By Kate Owens, Instructor, Department of Mathematics, College of Charleston
In the past, I was frustrated with grades. Usually they told me very little about what a student did or didn’t know. Also, my students didn’t always know what topics they understood and on what topics they needed more work. Aside from wanting to do well on a cumulative final exam, students had very little incentive to look back on older topics. Through many conversations on Twitter, I learned about Standards Based Grading (SBG) and I implemented an SBG system in several consecutive semesters of Calculus II.
The goal of SBG is to shift the focus of grades from a weighted average of scores earned on various assignments to a measure of mastery of individual learning targets related to the content of the course. Instead of informing a student of their grade on a particular assignment, a standards-based grade aims to reflect that student’s level of understanding of key concepts or standards. Additionally, students are invited to improve their course standing by demonstrating growth in their skills or understanding as they see fit. In this article I will explain the way I implemented SBG and describe some benefits and some drawbacks of this method of assessment.
I chose Calculus II to try an SBG approach because it was my first time teaching the course, so I could build my materials from the ground up. Also, unlike several other courses I teach, the student count remains low — approximately 25 per section. Before the start of the semester, I created a list of thirty course “standards” or learning goals. Roughly, each goal corresponded to one section of the textbook. I organized the thirty standards around six Big Questions that I felt were the heart of the course material. One Big Question was, “What does it mean to add together infinitely many numbers?” The list of standards served as answers to these Big Questions. The list of standards and a description of the grading system were distributed to the students on the first day of class. During the semester, students were given in-class assessments in the form of weekly quizzes, monthly examinations, and a cumulative final examination. The assignments themselves were similar to those found in courses using a traditional grading scheme, but they were assessed differently. Rather than track a student’s total percentage on each particular assignment, for every problem I examined each student’s response and then assigned a score to one or more associated course standards. I provided suggested homework problems both from the textbook and using an online homework platform, but homework did not factor directly into a student’s grade. Instead, if I noticed a student needed more practice at a particular sort of problem, I would direct her to the associated homework problems for additional practice.
During in-class assessments, a single quiz or exam question asking a student to determine if an infinite series converged might also require the student to demonstrate knowledge of (a) “The Integral Test,” a strategy for determining if a series converges or diverges; (b) “Improper Integrals,” the process used to evaluate integrals over an infinite interval; (c) some method of integration, such as “Integration by Parts,” and (d) some prior knowledge about how to evaluate limits learned earlier in Calculus I. For each of these concepts, I assign a different score (on a 0-4 scale), roughly correlated with a GPA or letter-grade system. During the semester, I tracked how well each student did on each of the thirty standards.
Since some standards appeared in a multitude of questions throughout the semester, a student’s current score on a standard was computed as the average of the student’s most recent two attempts. Outside of class, each student could re-attempt up to one course standard per week. Usually these re-attempts occurred during office hours and were in the form of a one- or two-question quiz. My rationale for continually updating student scores is that I want grades to reflect a current level of understanding since I want students to aim for a continued mastery of course topics. Over the course of the semester, their scores on standards can move up or down several times. Students are motivated to continue reviewing old material since they know that they might be assessed on those ideas again and their previous grades could go in either direction.
At the end of the term, each student had scores on approximately thirty course standards. To determine a student’s letter grade, I used the following system:
- To guarantee a grade of “A”, a student must earn 4s on 90% of standards, and have no scores below a 3.
- To guarantee a grade of “B” or higher, a student must earn 3s or higher on 80% of course standards, and have no scores below a 2.
- To guarantee a grade of “C” or higher, a student must earn 2s or higher on at least 80% of course standards.
I adapted this system from one Joshua Bowman used. I like it because it captures my feeling that an “A-level” student is a student who shows mastery of nearly all concepts and shows good progress toward mastery on the others; meanwhile, a “B-level” student is one who consistently does B-level work. Also, this system requires students earn at least a passing grade on each course topic. In a traditional system, a student might do very well in some parts of the course, very poorly in others, and earn an “above average” grade. In the system I used, for a student to earn an “above average” grade, they must display at least a passing level of understanding of all course concepts. While students aren’t initially thrilled with this requirement, most are happy once I explain they can re-attempt concepts often (within some specific boundaries) and so the only limit on improving performance is their motivation to do so.
