*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.

*Image: **The Integrity of the Grade, courtesy of Dr. Justin Tarte, @justintarte*

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

Hello – I am a senior studying math education at the University of Illinois. I will be student teaching Algebra 1 and Geometry next semester, both of which use Standards Based Grading methods. To be honest, prior to reading your blog post I did not have a very positive opinion of SBG. To me, it seemed like too discrete a way of assigning students an assessment score. However, the comment you stated that I really liked and will stick with me is, “I want grades to reflect a current level of understanding since I want students to aim for a continued mastery of course topics.” This really got me thinking, since I remember all the times both in high school and college when I thought, “If only I had another chance…I really knew that material, but I wasn’t in the right mindset in that moment.” You’re right…SBG allows this to happen, and from a student’s perspective, I can see why this would probably be preferred. It seems like it’s worked really well at the college level with your Calculus students. My one worry is that since I will be using this with freshmen/sophomore students in high school, they will avoid doing well on exams from the start since they know they can just retake it if they don’t do well. While it is clear your students’ motivation increased with your SBG implementation at the college level, I’m not so sure about how to make it work so effectively next semester with my high school students. Do you have any advice on strategies I can use to make it seem like the optimal strategy and have students get the most out of it?

Hi Cam! Thanks for your comment. I hope to throw together some of my thoughts in reply, but please ask me again if I miss a key concern or question.

As it turns out, many of the educators pioneering non-traditional grading approaches are in the K12 community. For example, Frank Noechese (@fnoschese on Twitter; website https://fnoschese.wordpress.com/about/) is a Physics teacher at a secondary school whose standards-based grading philosophy inspired me to make the leap. I have joined a Gooogle+ community of standards-based learning educators and we would love to have your insight as you navigate your own path — join us at https://plus.google.com/communities/117099673102877564377 . Indeed, as the community formed, a few people in the K12 community were happy to sign up. Their experiences will possibly be more aligned with what you’ll see next year than my own. I consider myself a relative newcomer to the SBG/non-traditional grading movement.

As far as your specific concern: “[T]hey will avoid doing well on exams from the start since they know they can just retake it if they don’t do well.” I was worried about this, too. What I found is that limiting the number of standards that could be attempted weekly helped quite a bit. I have 30 standards per 16 weeks, and at a one standard per week cap, students realize they must get close to mastery on at least some topics. Additionally, after the first exam, I try to encourage students as much as possible to come to my office, even if they believe they aren’t ready to re-attempt yet. Sometimes I find that what they are lacking isn’t mathematics, but instead confidence; after a brief chat, I can tell they know the material, and what they seek is encouragement instead of insight.

I think at the heart of your concern is something every educator must face — occasionally we all have students who, for whatever reason, don’t put 100% of their effort into their studies. I wish SBG was a magic wand for this issue, but it isn’t. In my experience, a student who earns a C-minus in a traditional course is very likely to earn a C-minus in my standards-based course for exactly the same reasons. As an instructor, my target is those B or C level students who have a lot of motivation & work ethic (but perhaps who lack confidence) to improve their standing. If a student is determined to fail a course, there isn’t much I can do — but if a student really wants to learn and demonstrate mastery of the material, I see it as my job to cheer them on as they work toward this goal.

I hope that this helps and that you’ll come join our Google+ community and conversation; or find me on Twitter: @katemath.

I am also a senior studying Math Education at the University of Illinois at Urbana-Champaign. I will be student teaching next semester in a high school in Champaign that also uses SBG.

I think it’s really interesting that you were able to implement this at the college level. I’ve only heard of this being used in K-12 like you’ve mentioned in your reply to another commenter. Do you feel that this method of grading can be applied more widescale at the college level? I feel like for students who were recently introduced to SBG from a traditional style and then going back to traditional in college is unhelpful to students in the long run. What are your thoughts on this?

Hi Peter,

I am hoping to develop an SBG approach in many of my college courses. Next semester, I’ll be implementing an SBG system in a very different course — “College Algebra”, which is the lowest level mathematics course offered at the College of Charleston. My process of switching to an SBG philosophy has been strongly supported by the advice, knowledge, and experience of several online colleagues. I have found that asking lots of questions has led to many fruitful conversations about these issues, so I encourage you to keep asking whatever pops to mind.

As far as students switching from SBG to traditional (or the other direction), this is something I have also wondered about. My own conclusion is that my students face a similar transition between any two instructors. For example, one instructor might focus a lot on grading homework, whereas another doesn’t grade homework but has daily graded quizzes. These challenges are common in every college experience, regardless of grading approach or philosophy. My own experience makes me believe that I should do what I feel is in the best interest of my students, even if this is a different approach than the one taken by my colleagues. I believe that having an open and honest dialogue with both groups — both my colleagues and my students — is important.

