Classroom discourse is critical to helping students learn mathematics. Interacting with peers and the teacher within a classroom community assists students in building their understanding of mathematical concepts. A discourse community, sometimes referred to as a math-talk learning community, is "a classroom community in which the teacher and…

In this article, Lindsey Fowler describes how an animal rhyme--that she shared with her fifth-grade students with the intention of assisting them with the concept of metric conversions--made fostering the Standards for Mathematical Practice (SMP) more difficult. The addition of animals, which added an extraneous element that students mistakenly…

At the start of every school year, teachers typically wonder what their new students know coming into the grade level. Sometimes, though, they place too much emphasis on what children do not know or have forgotten over summer break. After all, those gaps can be glaring. Helping their students grow is like helping an acorn grow; they must watch for…

One of the most important jobs mathematics teachers have is supporting students and helping them to develop confidence in their own capabilities as mathematical thinkers. Children who do not believe in themselves are unlikely to share their ideas, persevere through challenges, or take risks that lead to new insights. Yet many students have no…

Gesture is a powerful and frequent means of mathematical communication. It is a rich modality through which we may reach out to students and they may reach out to teachers, and this is particularly true for instances in which spoken language is not necessarily a commonality among classroom participants. Indeed, our movements help us share more…

Acknowledging the critical role of mathematics coaches in enhancing teacher capacity, positively influencing teacher beliefs, and increasing teacher investment in professional development, NCTM's "Principles to Actions: Ensuring Mathematical Success for All" (2014) calls on coaches to "take action." However, coaches seek…

Increasing availability of digital devices in elementary school classrooms presents exciting new opportunities for teachers to support the teaching and learning of mathematics. Although many of the math applications available for these devices focus on drill and practice of mathematical procedures, screencasting apps can help support effective…

Arithmetic is a major mathematical focus in elementary school curriculum, and researchers such as Mason (2008) claim that "algebraic thinking is required in order to make sense of arithmetic" (p. 58). When adding, subtracting, multiplying, and dividing, learners must rely on a small set of fundamental properties also important for the…

In the mathematics classroom, making sense of story problems can be a challenge for all students. Strategies that promote student discourse offer teachers one way to support their students' sense-making processes. In this article, the authors present a mathematical discourse strategy that was introduced to elementary school teachers during Project…

This article introduces the formative assessment probe--a powerful tool for collecting focused, actionable information about student thinking and potential misconceptions--along with a process for targeting instruction in response to probe results. Drawing on research about common student mathematical misconceptions as well as the former work of…

Teachers use the word assessment to describe any method of gathering information about student learning. Whether it be formative assessment (intended to guide instructional decisions) or summative assessment (a reflection on the entirety of student learning from prior instruction), teachers are constantly working to identify what their students…

The Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) highlight the mathematical habits that educators should be fostering in mathematics classrooms throughout K-grade 12 education. That argumentation and discourse are important components of developing mathematically proficient…

This article shows how to modify classroom evaluation items to avoid four potential difficulties that limit a teacher's insight into students' mathematical understanding by addressing these issues: (1) poor choice of numbers; (2) implausible or inappropriate contexts; (3) inclusion of graphics that do not help make learning visible; and…

The improvement of mathematics teaching and learning is a complicated undertaking. It relies on teacher understanding of math curriculum in addition to awareness of how children acquire mathematics concepts. It also depends on teachers' abilities to translate these understandings into learning tasks and instructional routines, as well as the…

This is a story about teachers engaging in mathematics teacher leadership. The focus is on the teachers' learning, and the purpose is to illuminate the process. The setting is a semester-long graduate class called Teacher Leadership in Mathematics Education, and the characters are elementary and middle school teachers. Those in this group…