Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

What comes to mind when one thinks about building? One may envision constructions with blocks or engineering activities. Yet, constructing and building a number system requires the same sort of imagination, creativity, and perseverance as building a block city or engaging in engineering design. We know that children invent their own notation for…

The Great Mini-Golf Project requires students to use a ruler to identify measurements to the quarter-inch, with careful precision and accuracy, which supported the Standards for Mathematical Practice 5 and 6: using appropriate tools to solve mathematical problems with precision (NGA Center & CCSSO, 2010). This project also supported Standard…

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

Mathematics assessments should allow all students opportunities to demonstrate their knowledge and skills as problem solvers. Looking at textbook word problems, the authors share a process for revising them using Universal Design for Learning (UDL). Outlined in detail here are problems for kindergarten, grades 5 and 7, and high school (algebra).

The National Council of Teachers of Mathematics's "Principles to Actions" (NCTM, 2014) cites posing purposeful questions and eliciting and using evidence of student thinking as effective mathematics teaching practices. Interviewing students creates opportunities for teachers to develop these practices. Through interviewing, they can try…

During the past few years, the social interactions of students have been limited. The act of social distancing has not only exacerbated developmental gaps in social and emotional learning (SEL) (Vaillancourt et al. 2021) but also interrupted mathematics instruction (Lewis et al. 2021). Teachers are searching for strategies that promote…

The article describes how one fifth-grade teacher helped her students to exercise their Rights of the Learner (e.g., to be confused; to claim a mistake; to speak, listen, and be heard; and to write, do, and represent what makes sense) as they learned to graph and interpret non-linear data.

We share ideas for preparing for and enacting high-cognitive demand tasks in ways that support students in articulating and justifying their ideas. We offer strategies for developing and posing several types of purposeful questions: (1) eliciting thinking, (2) generating ideas, (3) clarifying explanations, and (4) justifying claims.