E-Example 5.1.2: Communicating about Mathematics Using Games


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Communicating about Mathematics Using Games:
The Role of the Teacher

Playing Fraction Track

The Role of the Teacher

Communication among Students

Reflecting on Practice

Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. The first part of this example, Playing Fraction Track, contains an interactive version of a game (based on the work of Akers, Tierney, Evans, and Murray [1998]) that can be used in the grades 3–5 classroom to support students' learning about fractions. By working on this activity, students have opportunities to think about how fractions are related to a unit whole, compare fractional parts of a whole, and find equivalent fractions, as discussed in the Number and Operations Standard. In this second part, The Role of the Teacher, two video clips illustrate communication about mathematics among a teacher and her students. The third part, Communication among Students, shows how activities like this allow students to use communication as a tool to deepen their understanding of mathematics, as described in the Communication Standard. In the fourth part, Reflecting on Practice, the teacher reflects on her own mathematical learning that occurs as a result of using activities like this game with her fifth-grade students.

Video Segment

Watch the two video clips below, which are segments from the same class. Find specific instances in which you think the teacher is effectively fostering communication in her students. What mathematics learning seems to be occurring as a result?

QuickTime 4.0 is required for viewing this video clip

Running time—37 sec.
File size—7.3Mb

Video Transcript
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QuickTime 4.0 is required for viewing this video clip

Running time—56 sec.
File size—11.0 Mb

Video Transcript
(Click on and drag the text below to scroll.)

Discussion

Games afford students an opportunity to communicate their ideas and justify their thinking. In using games such as Fraction Track, the teacher plays an important role in encouraging students to explain their thinking and in keeping students focused on mathematical ideas. Requiring students to explain and justify their moves during a sample round of the game played as a whole class models the type of thinking and communicating that is important for students to use later when they play the game in pairs. The ability to pose questions that elicit, extend, and challenge students' thinking is essential to creating a classroom environment in which intellectual risks, sense making, and deep understanding are expected. In daily lessons, teachers must make on-the-spot decisions about which points of the mathematical conversation to pick up on and which to let go, and when to let students struggle with an issue and when to give direction.

Take Time to Reflect

What mathematical ideas are being developed by the students in these video clips? Does each student seem to understand these mathematical ideas? What evidence can you find?
Does the teacher ask questions that elicit, extend, and challenge the students' thinking? Which questions seem to work best?
What other questions could the teacher have asked these students in order to further challenge their mathematical thinking or to address their misunderstandings?
Do you think the teacher's questioning of these students will help other students in the class develop their understanding of fractions? Why?

Video Credit

WGBH, Boston. "Fraction Tracks." In Teaching Math: A Video Library, 5–8. Funded and distributed by the Annenberg/CPB Math and Science Project, P.O. Box 2345, S. Burlington, VT 05407-2345, 1-800-LEARNER.