Creating a Proof Error Evaluation Tool for Use in the Grading of Student-Generated “Proofs”

Abstract

The fact that students have difficulties in constructing proofs is well documented. However, some of these difficulties may be lessened if instructors and students have access to a common evaluation framework. Operating in the theoretical tradition of heuristic inquiry, a proof error evaluation tool (PEET) is constructed that may be used by instructors at the postsecondary level to give students feedback on their proof work. This PEET was generated by a four-phase process involving category generation, triangulation, merging, and refinement. The PEET was calibrated using faulty proofs from classroom situations and faulty proofs contained in research articles. This tool does not suggest point value deductions but instead labels what errors are present in student generated proofs. It may be used in all undergraduate- and graduate-level proof-writing courses.

Keywords:

• Proof
• grading
• evaluation
• feedback to students
• rubrics