Rubrics can be excellent tools to use when assessing students’ work for several reasons. You might consider developing and using rubrics if:
- You find yourself re-writing the same comments on several different students’ assignments.
- Your marking load is high, and writing out comments takes up a lot of your time.
- Students repeatedly question you about the assignment requirements, even after you’ve handed back the marked assignment.
- You want to address the specific components of your marking scheme for student and instructor use both prior to and following the assignment submission.
- You find yourself wondering if you are grading or commenting equitably at the beginning, middle, and end of a grading session.
- You have a team of graders and wish to ensure validity and inter-rater reliability.
What is a rubric?
A rubric is an assessment tool that clearly indicates achievement criteria across all the components of any kind of student work, from written to oral to visual. It can be used for marking assignments, class participation, or overall grades. There are two types of rubrics: holistic and analytical.
Holistic rubrics group several different assessment criteria and classify them together under grade headings or achievement levels.
For a sample participation rubric, see the Appendix of this teaching tip. Our Responding to Writing Assignments teaching tip includes holistic rubrics specifically designed for writing assignments. See also Facione and Facione's (1994) "Holistic Critical Thinking Rubric [PDF]," useful in many disciplines.
Analytic rubrics separate different assessment criteria and address them comprehensively. In a horizontal assessment rubric, the top axis includes values that can be expressed either numerically or by letter grade, or a scale from Exceptional to Poor (or Professional to Amateur, and so on). The side axis includes the assessment criteria for each component. Analytic rubrics can also permit different weightings for different components.
See the Teamwork VALUE Rubric [PDF], one of the many rubrics developed by the American Association of Colleges and Universities, or (AAC&U).
How to make a rubric
- Decide what criteria or essential elements must be present in the student’s work to ensure that it is high in quality. At this stage, you might even consider selecting samples of exemplary student work that can be shown to students when setting assignments.
- Decide how many levels of achievement you will include on the rubric and how they will relate to your institution's definition of grades as well as your own grading scheme.
- For each criterion, component, or essential element of quality, describe in detail what the performance at each achievement level looks like.
- Leave space for additional, tailored comments or overall impressions and a final grade.
Developing rubrics interactively with your students
You can enhance students’ learning experience by involving them in the rubric development process. Either as a class or in small groups, students decide upon criteria for grading the assignment. It would be helpful to provide students with samples of exemplary work so they could identify the criteria with greater ease. In such an activity, the instructor functions as facilitator, guiding the students toward the final goal of a rubric that can be used on their assignment. This activity not only results in a greater learning experience, it also enables students to feel a greater sense of ownership and inclusion in the decision making process.
How to use rubrics effectively
Develop a different rubric for each assignment
Although this takes time in the beginning, you’ll find that rubrics can be changed slightly or re-used later. If you are seeking pre-existing rubrics, consider Rhodes (2009) for the AAC&U VALUE rubrics, cited below, or Facione and Facione (1994). Whether you develop your own or use an existing rubric, practice with any other graders in your course to achieve inter-rater reliability.
Give students a copy of the rubric when you assign the performance task. These are not meant to be surprise criteria. Hand the rubric back with the assignment.
Integrate rubrics into assignments
Require students to attach the rubric to the assignment when they hand it in. Some instructors ask students to self-assess or give peer feedback using the rubric prior to handing in the work.
Leverage rubrics to manage your time
When you mark the assignment, circle or highlight the achieved level of performance for each criterion on the rubric. This is where you will save a great deal of time, as no comments are required.
Include any additional specific or overall comments that do not fit within the rubric’s criteria.
Be prepared to revise your rubrics
Decide upon a final grade for the assignment based on the rubric. If you find, as some do, that presented work meets criteria on the rubric but nevertheless seems to have exceeded or not met the overall qualities you’re seeking, revise the rubric accordingly for the next time you teach the course. If the work achieves highly in some areas of the rubric but not in others, decide in advance how the assignment grade is actually derived. Some use a formula, or multiplier, to give different weightings to various components; be explicit about this right on the rubric.
Consider developing online rubrics
If an assignment is being submitted to an electronic drop box you may be able to develop and use an online rubric. The scores from these rubrics are automatically entered in the online grade book in the course management system.
