Learning trajectories help teachers challenge children at just the right level for their best learning.
Douglas H. Clements, Shannon S. Guss, and Julie Sarama
Chunlian Jiang and Eunmi Joung
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.
Eric Cordero-Siy and Hala Ghousseini
Three deliberate teaching practices can help students strengthen multiple connections to a unifying concept.
Noah Brown, Jonathan D. Bostic, Timothy Folger, Laura Folger, Tiara Hicks, and Shay Nafziger
Mathematics assessments should allow all students opportunities to demonstrate their knowledge and skills as problem solvers. Looking at textbook word problems, we share a process for revising them using Universal Design for Learning.
Design projects to encourage your students’ self-efficacy and motivate mathematics learning by helping them apply their prior knowledge from real-world experiences.
Amanda T. Sugimoto and Heidi Meister
The authors draw on collaboration with a group of teachers to describe how three-act tasks could be (re)designed and implemented for online synchronous and asynchronous learning, identifying technological factors that teachers might consider.
Lara K. Dick, Mollie H. Appelgate, Dittika Gupta, and Melissa M. Soto
A group of mathematics teacher educators (MTEs) began a lesson study to develop a research-based lesson to engage elementary preservice teachers with professional teacher noticing within the context of multidigit multiplication. Afterward, MTEs continued teaching and revising the lesson, developing an integrated process that combined lesson study with the continuous improvement model. This article introduces the continuous improvement lesson study process, shares an example of how the process was used, and discusses how the process serves as a collaborative professional development model for MTEs across institutions.
Megan H. Wickstrom
Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.
Katherine Baker, Scott A. Morrison, and Alyssa Herrmann
This article features a third-grade multiplication exploration that integrates materials from nature and outside spaces. Teaching and learning mathematics with and in nature foster connections—mathematical, interpersonal, and with the natural world.
Min Wang, Candace Walkington, and Koshi Dhingra
An example of an after-school club activity gives educators some tools and suggestions to implement such an approach in their schools.