Lastly, I’ve received a lot of feedback from prior students that my SBG implementation has changed the way they approach their education for the better. They value our conversations on what it means to learn, on why I think the SBG approach is in both their interest and my own, and also on how their education is essentially their responsibility. It is my job to give them a clear picture as to what they know, where they can improve, and support that improvement whenever possible; it is their job to “do the work,” face the challenge head on, and strive to do the best that they can. I hope to be more of a cheerleader or coach for them, rather than a judge & jury. Students seem to agree that an SBG philosophy allows me to do this and they appreciate the extra work it takes, on their side and my own.

Come join our Google+ community if you’re interested in perspectives apart from my own! We are looking forward to continuing this conversation.

I have been slightly exposed to standards based grading in my last two years of college, and I like it for a few reasons. Namely, I like that it allows for better understanding of individual progress in actual learning than traditional grading, and that it redefines success by allowing students to retest and continue to demonstrate learning and improvement. You also mention several disadvantages, but many of them are results of SBG not being “mainstream”. Clearly, this post shows that standards based grading is a success for Calculus II, and probably for most other math courses, so why is it so difficult to facilitate a switch to SBG several orders of magnitude larger than a single classroom? I understand that education reform is slow to begin with, and gets slower the more you try to reform, but don’t many educators share your perspective on SBG? I know that as a student, I would appreciate standards based grading far more, as it just feels more like learning than traditional grading does. As a future teacher, I want to afford my students this opportunity, but I fear the community and department backlash for being a “new teacher” with new tools. Is there a strategy better than just buckling down and grading in this manner regardless of what anyone else says?

Hi Kyle,

I am in the process of planning for next semester. I’ll be teaching several sections of our “College Algebra” course for the first time, and I’m developing an SBG-approach for this class. The class will be quite different than Calculus II. First, there will be many more first-year students. Second, many of them won’t be in science or mathematical majors. I am excited to see how they respond. Third, I’ll have many more students than I did in Calculus II. I’m hoping that it goes well; I plan to blog about what I learn at my own blog (http://blogs.cofc.edu/owensks) and also share my experiences with our Google+ community (https://plus.google.com/communities/117099673102877564377).

You mention: “I fear the community and department backlash for being a “new teacher” with new tools.” I’d be lying if I said this hadn’t crossed my mind as well, especially considering that this semester (Fall 2015) I faced my Third Year Review as part of our Tenure & Promotion process. With that said, I believe it’s my job to use my best professional judgement to figure out what I think is best for my students — meanwhile focusing on being completely transparent about the hows & whys of my choices, whether to my department, my administration, or my students. For me, I can’t imagine going back to a traditional grading philosophy because of the experiences I’ve had in my SBG courses. In outlining the “hows and whys” in my T&P documents, I found that my colleagues were very supportive of my non-traditional approach. After ten years in the university classroom, I have found all the departments I’ve worked with to be places that welcome innovation, so long as that innovation is well-supported by strong professional judgment and honest, ongoing conversations.

Come join our Google+ community and see if everyone else will echo my experience. (I’d be curious to know what they have thought throughout their careers!) Check out https://plus.google.com/communities/117099673102877564377 .

The SBG system is a great step forward in the way teachers and professors approach learning. Speaking from personal experience, this system of grading allows for students to learn at their own pace, to be in charge of their own mastery of the material, and ultimately reinforces the subject matter. With this system, it also prevents one “bad day” from tanking the students grade. Of course their are limits to where and how the SBG system can be applied, but for Calc II, it worked beautifully. Dr. Owens was able to teach one of the best — and yet one of the hardest — classes I’ve ever taken, while allowing me to learn at a rate that suited me and promoted my learning. At least for every math class I have ever taken, SBG would’ve improved the experience by promoting learning as opposed to memorizing.

I have been exposes to SBG along with the concept of visual learning and I have fallen in love with the idea of both of these, but I am getting nervous implementing them in my classroom. I appreciated that you highlighted the pros and the cons that you discovered. The thing that encourages me the most about your review is that you said in your office, discussion went from partial credit to math topics. Isn’t that what the discussions should be? Student learning seems like it would increase so much if students were concerned about learning, not their grade. I think the fact that you said student buy-in is crucial and your four questions are exactly on point. One thing I am really nervous about is the amount of time it seemed as though you put in – and you mentioned that it was for smaller class sizes. Do you have any advice for SBG in a high school with 35 kids to a classroom and 6 difference classes? I think it would be a great benefit to my students and school to move toward SBG but I am afraid to take that first step.

