This article focuses on one common type of many different classroom discussions, open-strategy sharing (OSS), because it offers a starting point for teachers new to mathematical discussions. The goal of an OSS discussion is to explore multiple possible ways to solve a single mathematical task. Students share strategies, listen to others'…

Because talking about their mathematical ideas is difficult for emergent bilinguals if they do not have experience with the language used to represent those ideas, constructing math lessons wherein the materials and tasks support the development of fruitful talk is an important task for the teacher. Waiting until emergent bilinguals are fully…

In this article, the authors illustrates techniques for integrating diverse learners in shared mathematical contexts while providing differentiated support or challenge, as necessary. The techniques described were developed for a curriculum project entitled Learning Mathematics through Representations (LMR). A premise of LMR is that students'…

NCTM's "Principles to Actions: Ensuring Mathematical Success for All" (2014), outlines eight teaching practices for effective teaching and learning mathematics. One of them, facilitate meaningful mathematical discourse, states, "Effective teaching of mathematics facilitates discourse among students to build shared understanding of…

Many teachers try to engage their students in meaningful mathematical discussions in which one or more students share their thinking about a problem while the other students are expected to listen and learn from the sharing. Indeed, such discussions can help students learn from one another and promote high levels of mathematical proficiency.…

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…

To challenge students' reasoning and to align with a physical fitness unit that students were studying, teachers and authors, Scott Frye and Signe Kastberg adapted a ratio comparison problem from Susan Lamon, "Ratio and Proportion: Connecting Content and Children's Thinking," (1994) to include athletes and doctors who share…

"Strategy sharing" is a certain type of discussion that centers on students' ideas and occurs when children present different approaches to problems and provide information about how they solved the problem (Wood, Williams, and McNeal 2004). A teacher may orchestrate a strategy-sharing discussion to achieve one or more of the…

As mathematics becomes more complex and abstract in the higher grades, helping students find purpose and meaning for doing it becomes more important. Juvenile literature can serve as a powerfully motivating force for students in intermediate elementary school grades to learn mathematics, often providing an intrinsically interesting, real-world…

Finding ways to help primary-grade students overcome difficulties in solving mathematical word problems can be a daunting task for teachers in a regular classroom setting. Student challenges may include: (1) difficulty with vocabulary; (2) lack of confidence when solving problems; (3) confusion on the proper operation to use when solving a…

Classroom video excerpts are often used to help preservice and practicing teachers explore students' mathematical ideas. This article describes several types of video clips that the authors have found to be particularly productive for this purpose. The authors also discuss three dimensions that can be used to characterize the student thinking…

Encouraging children to think--independently and publicly--is possibly one of any teachers' most challenging and rewarding responsibilities. Young children's less-developed language and listening skills further complicate teachers' work at the early elementary level. Yet, the author has been fortunate to work with many teachers who have embraced…

David Schwartz's classic book "How Much Is a Million?" can be the catalyst for sparking many interesting mathematical investigations. This article describes five episodes in which children in grades 2-5 all heard this familiar story read aloud to them. At each grade level, they were encouraged to think of their own way to explore the concept of…

A mathematical problem is presented. Teachers are advised to spend time discussing the problem with their students, but they should avoid giving them too much guidance.

The situations created by individual style of problem solving in mathematics by children are discussed. Children can solve their mathematical problem by correcting their misconceptions on their own with the use of open discussions with others.