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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Alice Aspinall
This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.
Justin Gregory Johns, Chris Harrow, and Peter Nikolai
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.
Mindy Kalchman
Process-oriented, question-asking techniques provide a framework for approaching modern challenges, including modality pivots and student agency.
José N. Contreras
Paula Beardell Krieg
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.
Blake Peterson
Examining the covariation of triangle dimensions and area offers a geometric context that makes analyzing a piecewise function easier for students.
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.
Justin Gregory Johns, Chris Harrow, and Kaitlyn Alexander
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.
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.
