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## 5.1.2 The Role of the Teacher

 The Role of the Teacher  (video)Two video clips illustrate communication about mathematics among a teacher and her 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?

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Teacher:  The card we said we were going to talk about this morning was eight-tenths.  Did anybody think of a way in which you can move your piece across to the other side if our card was eight-tenths?

Student 1: Instead of using eight-tenths, you could use two-fifths, and you ... no four-fifths. And you could go to four-fifths or eight-tenths.

Teacher:  So I could go to four-fifths or eight-tenths?  So one or the other?

Student 1: Yeah.

Teacher:  How did you know four-fifths was a good move?

Student 1:  Because eight-tenths and four-fifths are equivalent.

Teacher:  Ok.

Student 1:  So both of them would work.

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Teacher:  Is there a way that I could move two pieces rather than just one? Because the way in which you described it, Rebecca, I have to use either on the fifths line or the tenths line, but I couldn't use both.  Is there a way I could start again and try and use both?

Student 2:  You can first go to four-tenths.

Teacher:  Four-tenths.  Ok.

Student 2:  And that would be half way.

Teacher:  All right.

Student 2:  And then you can go to four-fifths.

Teacher:  Four-fifths?  Tell me what you are thinking about that?

Student 2:  Since they're both equivalent, so when you go half way,

Teacher:  But now I moved four-tenths.  Can I move the whole four-fifths now?

Student 2:  Two-fifths.

Teacher:  Two-fifths?  Because then if I moved two-fifths, because two-fifths plus four-tenths would then equal how much?

Student 2:  Eight-tenths.

Teacher:  Eight-tenths.

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Discussion

Games afford students an opportunity to communicate their ideas and justify their thinking. In using games such as Fraction Tracks, 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.

Also see:

• 5.1  Communicating About Mathematics Using Games
• 5.1.1  Playing Fraction Tracks
• 5.1.3  Communication among Students
• 5.1.4  Reflecting on Practice