Vary the intensity of pedagogical scaffolding along three dimensions—grouping, structure, and language—with the same rigorous prompt.
Varying the Intensity of Scaffolding for English Learners
Haiwen Chu, Jill Neumayer DePiper, and Leslie Hamburger
Let’s Give Them Something to Talk About
Nicola M. Hodkowski and Carolyn Carhart-Quezada
Different types of open tasks can be used as a tool to promote rigorous student mathematical discourse and considerations for facilitation.
Reconsidering Mathematical Authority
Michael D. Hicks, Jessica Pierson Bishop, Christina Koehne, and Mai Bui
Who has mathematical authority in your classroom, and what does authority look like? Find out different ways you can help students gain authority.
Using Public Records to Scaffold Joint Sense Making
Keith R. Leatham, Blake E. Peterson, Ben Freeburn, Sini W. Graff, Laura R. Van Zoest, Shari L. Stockero, and Nitchada Kamlue
Teachers can more productively use board work to scaffold joint sense making.
Ways to Help Students Become Powerful Mathematical Thinkers
Alan H. Schoenfeld
Ear to the Ground features voices from several corners of the mathematics education world.
Discuss It! Collaborating on the Tortoise and Hare Task
K. Ann Renninger, Maria Consuelo De Dios, Annie Fetter, Maeve R. Hogan, Moe Htet Kyaw, Ana G. Michels, Marina Nakayama, Richard Tchen, Stephen A. Weimar, Helena Werneck de Souza Dias, and Feven Yared
The authors share an online collaborative problem-solving activity that integrates support for students’ developing conceptual understanding, focused engagement, and positive feelings of agency and identity.
Prove It! Graph Theory and Induction: The Next Big Thing
Jeffrey P. Smith
Eighth-grade students participated in a two-day lab exploring graph theory. In addition to learning about a completely new topic, they experienced a subtle introduction to proof by induction.
Filling Vases and Making Tanks
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.
GPS: Teaching Shapes Inclusively
Samuel Otten, Tiffany J. LaCroix, Faustina Baah, and Rebekah Hanak
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.