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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
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Positive Points
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- 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
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+3 points
+3 points
+2 points
+2 points
+2 points
+3 points
+1 point
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Negative Points
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- Not paying attention or distracting others
- Interrupting
- Making an incorrect assumption
- Making a personal attack
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-2 points
-2 points
-2 points
-3 points
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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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