Assessing Proofs with Rubrics: The RVF Method

Document Type

Conference Paper

Journal/Book Title/Conference

Proceedings of the 13th Conference of the Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education

Publication Date



We present an easy-to-implement 3-axis rubric for the formative and summative assessment of open-ended solutions and proofs. The rubric was constructed for the use on the written work of students in a Discrete Mathematics class at a research-oriented university, with the following in mind: (1) To aid in the efficiency and consistency of assessment of proofs and open-ended solutions, with the possibility of being comfortably implemented by an undergraduate assistant; (2) To provide the simultaneous formative and summative assessment of the students’ written work. Thus, the questions we address are: How can we foster good technical writing skills in a way that improvement can be measured? How can large amounts of written work be processed and assessed so that summative and formative judgments are passed but without much time used by the instructor/professor/TA? The axes we use are labeled validity, readability, and fluency, corresponding to (respectively) correctness of calculations and deductions, the ease with which the solution or proof can be read, and the extent to which a student is able to use and communicate via the technical notions relevant to the problem or proof — for example appropriateness and correctness of notation. The rubric format is communicated to the students and discussed in class before any written work is assessed. The rubric has been implemented by professors and teaching assistants only after being trained in its use.

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