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.
Two classic hands-on tasks address conceptual understanding of functions. The tasks center student discourse and rough draft mathematics as students grapple with the relationship between input and output.
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 email@example.com. If published, the authors of problems will be acknowledged.
Krystal Jones Carter
A well-crafted classroom engineering challenge can effectively answer compelling questions about social and global responsibility.
Casey Hawthorne and John Gruver
This instructional sequence develops your students’ meaningful understanding of algebraic expressions.
John K. Lannin, Christopher Austin, and David C. Geary
Explore two ways that algebra students interpret mathematical expressions. Learn instructional tasks to help students develop meaning.
James A. Gerald and David Jay Hebert
Happy Numbers offer a fun platform for exploring numerical patterns, making conjectures, and investigating mathematical thought in recreational mathematics.
Alison Williams and Lisa Lamb
Easy to implement, this strategy has a powerful positive impact in mathematics classrooms.
Isabel White, Michael Foster, and Joanne Lobato
Explore three challenges that students faced and how they made progress.