, Ji-Won Son, and Ji-Yeong I
Use a COVID-19 lesson as an example of how to apply a framework aligned with research recommendations to support students as they apply mathematics to real life.
