Language is a conduit for communicating and understanding mathematical ideas. In this article, the authors describe how literacy relates to modes of reading, writing, speaking, and listening. They then share a strategy for supporting student literacy in mathematics--judicious telling--and provide examples of what this approach looks like in the…

On the surface, the number line may seem like a basic tool with obvious applications. However, using a number line is not always intuitive for students. Students may not recognize significant features such as the size of the unit, how units are represented by iterated equal lengths, or that the accumulation of iterated units is a magnitude of…

Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

A one-degree angle would certainly be difficult to draw accurately, especially without the aid of other tools like a protractor. However, mentally making a one-degree angle in visualized imagination is not only possible, but it is important for students' emergent understandings of angular measure. When students begin learning about length,…

Grade 8 students were given a task that had pairs of shapes that had been transformed (i.e., preimages and images). Students were to identify which of the three rigid transformations--reflections, rotations, or translations--were used to map the preimage to the image. Students were also asked to give a justification for their choice of…

This article introduces basic strategies for teachers initiating translanguaging pedagogy for emergent bilingual students in mathematics classrooms to support linguistic identities, create inclusive environments, and enhance learning. The authors collaborated with Algebra 1 teachers who exclusively taught emergent bilingual students, implementing…

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…

Current gaps in achievement among students from diverse backgrounds and their culturally dominant counterparts imply that theoretical ideas, such as culturally responsive teaching (CRT), that focus on increasing the achievement of diverse populations are sound yet difficult to translate into everyday practice. CRT is intricate and complex and…

This article examines a school district's effort to create a unified culture of mathematical excellence through which everyone would know what high-quality instruction should look like and how they would shift their practices to those that aligned with their vision. This is accomplished through their Mathematics Teaching Practices Inventory…

This article examines the mathematical activity of five-year-old Liam to explore the difference between the mathematics games designed for children and the children's games that emerge through playful activity. We propose that this distinction is a salient one for teachers observing mathematical play for evidence of mathematical sense making.

Delve into the transformative journey of teachers and administrators from a rural school district as they bring "Principles to Actions" to life. Pawnee City Public Schools believes effective teaching affects student learning and implemented a successful district-wide plan to improve student learning through the eight Mathematics Teaching…

As 2020 draws to a close, so does this first volume of Mathematics Teacher: "Learning and Teaching PK-12" ("MTLT"). Ascribing to a digital-first philosophy, the articles comprising this first volume included digital assets such as classroom videos, author introductions, and digital applications (e.g., Desmos apps) and addressed…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…

According to former National Council of Teachers of Mathematics (NCTM) president Cathy L. Seeley (2014), students experience more success when they engage in doing mathematics (i.e., writing about or discussing mathematics, modeling situations, or exploring ideas in the classroom). She further recommended that teachers pose challenging problems or…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…