Mathematics education at the high school level is not working for many students. Although there has been steady improvement in mathematics learning at the elementary and middle school levels across the United States, for the past decade, student achievement has remained essentially flat at the high school level (NCES 2015, 2016). One possible…

There are fundamental questions that teachers should ask themselves and their students as they prepare lessons on calculating area. Area measurement is commonly used in everyday life (perhaps to carpet a room or organize a space) and plays a foundational role in mathematics from multiplication all way up to calculus. Despite the usefulness of area…

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…

A "repeating pattern" is a cyclical repetition of an identifiable core. Children in the primary grades usually begin pattern work with fairly simple patterns, such as AB, ABC, or ABB patterns. The unique letters represent unique elements, whereas the sequence of letters represents the core that is repeated. Based on color, shape,…

Four elementary school instructors offer insights into their classrooms, their unique professional roles, and their leadership approaches as they reflect on their journey to advance teacher and student mathematics learning. They note a "teacher leader" serves as an example to other educators and strives to impact student learning;…

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…

The authors elucidate what they saw as three important challenges to overcome along the path to becoming elementary school mathematics teacher leaders: marginal interest in math, low self-confidence, and teaching in isolation. To illustrate how these challenges were mitigated, they focus on the stories of two elementary school teachers--Laura and…

Beginning in third grade, Pennsylvania students are required to take the Pennsylvania State Standardized Assessment (PSSA), which presents multiple-choice mathematics questions and open-ended mathematics problems. Consistent with the Communication Standard of the National Council of Teachers of Mathematics, while solving the open-ended problems,…

What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

This article presents a descriptive account of an after-school study. The participants--Allan (male, ten years), Veronique (female, nine years), and William (male, ten years)--all spoke English as their first language and were considered by their classroom teachers to be meeting the provincially set expectations for the fifth-grade curriculum…

The widely adopted Common Core State Standards for Mathematics (CCSSM) are designed to deepen instruction of number sense and will demand that elementary school teachers have a strong understanding of number. These changes arrive at a time when it is still understood that teachers and the curriculum in the United States have not been fundamentally…

Elementary school teachers are responsible for constructing the foundation of number sense in youngsters, and so it is recommended that teacher-training programs include an emphasis on number sense to ensure the development of dynamic, productive computation and estimation skills in students. To better prepare preservice elementary school teachers…

Mathematics specialists play a significant, meaningful, and integral role in supporting elementary school teachers in this mathematically connected world. These teacher leaders (coaches, resource teachers, math leads, and so on) work closely with all members of the school community--students, teachers, and administrators--and have a range of…