The Common Core State Standards for Mathematical Practice asks students to look for and make use of structure. Hence, mathematics teacher educators need to prepare teachers to support students’ structural reasoning. In this article, we present tasks and rubrics designed and validated to characterize teachers’ structural reasoning for the purposes of professional development. Initially, tasks were designed and improved using interviews and small pilot studies. Next, we gave written structure tasks to over 600 teachers in two countries and developed and validated rubrics to categorize responses. Our work contributes to the preparation and support of mathematics teachers as they develop their own structural reasoning and their ability to help students develop structural reasoning.
Stacy Musgrave, Cameron Byerley, Neil Hatfield, Surani Joshua, and Hyunkyoung Yoon
The Trammel of Archimedes traces an ellipse as the machine’s lever is rotated. Specific measurements of the machine are used to compare the machine’s actions on GeoGebra with the graph of the ellipse and an ellipse formed by the string method.
Sarah Stecher, Luke Wilcox, and Lindsey Gallas
The EFFL model empowers students to build strong conceptual understanding of mathematics through carefully designed, equity-minded activities that disrupt the traditional lecture-based classroom.
Darien DeWolf and Balakrishnan Viswanathan
This article provides a series-focused approach to computing Pythagorean triples.
Arsalan Wares and David Custer
This pattern-related problem, appropriate for high school students, involves spatial visualization, promotes geometric and algebraic thinking, and relies on a no-cost computer software program.
Kira Rivera and David Peabody
When students create their own exponent mazes, their creativity and problem-solving abilities flourish.
Alessandra King, Sophia Ouanes, and Claire Doh
Students and teachers enjoy exploring the boundaries between mathematics and art.
Jeffrey Connelly and Pablo Garcia
Two teachers use homemade pendulums for their students to explore phase shift in sine curves. The use of Desmos’s Activity Builder enabled students to become mathematical explorers and supported their sense of mathematical agency.
Gail Burrill, Joan Funderburk, Becky Byer, and Rachael Gorsuch
Classroom stories show how using technology to investigate the wage gap provided opportunities to develop students’ identities and agency and enabled a classroom culture of sharing and risk-taking.