By Barbara A. Swartz, posted January 19, 2016 —

Last month on the Mathematics Teacher blog, Jerry Brodkey wrote about how and why we should start deemphasizing grades in our mathematics classes. I was excited by his post because I too have been trying out this approach and gradually converting some other teachers to the idea. My solution was to stop assigning grades (on selected assignments)!

Jo Boaler advocates changing our practices from “assessment of learning” to “assessment for learning” in chapter 5 of What’s Math Got to Do With It? (2008) and mentions a study (Butler 1988) on assessing student work in three different ways: using feedback, using grades, or using both. The students who received only comments significantly increased their performance, whereas, surprisingly, the students who received both grades and comments did as poorly as those who received only grades without any comments on their work. Black and Wiliam (1998) report that checking in regularly on students’ understanding is more helpful than an end-of-unit summary of mastery. More recently, NCTM reminds us that assessment is an essential piece of classroom instruction and not just “the final stage in the traditional teach-learn-assess cycle” (NCTM 2014, p. 94).

These results prompted me to simply stop putting grades on the top of students’ quiz papers and instead use comments as a means of providing feedback. For the last three years in each of my mathematics content courses for preservice elementary school teachers, I have instituted biweekly quizzes that did not carry a grade. These “quizzes” were short written assessments that asked students questions similar to those that would be on the course’s summative assessments (midterms and final exams). They provided students with an opportunity to practice formalizing their thoughts on paper. I evaluated these quizzes for correctness by writing comments on the students’ written responses but never assigned a numerical or letter grade. The comments asked students to explain their thinking further and to clarify their mathematical language; they also affirmed students’ thinking when they provided thorough explanations, so that each student knew whether or not his or her understanding of the topic was sufficient.

I then wanted to find out how the students felt about these “quizzes” that did not carry a grade, to see whether or not their thoughts corroborated Butler’s (1988) findings. In my end-of-course evaluations, I asked students what they thought of these formative assessments. The result was overwhelmingly positive. One student’s comment captures the overall sentiment: “I liked the formative assessments. They helped me to gauge my understanding of the material above and beyond just the reading and taking notes that happens in my journal. I found it was easy to think I knew things, but, when confronted with the Formative Assessment, I was able to better determine my understanding.”

In addition, almost all students across all eight courses stated that they would not have preferred a grade on the assessment; they were able to focus on the feedback they received to deepen their understanding instead of being distracted by the (potentially poor) grade. These students’ responses reveal that an evaluative mark on their work would not have any added value to their learning or thinking, supporting Butler’s claims from almost thirty years ago.

At the 2014 NCTM Regional Conference in Richmond, Virginia, I presented the use of this assessment strategy and my success with nongraded quizzes. About six months later, I received an email from one of the session participants saying that she had implemented this assessment strategy in her precalculus classes and was having similar success with it! Another teacher has implemented these nongraded quizzes with his ninth-grade Algebra 1 class and also in his College Algebra/Trigonometry course. Both teachers have had nearly identical results with their students, and the first teacher even found statistically significant differences in the class averages of her precalculus courses when she used the nongraded quizzes.

My challenge to those reading this blog is to resist putting a grade at the top of your students’ quizzes, both to deemphasize the importance of the grade and to place the value on your students’ understanding. Use these recurrent assessments as a means for feedback and a way for your students to start to view their learning as a process through which they can practice, make mistakes, and learn from those mistakes to improve their understanding.

References

Black, Paul, and Dylan Wiliam. 1998. “Inside the Black Box: Raising Standards through Classroom Assessment.” The Phi Delta Kappan 80 (2): 139–48.

Boaler, Jo. 2008. What’s Math Got to Do with It? New York: Penguin Group.

Butler, Ruth. 1988. “Enhancing and Undermining Intrinsic Motivation: The Effects of Task-Involving and Ego-Involving Evaluation on Interest and Performance.” British Journal of Educational Psychology 58: 1–14.

National Council of Teachers of Mathematics (NCTM). 2014. Principles to Action: Ensuring Mathematical Success for All. Reston, VA: NCTM.

BARBARA A. SWARTZ, [email protected], is an assistant professor of mathematics education at McDaniel College in Westminster, Maryland. She is interested in mathematics teacher education and teaches mathematics courses for prospective elementary and secondary school mathematics methods.