Facione, P. & Facione, N. (1994). The holistic critical thinking rubric [PDF]. Insight Assessment/California Academic Press.
Rhodes, T. (2009). Assessing outcomes and improving achievement: Tips and tools for using the rubrics. Washington, DC: Association of American Colleges and Universities.
CTE teaching tips
- Huba, M. E., & Freed, J.E. (2000). Using rubrics to provide feedback to students. In Learner-centered assessment on college campuses (pp. 151-200). Boston: Allyn & Bacon.
- Lewis, R., Berghoff, P., & Pheeney, P. (1999). Focusing students: Three approaches for learning through evaluation. Innovative Higher Education, 23(3), 181-196.
- Luft, J. A. (1999). Rubrics: Design and use in science teacher education. Journal of Science Teacher Education, 10(2), 107-121.
- Stevens, D. & Levi, A. (2013). Introduction to rubrics: An assessment tool to save grading time, convey effective feedback, and promote student learning (2nd ed.). Virginia: Sylus.
- Stevens, D., & Levi, A. Introduction to rubrics companion site.
- iRubric: an online rubric design system for using, adapting, creating, and sharing rubrics.
- Association of American Colleges & Universities VALUE rubrics
Appendix: sample holistic participation rubric
- Always prepared and attends nearly every class
- Participates constructively in class, models leadership for others and on teams
- Exhibits preparedness and punctuality in class/class work
- Demonstrates initiative and improvement without prompting
- Seeks to understand and acknowledge others’ thoughts
- Often reaches full potential by challenging self
- Exceptional content knowledge readily integrated into new problems or settings
- Challenges his/her own thoughts and ideas
- Usually prepared and attends most classes
- Participates constructively in class, works well with others, and is a team player
- Excellent content knowledge
- Completes all class assignments; occasionally adds something extra
- Demonstrates initiative and improvement with some prompting
- Seeks to understand and acknowledge others’ thoughts
- Stretches to reach full potential when prompted
- Open to challenges to thoughts and ideas from others
- Sometimes prepared and attends many classes
- Average content knowledge
- Occasionally or only challenges thought when encouraged by others
- Assignments reflect average work
- Sometimes an active participant in class; works fairly well with others
- Occasionally accepts and attends to challenges and feedback
- Rarely prepared and attends some classes
- Rarely participates constructively in class
- Assignments are late, incomplete, or not turned in at all
- Low level of content knowledge
- Inactive participant; works reluctantly with others
- Sometimes shows a close-minded disposition with regard to feedback and challenge
- Clearly unprepared and nearly always absent
- No participation or harmful participation
- No assignments turned in
- No assignments available to assess content knowledge
- Not present enough to judge participation and interaction, or undermining others
- Close-minded disposition with regard to feedback, challenge, and course content
This Creative Commons license lets others remix, tweak, and build upon our work non-commercially, as long as they credit us and indicate if changes were made. Use this citation format: Rubrics: useful assessment tools. Centre for Teaching Excellence, University of Waterloo
As you give students feedback on their writing, you might consider commenting on mathematical correctness, clarity, flow and organization, and other general principles of communicating mathematics. A balance must be found among verbose commenting, a reasonable time investment, and what’s most helpful for students. Some suggestions:
- Consider your purpose for commenting and craft your comments to achieve that purpose.
- To gain a sense of the effect of comments on students, see the video “Beyond the Red Ink: Teachers’ Comments through Students’ Eyes.” Although these students are first-year humanities students, experience suggests that upper-level mathematics students are not far different.
- Consider meeting with each student to provide feedback. Although scheduling meetings can be a hassle, feedback given in person is often more efficient and richer than feedback given in writing, and you’ll get to understand the students better as writers by hearing their responses to your comments.
- Point out what the student does well. Positive feedback is remarkably effective.
- Remind yourself to consider the text at all scales: it’s easy to overlook large issues when you’re focused on details. Research suggests that students’ revisions will be limited to those aspects of writing that your comments imply are of greatest importance to you. (Bracey 2013)
- Consider how much the student can learn in the available time: there’s no need to list all types of problems in a paper. Decide what the student most needs to learn at this point and consider giving only those comments. [When planning an assignment, consider scheduling multiple revisions so large-scale issues may be addressed during the first revision and smaller-scale issues may be addressed during later revisions.]