Hi Ali,

I was nervous too, before my first SBG class. I think this is just part of the process we all go through when making big changes to our courses. As far as particular advice about your high student count (35*6), I would suggest designing a system that is easy (perhaps Pass/No Pass?) and somewhat automated — for example, if you have access to test generation software, using that to create multiple versions of a single re-assessment rather than having to write each one individually. You’re welcome to join our Google+ community (the link is above) and there you might find people whose SBG experience is more akin to your situation & who can offer even more insight than I can. Good luck 🙂

Hi Kate,

This is amazing! I do have one question for you: How do you go about recording your grades? What gradebook program do you use?

Same question. Also, on the retakes … were there problems about access? I mean, that some students could make the office hours and others could not?

Hi Kevin. I didn’t have any access problems. I tried to schedule my office hours around times I knew the students would be free. Occasionally, I’d set up an appointment to meet with someone if they really had a conflict. In cases of a busy week, our admin assistants help us proctor, so rarely (once or twice) I left a re-assessment quiz with them for a student to take during normal business hours. I didn’t like this option since I always wanted to sit down and chat with the student before they tried another problem, just to help clear up any underlying misunderstandings of the material.

Since writing this post, I’ve started using our online LMS gradebook. It isn’t a great fix. For example, since students take quizzes a different number of times, this data can’t really be stored in the gradebook. We have a D2L product. I did figure out how to do a “Selectbox” grade, so I have my EMRN system there. I have one column per standard and I update the dropdown menu each time a student makes an attempt at a standard. I also save some data in Excel on my office computer where I feel like I have more control over how calculations are handled.

Hope this helps!

Hi, I am a high school math teacher that teaches a variety of classes from Algebra 1 to co-teaching Dual Credit College Algebra. I really am interested in SBG because it sounds like it focuses more students on math topics instead of their grade all the time. I come across the topic of grades almost every day and I really feel like students are so wrapped up in the grade that they aren’t really learning as much; instead they are trying to memorize. I already implement a rework process within my regular grading system because I really like to see my students find their errors and learn from them. However, I don’t know how well SBG would work in the high school setting. Is SBG something that should be implemented school-wide to help the students understand the process or will in not matter if I am the only one in the high school to implement this? How many of your colleagues use this same system?

Hi Kristie,

So far, none of my colleagues in my department are using an SBG approach. However, there are a few folks around the university who are trying either specifications grading or SBG outside of the math department. I think your students would benefit from this approach even if you’re the only one using it.

Thank you for sharing!! I have just started my 3rd year at a High School and am teaching a new prealgebra course with students who have failed math classes in the past. I felt the SBG would be a good way to get these students back into a growth mindset. So far they have fought against it quite a bit, but mainly because they don’t like change. They also seem opposed to not having extra credit opportunities. I am curious, do you have any thing in SBG that is similar to extra credit?

I felt like EC wouldn’t really fit a SBG approach where learning must be shown. Sinced once you show you have mastered a standard, your grade will reflect that growth and the EC would not be needed.

Kate,

This post is one of the most concise and comprehensive sources on Mastery-Based Grading I’ve read. And I’ve read a lot, because I am currently creating my Mastery model. Right now I am struggling with balancing my general and specific outcomes. This is why I am especially interested in your 6 Big Questions and how your specific standards answer these questions.

Here is my question: Have you used these Big Questions in your grading in any way? How were they present in your system? In other words, did they play any other role other than helping to create a meaningful structure of the course (which is already a lot!)?

Thank you!!!

Hi Yelena,

One of the big struggles with moving to an SBG system is you really have to figure out what it is you want your students to learn. For me, using Big Questions has been really helpful in my course prep because it focuses my attention on what the point of the course is. Also, in past semesters, I’ve often asked students on the final exam “What were the Big Questions in this course?” and I’ve been really impressed with their responses.

I realize that my students will probably, at some point, forget how to do things I’ve taught them (think: quotient rule! integration by parts!). And I think I’m OK with this. What I would like them to remember from my course, even if they forget the details about the methods we’ve implemented, is what kinds of questions we were asking. So in my instruction and documentation, I try to make clear “This is the Big Question we’re struggling with right now”.

So, specifically:

1. I don’t think the Big Questions really are part of their grade (although sometimes I ask my students if they remember them or not).

2. They are present in my system as an organization tool, both when I’m writing my standards at the start of the course, and also as a structure within the semester to bring the conversation back to “What are we even trying to do today?”

I hope this helps!

Thank you Kate, it definitely does! And I can see how important it is for a Calculus course. My general outcomes/big questions for a high school Algebra 2 course may not be so profound, although just like in Calculus, I’d like my student to internalize big ideas about relationships between real world processes, functions, equations, graphs etc. rather than necessary particular types of equations and graphs. So I can totally accept your philosophy and practice!

Thanks again,

Yelena