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.
GPS: Teaching Shapes Inclusively
Samuel Otten, Tiffany J. LaCroix, Faustina Baah, and Rebekah Hanak
Deanna Pecaski McLennan
Mathematical Explorations: A New Twist on Collaborative Learning
Stephanie M. Butman
Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).
Amy F. Hillen and Tad Watanabe
Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.
Changing the Rules to Increase Discourse
Lisa A. Brooks and Juli K. Dixon
A second-grade teacher challenges the raise-your-hand-to-speak tradition and enables a classroom community of student-driven conversations that share both mathematical understandings and misunderstandings.
Develop Reasoning through Pictorial Representations
Wendy P. Ruchti and Cory A. Bennett
Solutions coupled with drawings can illustrate students' understandings or misunderstandings, particularly in the area of proportional reasoning.
Capturing Thinking on the Talk Frame
Tutita M. Casa
This instructional tool helps students engage in discussions that foster student reasoning, then settle on correct mathematics.
Developing Formal Procedures through Sense Making
Jeffrey M. Choppin, Carolyn B. Clancy, and Scott J. Koch
Allowing students to reason and communicate about integer operations, or any idea, before these ideas are formalized can be an important tool for fostering deep understanding.
Informing Practice: Examples as Tools for Constructing Justifications
research matters for teachers
Kristen N. Bieda and Jerilynn Lepak
Research explores how to help students build from, instead of building with, examples when justifying mathematical ideas.