The elementary classroom teacher helps students to build the foundations necessary for communicating effectively about mathematics. Ensuring that students begin to learn how to “use the language of mathematics to express mathematical ideas precisely” (NCTM Communication Standard) begins in the early grades. Teachers provide opportunities for communication and facilitate the discussions their students have in classroom and small group settings.

This collection of resources includes a research article, a webinar, and several videos that show and discuss the challenges teachers face as they attempt to facilitate productive discussion, and suggestions of strategies that enable teachers to effectively overcome these challenges. The teacher’s role is defined and specific practices are described.

One set of related resources includes an “e-example” from the NCTM website describing how mathematical games can be used to encourage high quality student discussion. A video showing students communicating their thoughts and strategies as they play “Fraction Tracks” is included. Games of this type are interesting to students and allow students to engage in thoughtful mathematical discussions. Participating in these activities also allows students to learn to analyze and evaluate other students' strategies.

A second set of related resources provides an article about using “low threshold, high ceiling” activities, a mathematical puzzle fitting this description, and two videos in which a mentor works with several teachers as they learn how to use the puzzle with their students. Activities of this type allow teachers to encourage students to communicate their ideas, as well as to listen to and analyze ideas presented by other students.

Providing opportunities for students to communicate with one another using the language of mathematics is an expectation that crosses all grade levels. Teachers at the elementary school level who set these goals early and provide many situations in which students practice discussing, analyzing, and communicating about mathematics ensure their students’ future success.

This 4-page research-based monograph discusses how teachers can support meaningful student dialogue in the math classroom. The author summarizes recognized benefits of student interaction and the challenges facing teachers in promoting it. She outlines the teacher's role in facilitating "math talk" and offers strategies and guidelines for encouraging high-quality student interaction. The author includes an extensive list of references for further exploration.

This web page contains links to a video and several downloadable pdf files documenting the efforts of a third grade class to prove a set of conjectures about even and odd numbers. Included are a 4-minute Blue Stream video segment in which students discuss a classmate's conjecture that the sum of two odd numbers always equals an even number, a document providing background information on the investigation that led to the discussion, a transcript of the video, and the teacher's journal entry reflecting on the discussion and its implications.

In this webinar, recorded in October 2011, Margaret Smith describes 5 practices which can help teachers make student-centered discussions more manageable and coherent by moderating the degree of improvisation required by the teachers. She provides a sample problem and student work to illustrate each step of her process. A pfd version of her slides are available to download (the recommended way to follow her talk, as there were technical problems with her slides during the webinar).

This 5-minute video follows Carlos and Sara, students in Jennifer Saul's third grade class, as they explain different strategies, both mental and written, for adding multi-digit numbers. These children demonstrate effective presentations skills, while their classmates exhibit the established expectations for being a supportive audience. The page provides reflection questions for the viewer and downloadable supporting materials, including a transcript of the video (doc) and problem solving work samples from Carlos and Sara (pdf).

This article by Wendy Petti contains an updated version of Bloom's Taxonomy and sample questions that encourage dialogue with students. The article also includes suggestions for teachers about how to create questions that stimulate higher order thinking. Although there are advertisements on this webpage, the content of the freely available article is a valuable resource for teachers.

This brief article defines "low threshold high ceiling" mathematical tasks (LTHC) and explains how they allow all students to develop mathematically. They provide a simple entry point so that struggling students can succeed, and at the same time involve rich mathematical concepts that challenge high achieving students. The article cites examples of LTHC problems from all levels of the NRICH archives. Several are cataloged separately: Magic Vs, Noah, Incey Wincey, Square It.

This problem provides an opportunity for students to form and test conjectures, and make generalizations, while exploring the effect of parity on simple whole number sums. Solvers are asked to arrange given sets of numbers in a V formation so that the sums of the numbers in each "arm" are equal. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, a printable record sheet (pdf) and links to two YouTube videos demonstrating use of the problem in a professional development setting (videos cataloged separately).

In this 10-minute video Lynne McClure introduces NRICH's Magic Vs problem to a small group of teachers in a professional development setting. She demonstrates how a "Low Threshold, High Ceiling" problem, with minimal skill requirements, can be approached by nearly all learners, and yet can elicit sophisticated mathematical thinking. As Lynne leads participants through a sequence of challenges, she models good questioning and communication practices and discusses instructional strategies. The Magic V problem and a follow-up video are cataloged separately.

In this 7-minute video, a follow-up to "Lynne McClure - Magic V - Part 1," the leader continues her discussion of NRICH's Magic Vs problem with a small group of teachers. This episode illustrates how a simple but rich problem can be extended to elicit deeper mathematical thinking. As Lynne leads participants through a sequence of challenges, she models good questioning and communication practices and discusses instructional strategies. The Magic V problem and video Part 1 are cataloged separately.

This four-part E-Example from Principles and Standards for School Mathematics of the NCTM standards highlights how mathematical games can foster mathematical communication as students explain and justify their moves to one another in a fraction game. In addition, a video is included that demonstrates students engaged in thinking about and applying their mathematical concepts and skills. The game "Playing Fraction Tracks" is cataloged separately.

This interactive game, similar to "Fraction Game" (catalogued separately) allows two students an opportunity to think about how fractions are related to a unit whole, compare fractional parts of a whole, and find equivalent fractions. Two players move markers a total distance (forwards and backwards directions) that equals the random target fraction box, along their choice of seven parallel number line tracks, which are divided into different fractional parts. The goal is to move each of the seven markers to the right side of the game board before your opponent does. Instructions and discussion questions are given.