This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.
Jere Confrey, Meetal Shah, and Alan Maloney
Three learning trajectories and their connections show how to promote vertical coherence in PK–12 mathematics education.
Linda L. Cooper
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.
Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton
We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.
Esther M. H. Billings and Barbara A. Swartz
For two decades, teacher educators have called for practice-based approaches in teacher education (
Amber G. Candela, Melissa D. Boston, and Juli K. Dixon
We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.
Sarah B. Bush, Karen S. Karp, Jennifer Nadler, and Katie Gibbons
By examining ratios in paintings and using a free educational app, students can size up artists' use of proportional reasoning in their creations.
A cartoon exploring a problem about order of operations is coupled with a full-page activity sheet.
Kami M. Dupree
Abandon mnemonics and make stronger connections between the operations and properties of arithmetic.
Nicole Panorkou and Alan P. Maloney
Develop fifth-grade students' early expression of pattern relationships through instructional tasks.