A Proof Rubric

For Group Interaction1

          A classroom proof is a demonstration that a demonstration exists. It is a type of improvisational play with characters and at times an audience. Also, it is a group playing through the actions of a logical type discussion perhaps with use of some physical representations, models, drawings or graphs.

          Each part of a demonstration relates a way that ideas fit together to form a new key idea. The way that these ideas fit together could be considered a path which has a beginning, a route and an end. The route should be well known by all. Each route is related to a known general concept.

          The main character is the demonstrator in the group. A demonstrator wishes to establish a new key concept to other members of a cast and audience. The demonstrator may assume that certain concepts are accepted by group members. In this playing process, a demonstrator may ask an audience about their common knowledge of some concepts needed for background in the demonstration.

An audience hears a demonstration and through this playing process accepts the new concept as true. Any audience response to a demonstrator's questions, or any listener's inquiry about the routes of the demonstration, lead each participant into demonstrator type roles. If a demonstrator has some point of a demonstration that needs clarification, then anyone may provide that clarification.

          An audience transforms into the cast of a demonstration play. Eventually, each member of a group needs to practice the role of demonstrator. A proof is complete when each member of a group has accomplished a proof demonstration to the satisfaction of the group. That is the point when no additional demonstrations are needed to support the new key concept needing proof.

          Examples of proofs written by the instructor in class can be supported by students. In fact, students can generate a proof while the instructor writes as fast as students spell out each route!

          On the other hand, one person in a group telling a story or reading pages from a book may be involved in promoting a fable which may or may not be true for this group.


1Definitions:

First: a classroom of students is partitioned into groups. Each group is given a key concept, theorem, to prove.

Here: Group is used as a cast of characters, the lead character is the demonstrator. The demonstrator has the support of her/his group when support is needed. A member of a group may not see why a route given in the demonstration is true so must ask the demonstrator or other group members why. Otherwise, the demonstrator is responsible for an accurate proof.

Here: the audience is all members of the class not in the group for a given proof.

A demonstration that a demonstration exists then means that if in the initial demonstration some part is not understood, then additional demonstrations must be given. Every route in a demonstration must be proven. A demonstration can go to whatever depth is required to get the most elementary concepts worked out and understood.


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