Teachers' questions shape the instructional environment and the direction of mathematics discussions in critical ways. This article is the product of a research study on the relationship between teachers' questions and student engagement in the Standards for Mathematical Practice (SMP) during whole-class discussions. Using classroom video gathered…

The first author's initial attempts at a whole-class mathematics discussion were woefully dysfunctional. Ten second graders showing their answers to a missing addend question about the number of children left riding a school bus did not result in the mathematical epiphany that the textbook promised. She did not give up on using mathematical…

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…

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…

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…

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…

Mistakes are a window into students' mathematical understanding. Taking the time to analyze mistakes can inform you of where students are in their thinking. They can also guide you with respect to how to proceed with instruction. Introduced here are two categories of mistakes: meaty mistakes and minor mistakes. Meaty mistakes demonstrate gaps in…

Children's literature can provide useful contexts for teaching mathematics. In this article, the authors discuss the use of the children's book "Measuring Penny" (Leedy 1997) to support Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) related to length measurement. The authors first describe three types of misconceptions…

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…

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…

Word problems are an essential component of providing a context for computation but are also recognized as an enduring struggle for students. Students are challenged to solve these story-based problems, often resorting to trial and error. This article presents meaningful alternative approaches to helping students make sense of word problems.

The standards from the Operations and Algebraic Thinking (OA) domain in the Common Core State Standards for Mathematics (CCSSM) build on one another across the grades (CCSSI 2010). Understanding each grade level's OA standards is necessary within the broader context of the K-grade 5 OA standards. In this article, the authors share their…

The right types of technology can create new opportunities for students to demonstrate mathematical understandings and can strengthen existing formative assessment practices. The authors write that they frequently use the Math Learning Center apps--covering the range of manipulatives and models--to empower students to explain their thinking. The…

Early career K-grade 2 teachers in a yearlong project explored discourse and mathematical argumentation through monthly professional development (PD) sessions. The goal of the project was to develop an understanding of the types of K-grade 2 tasks that promote argumentation, the types of discourse and argumentation that K-grade 2 students engage…

As part of the Foundations for Success in STEM project at Florida State University, more than thirty teams of teachers have used the Formative Assessment Collaborative Team (FACT) meeting model to work together toward better understanding of their students' mathematical thinking and its implications for instruction. This article provides a brief…