- If you feel you must provide many comments, you can help students recognize the relative importance of the various comments by drawing attention to the most important ones in a summary note.
- Less important issues can be de-emphasized through the use of coded comments (see this example of comment codes from an engineering class).
- Do not mark each instance of a recurring problem: instead tell the student how to identify the problem for him/herself.
- If you’re distracted by an error until you mark it, very briefly mark errors on a scratch paper or in a temporary document, providing only enough information for yourself. Then when you’ve finished reading, decide which comments to give the student.
- If the writing will not be revised, then limit yourself to general comments that apply to future writing.
- Suggest that the student keep an editing checklist of mistakes he or she often makes.
- The student is the author, so when you draw attention to a problem, avoid dictating a solution unless necessary.
- To avoid comments being taken personally, refer to the text, not to the student: “This paragraph could be more concise.” not “You don’t write concisely enough.” To write helpful comments, consider these dimensions of commenting.
- Reading papers is time consuming and occasionally frustrating. Take care to remain professional.
For further explanation of the above suggestions, see these two pages about Commenting.
In addition to or instead of giving individualized feedback, you may choose to give feedback to the class as a whole. Example: Guidance for revising an algorithm assignment.
Choosing grading criteria
To assign grades, it can be helpful to first decide what writing characteristics you value and then use those characteristics to create a grading rubric.
For a detailed explanation of this strategy, see this grading handbook, which includes sample lists of characteristics of good mathematical writing and sample rubrics, as well as guidance for grading drafts, etc.
Grading for small writing assignments
One strategy is to assign two grades to each small writing assignment: one for mathematical content and one for quality of exposition. To speed up grading, you may want to assign an overall exposition grade rather than one for each problem on the assignment (if there are multiple). Make sure your students are aware that effective communication is being evaluated and will contribute to their grade. If possible, give them a rubric or a sample of what you are looking for.
Example: 18.310C rubric for grading heapsort algorithm
If you give students a rubric before the assignment is due, they are likely to write to the rubric. Consider not providing a rubric for the first writing assignment, so you have the opportunity to see how students write on their own. You may then design future rubrics to emphasize whichever writing characteristics you most want students to emphasize.
Grading for large projects
The grading of the final project should reflect all of its aspects: proposal, any intermediate drafts, peer-review, and final product. It may be helpful to the students to see the grading rubric you will use; many of them will not have written a long piece of mathematics before.
Here is an example of a rubric for grading a draft. Two grades are assigned: the grade that counts is based on effort/completeness, but students are also given a temporary “advisory grade” based on the rubric for the final paper. This strategy rewards effort while allowing room for improvement and giving information about how much improvement is needed.
For the final paper, you may want to grade the following:
- Correctness of mathematics
- Clarity of exposition
- Flow and organization of paper
- Other general principles of communicating math that you consider to be most important
- Extent to which feedback was incorporated. (Some students may be disinclined to incorporate feedback unless doing so is built into the grading.)
A sample rubric for the final paper is included with the rubric for the draft (above). Another option is to use a more detailed grading grid.
Encouraging students to do more than superficial revision
Sometimes students revise only superficially when major revisions are needed. To help students understand the extent of revision needed, and to encourage them to make significant revisions when those are required, consider the following strategies:
- If major revision is needed, give only high-level comments. Giving detailed comments will cause students to focus on details and may cause them to lose sight of the big picture, thus preventing major revision.
- Explicitly tell students which sections of the paper ought to be “rewritten” rather than “revised.”
- Avoid scheduling revision at the end of the term when students are pressed for time.
- Meet with students individually to give them a chance to ask questions about feedback. The one-on-one attention also makes clear to students that you consider the quality of writing to be important.
- If you have a writing workshop in which you show students drafts of your own writing, choose drafts that exhibit major revision. By modeling major revisions yourself, you’ll help students to realize that they may also need to make major revisions.
- Have students assess the quality of their own writing and submit a revision plan.
- Require students to indicate which changes they made and explain why changes were not made.
- Include in the grade the extent to which instructor and peer comments were addressed.
Literature on assessing writing
- Patrick Bahls’ 2012 book Student Writing in the Quantitative Disciplines: A Guide for College Faculty contains a chapter on Assessing and Responding to Student Writing.
