In the primary grades, engaging in counting collections provides students with regular opportunities to make sense of numbers in dynamic ways, build social skills, and communicate about mathematics. This article aims to guide elementary educators through a team's process of planning and implementing counting collections in kindergarten. Counting…

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…

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…

Purposeful questioning is one of the most important elements to promote successful mathematics understanding (National Council of Teachers of Mathematics, 2014; Ontario Ministry of Education, 2011). Questioning helps teachers to elicit, interpret, and respond to student thinking (Stein et al., 2008) and supports students' understanding,…

In this article, the authors share the story of Diego, a kindergarten student, navigating issues of mathematical identity and competence--his own and those of his kindergarten classmates. The authors are a team of educators, including a kindergarten teacher (Sara) and a math teacher educator (Jody) who worked together on a quality improvement…

The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…

Teachers' actions matter greatly in the mathematics classroom, but it is not always clear what guides their actions or from where they come. As teachers strive to create rich and engaging learning environments, how they capitalize on a particular moment is often unclear. Sometimes just identifying potential pathways to take can be challenging. In…

The purpose of this article is to describe and illustrate learning trajectories (LTs) and introduce a new, comprehensive set of resources that support teaching meaningfully and joyfully. An LT for a topic has three parts: (1) a mathematical goal; (2) a developmental progression of levels of thinking; and (3) teaching practices (environments,…

Although kindergarteners often are excited to share their mathematical ideas, they may not be sure how to explain the underlying reasoning that brought them to their answers. Teachers seeking to use literacy skills in mathematics to support kindergarteners' reasoning can use writing to provide each student an avenue to communicate their individual…

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…

Researchers have suggested that initial attempts to change mathematics instruction often leave educators "with no framework for the kinds of specific, constructive pedagogical moves" they might make (Chazan & Ball, 1999, p. 2). The intent of this article is to introduce a framework for teaching and learning mathematics that is robust…

Grades K-12 institutions in the United States continue to have a more culturally, linguistically, and racially diverse student population, with Hispanic and Asian students increasing in record numbers (United States Census Bureau, 2023). As a result, K-12 mathematics teachers are expected more than ever to design, select, and implement…

In their work, the authors study what it looks like to build on a high-leverage student mathematical contribution--one that provides an in-the-moment opportunity to engage the class in joint sense making about the contribution to better understand the important mathematics within it. They have noticed that some "go-to" teacher practices…

In this article, the authors (a mathematics educator and a literacy educator) offer a framework to engage students with mathematics and children's literature through a read-aloud experience in which teacher and students engage with the text while problem solving. The authors describe the narrative-first approach as a strategy during which the…

The ability to interpret mathematical symbols and understand how they capture contextual relationships is a critical element of algebraic thinking. More often than not, students see algebra as merely a list of rules for manipulating abstract symbols, with limited to no meaning. Instead, for students to see algebra as a powerful tool and rich way…