Southwest Educational Development Laboratory
SEDL

Classroom Compass
Volume 2 Number 2
Spring 1996

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Scored Discussions for Upper Level Students

Thinking Aloud About Mathematics


This assessment actively involves an entire mathematics class in a problem-solving discussion. Eilene Leach explained this method of challenging her Colorado high school students in "An Alternative Form of Evaluation" in the November 1992 issue of The Mathematics Teacher.

Several days a week Eilene Leach begins class with the following scenario: a challenging homework problem is presented to a group of four students who sit in front of their classmates. The group is given five minutes to discuss and solve the problem while the rest of the class observes.

"When I first tried scored discussion, I was afraid the students would hate it. I was wrong. Those students in front of the class were trying their best, since they were working in front of their peers. The students in the audience listened intently. I learned more about how students reasoned than I had by watching them in cooperative groups....[After the timer bell rang] the audience could contribute to the suggestions.... Sometimes the students in the audience were so excited they could hardly keep quiet until the five-minute timer rang."

Leach has developed a rubric that she uses to score group members as they puzzle through the problem. Problem-solving skills and the successful use of appropriate mathematical strategies are valued, as are indications of skillful group interaction.

"By seeing the scored discussions the students learned how to discuss mathematics....When a group has a particularly difficult time with their problem, I pull my chair into the group and continue the discussion for several more minutes, modeling how to develop a strategy and how to involve all members in the solution process."

This activity provides the students an arena for public discourse about mathematics. It accommodates several NCTM curriculum standards including:

  • Learning to reason mathematically
  • Learning to communicate mathematically
  • Becoming mathematical problem solvers
The discourse sessions give every participant the possibility of success.

The sessions provide an alternative to paper-and-pencil assessments and let students explain their thinking and demonstrate their ideas.

Once or twice a semester, Leach devotes the entire period to scored discussions.

At the beginning of the semester, Leach explains the activity and enlists several students in a "trial run." She emphasizes problem-solving strategies and successful group techniques as well as ways students can lose points through interrupting or monopolizing the discussion. She gives the students copies of the score sheet so they will know expectations for a successful session. An added bonus: if the students solve the problem, it is not on that night's homework.


Discussion Scoring Guide

Positive Points
  • Determining a possible strategy to use
  • Successfully communicating a strategy
  • Correctly applying a property
  • Recognizing misused properties or arithmetic errors
  • Drawing another person into discussion
  • Asking a clarifying question
  • Moving the discussion along
+3 points
+3 points
+2 points
+2 points
+2 points
+3 points
+1 point
Negative Points
  • Not paying attention or distracting others
  • Interrupting
  • Making an incorrect assumption
  • Making a personal attack
-2 points
-2 points
-2 points
-3 points

Adapted with permission from "An Alternative Form of Evaluation That Complies with NCTM's Standards," by Eilene L. Leach (Mathematics Teacher), copyright November 1992 by the National Council of Teachers of Mathematics.
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