- Crannell, A., “Assessing Expository Mathematics: Grading Journals, Essays, and Other Vagaries,” Assessment Practices in Undergraduate Mathematics, MAA Notes #49.
- Emenaker, C.E., “Assessing Modeling Projects in Calculus and Precalculus: Two Approaches,” Assessment Practices in Undergraduate Mathematics, MAA Notes #49.
- Crannell, A., “How to grade 300 math essays and survive to tell the tale,” PRIMUS 4 (3), 1994.
- Houston, S.K., et al., Developing Rating Scales for Undergraduate Mathematics Projects, University of Ulster, 1994.
Using writing to assess understanding of mathematics
- Morgan, C., Writing Mathematically: The Discourse of Investigation, Falmer Press, 1998.
From the Google Books review: “…[using] written language to serve as ‘evidence’ of their mathematical activity and achievement,… raises two important questions. Firstly, does this writing accurately present children’s mathematical activity and ability? Secondly, do math teachers have sufficient linguistic awareness to support their students in developing skills and knowledge necessary for writing effectively in their subject area?”
- See also the general resources for assessing understanding of mathematics, listed on the Assessment page.
General resources and research (not specific to mathematics)
- How can I handle responding to drafts? The WAC Clearinghouse
These pages provide strategies for
- focusing your commenting energies
- using a grading sheet (including sample grading sheets)
- evaluating writing to learn assignments
- “Beyond the Red Ink: Teachers’ Comments through Students’ Eyes” Conversations with Bunker Hill Community College Students, Bedford/St. Martin’s
- John C. Bean’s Engaging Ideas: The Professor’s Guide to Integrating Writing, Critical Thinking, and Active Learning in the Classroom includes a clear and helpful chapter on Reading, Commenting On, and Grading Student Writing.
- Nancy Sommers’ Responding to Student Writing Bedford, St. Martins, 2013. (publisher’s page)
- Bracey, E., “The Will to Revise: Commenting, Revision, and Motivation in College Students“, Xchanges, Issue 9.1, 2013.
Bracey’s research supports some prior results by indicating that the revisions of students who use a writing center focus on those aspects of writing that are emphasized most in their professor’s comments: e.g., if the professor comments only on grammatical issues, the students focus only on grammatical issues and resist writing center assistance on clarity, coherence, etc. This 2013 article begins with a helpful review of research on the factors that motivate student revision.
- Taylor, S. S., “‘I Really Don’t Know What He Meant By That’: How Well Do Engineering Students Understand Teachers’ Comments On Their Writing?” Technical Communication Quarterly, Vol. 20, No. 2, pp. 139-166, 2011.
Teachers and engineering students from one institution were interviewed about the teachers’ comments on the students’ papers. Students recognized the focus of about three quarters of teachers’ comments but understood the reasons for only half of the comments. The results are broken down by type of comment and discipline of teacher. Recommendations are suggested, including that teachers provide more explicit explanations for comments. This 2011 article begins with a helpful review of research on response and on student reception of response.
- Summers, N., C. Rutz, and H. Tinberg. “Re-Visions: Rethinking Nancy Sommers’s ‘Responding to Student Writing.’ 1982.” CCC Vol 58, No 2 (2006) pp. 246-266.
This collection of three essays summarizes some past and current (as of 2006) research and thinking about responding to student writing. In the first essay, “Across the Drafts,” Nancy Sommers summerizes some of the findings from the Harvard Study of Undergraduate Writing, which followed the writing of and feedback received by 400 students over their four years at Harvard.
- Anson, Chris M. “Response Styles and Ways of Knowing.” Writing and Response Theory, Practice, and Research. Ed. Chris Anson. Urbana: National Council of Teachers,1989. 332-366.
- A case against machine-scoring of writing: an easy-to-read annotated bibliography written in 2013 by Human Readers, a group of concerned writing-program administrators and communication educators. See also Grading Writing: the Art and Science–and why computers can’t do it, by Doug Hesse.
A case for machine-scoring of writing: these pages of the ETS website include bibliographies of ETS’s research.
- See also the resources on this site’s general page about assessment.
Please suggest key research to add to this list.