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Teaching, Learning, and Communicating about Fractions


Learning about fractions is an important mathematical goal in grades 3-5. The activity shown in these video clips helps students develop an understanding of several important aspects of fractions, including fractions as parts of a unit whole, representing fractions on a number line, and equivalent fractions (see the 3-5 Number and Operation Standard). An important part of the activity is helping students explain and communicate their thinking.

The teacher plays an important role in facilitating and fostering communication so that powerful mathematical understanding is developed (see the 3-5 Communication Standard). Not only do teachers need to encourage their students to communicate mathematically, they also need to model good communication skills. The ability to pose questions that elicit, extend, and challenge students' thinking is an essential part of creating a classroom environment where intellectual risks, sense making, and deep understanding are expected.

The first video clip in this Reflection activity contains an explanation of the fraction activity that the students will be working on in class. The second and third video clips contain episodes of teacher/student dialogue - episodes in which the teacher plays an important role in fostering the students' ability to verbally communicate their mathematical thoughts.

 

A Fraction Activity

The fraction activity is played on the board shown in this video clip. The goal of the activity is to move all of the markers to the right side of this board, that is, to create wholes. Play begins when a student chooses a card from the pile. Suppose the student chooses a card with 8/10. The student then has to decide which markers to move. For example, the student may choose to move the tenths marker to 8/10, or the student may choose to split up the 8/10 and move two markers—the tenths marker to 4/10, and the fifths markers to 2/5 (because 4/10 + 2/5 = 8/10). Subsequent play continues with the next player picking a new card from the pile and moving markers accordingly.

QuickTime required for viewing this video clip


Running Time: 15 seconds; File Size: 365 K

 

Beginning the Activity — Moving One Piece

In this video clip, the teacher begins setting up the fraction activity with her class. As you watch this clip, consider the following focus questions.

Focus Questions

  • What mathematical ideas are being developed?
  • Does the student seem to understand the mathematical ideas?
  • Does the teacher ask questions that elicit, extend, and challenge the students' thinking?

 

QuickTime required for viewing this video clip


Running Time: 37 seconds; File Size: 674 K

 

Reflection Questions

  • Review and answer the Focus Questions above.
  • What other questions could the teacher have asked this student in order to further challenge her mathematical thinking?
  • Do you think the teacher's questioning of this student will help other students in the class develop their understanding of fractions?

 

Following Up — Moving Two Pieces

This video clip shows the teacher following up with another student. As you watch this clip, think about the following focus questions.

Focus Questions

  • Does the teacher ask different types of questions in this clip?
  • What does the teacher do when the student gives an incorrect answer?

 

QuickTime required for viewing this video clip


Running Time: 56 seconds; File Size: 1.2 M

 

Reflection Questions

The clip you just watched begins with the teacher asking a question in response to her dialogue with a student.

  • Do you think the teacher listens, responds, and adapts her questions effectively?
  • How does the teacher handle an incorrect answer?
  • Do you think the student understands the final answer, or is she just following the teacher's prompting without understanding?
  • Do you think this is an effective activity through which students learn important mathematical ideas?
  • How could you modify or extend this activity to teach other fraction concepts?

 

Copyright Notice

Video clips generously provided by WGBH Boston. All clips were taken from "Fraction Tracks," part of 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.

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