There are three major advantages of tracking scores on standards. First, I can quickly assess student performance:
Second, I can give meaningful advice to students:
Third, I can determine what topics are in need of review or additional instruction:
Students have noted that SBG has several benefits for them as well. They aren’t limited by past performance and can always improve their standing in the course. Many students who describe themselves as “not math people” or those who say they suffer from test anxiety appreciate that their grades can continue to improve, thereby lowering the stakes on any particular assessment. In my office, conversations are almost always about mathematical topics instead of partial credit, why they lost points here or there, or what grade they need on the next test to bring their course average above some threshold. The change in types of conversations during my office hours has been amazing, and for this reason alone I will stick with SBG in the future. Students review old material without prompting, they feel less stress over any individual assignment, we don’t have conversations about partial credit or lost points, and they are able to diagnose their own weaknesses.
With that said, the SBG system also has some disadvantages. First, it takes a thorough and careful explanation to students about the way the system works, why it was chosen, and why I believe it is to their benefit. Student buy-in is critical and it isn’t always easy to attain. I have found that spending a few minutes of class time discussing SBG every day for the first one or two weeks is more helpful than giving a lot of explanation on any particular day. Students need some time to think about what questions and concerns they have, and I encourage them to voice these in class whenever they like. Initially, students think that this system will be too much work for them, or that their course grades will suffer since past strong performance could be wiped out in the future. (In contrast, by the end of the semester, almost all students say they really appreciated this method and felt they learned more calculus than they would have in a traditionally graded course.) Second, several students complained that their grades were not available through our online learning management system; I still haven’t found a way to convince our online gradebook to work in an SBG framework. Instead, students must come to my office to review their scores with me outside of class time. Third, choosing both the correct number of course standards as well as a thorough description of each standard has been challenging. It’s difficult to balance wanting each standard to be as specific as possible while keeping the total number of standards workable from both my viewpoint and that of the students.
After several semesters of using an SBG framework, I believe the benefits to the students outweigh the disadvantages. At this point, I don’t have any firm data about student learning outcomes, but I do have some anecdotal evidence. The feedback from my students about this method of grading and, in particular, the details of my implementation has been very positive. I have received several e-mails from former students who, even semesters later, realize how much SBG changed their perspective on the learning process, or who wished their new instructors would switch to an SBG system. Comments on my student evaluations have mentioned that they feel their grade accurately reflects how much calculus they know, rather than how well they performed on a particular assignment, or how much they were punished from making arithmetic mistakes. As one student noted, “this class was not about how well you could take a test or quiz or do homework online that sucked. It was about the amount of calculus you understood and your effort to be better at it.” As a calculus instructor, this describes my exact goal for my course.
If you are interested in trying an SBG approach in your own courses, here are four questions to jump-start your journey:
- What are the core ideas of your course? What concepts or ideas do you want students to master?
- How many standards do you think you can track? You need them to be specific enough that students can understand exactly what each one means, but you also need to have few enough that your grading workload is manageable. I have 30 for a 16-week semester.
- Will you allow re-attempts? What kinds of limits will you set, if any? I found that limiting students to re-attempting only one standard per week was essential in cutting down my grading workload. This limit also gave students the opportunity to focus on one topic at a time, rather than re-attempting several at once just to see what would stick.
- How will a final assessment, project, or exam count? In my course, a student’s course score on each standard is a weighted average: 80% comes from their pre-final exam score and the remaining 20% comes from the score earned on the final itself. In this way, the final exam contributes about 20% to the student’s letter grade in the class, a figure in line with what is commonly used in my department.
- How will you convert all the scores on standards into a letter grade?
Online SBG Resources
- Twitter hastags: #sbg, #sbgchat, #sblchat
- http://tinyurl.com/SBGLiterature, Scholarly articles related to SBG (list maintained by Matt Townsley)
- http://thalestriangles.blogspot.com/search/label/sbg, SBG blog posts by Joshua Bowman (@Thalesdisciple)
- http://shawncornally.com/wordpress/?p=673, Standards-Based Grading FAQ by Shawn Cornally
- http://blogs.cofc.edu/owensks/tag/sbg/, my own blog posts about SBG
- https://plus.google.com/communities/117099673102877564377, a newly formed Google Plus community for anyone interested in conversations about standards-based or specifications-based grading