Introduction: *
This article covers an innovative assessment strategy that actively involves an entire mathematics class in a problem-solving discussion. Eilene Leach a long experienced Mathematic teacher explained this method of challenging her high school students in "An Alternative Form of Evaluation" in the November 1992 issue of The Mathematics Teacher.

A Group of Four:
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.

A Rubric for Assessment:
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 standards including:

• Learning to reason mathematically
• Learning to communicate mathematically
• Becoming mathematical problem solvers

Discourse Advantages:

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

* This article is based on an article titled Scored Discussions for Upper Level Students: Thinking Aloud About Mathematics,written by Elienne L.Leach and published in Classroom Compass(Spring 1996 , vol 2, no.2) Reviewed on March 23,2007