Our semester is wrapping up and we only have one more class meeting day after Thanksgiving. I’ve been teaching two sections of “Calculus II” using my standards-based grading system that I’ve mentioned before. I think I made several improvements this semester and I wanted to share them, along with a couple of things I’m still contemplating. But first, here are things I thought went well:

• I really liked having my standards organized by Big Questions. This is probably something I could have implemented outside of my grading system. Somehow writing and organizing my list of standards gave me the motivation and time and priority to think about the take-aways I wanted my students to get from our course.
• Last Spring, I had approximately 18 standards, meaning about one per week. They were large learning targets. Take, for example, the “Techniques of Integration” standard that encompassed a couple of weeks of class time spent talking about integration by parts, by trigonometric identities, by trigonometric substitution, by partial fractions, and so on. This semester, I wanted more standards that were more specific. I hit my goal of 30 standards for the semester and this number worked well. On the one hand, the standards were specific enough that students could focus on just one idea at a time. On the other hand, there weren’t an unreasonable number for me to assess. Roughly they correlated to one standard per textbook section, spanning about 1.5 classes per idea.
• Originally, I had a “policy of replacement” where a score would be updated each time a problem was attempted. In some cases, this seemed to harsh, since prior good work was “erased” easily. In some cases, this seemed to lenient, because sometimes an easy problem would earn a high score, but replace more thoughtful work on a harder problem. This semester scores were defined as the average of the scores from the last two attempts. This also made picking problems for re-assessments easier on me since I wasn’t as concerned about having them all be exactly the same difficulty. It also means that a score of 4 means a student demonstrated a strong level of mastery on two problems of a particular type, and that seems to work well.
• I limited the number of re-assessments to one re-assessment topic per week. For example, if a student were struggling with Taylor Polynomials, they could come in throughout the week and try re-assessments. In some cases, they would just solve one problem. In other cases, they might solve four or five problems, each time getting a little more of the correct solution. Previously I let them do 2 standards per week but I found two problems with this: First, some students would just always pick their lowest two scores and try them, without really ever focusing on a single idea and working toward mastering it. Second, having multiple re-assessments on multiple topics times multiple students meant my grading workload was higher. So, one per weeks seems like a more manageable number for them to work on and it makes my grading workload lighter. Lastly, since we had 30 standards (but only 16 weeks) this policy pushed them to demonstrate mastery on in-class assignments (quizzes, exams) without just punting them to re-assess in my office later on.

Two things I don’t have data on yet:

1. This semester I tried assigning online homework, with the homework contributing 5% to the overall course grade. I found assigning just textbook problems (and not grading them) did not work well. Perhaps I was not very good at motivating students to solve more problems on their own? I haven’t taken a detailed look at homework scores compared with course standing, so I am not sure if homework correlated with success on in-class assignments or not. I also feel a bit “icky” about assigning and grading homework, given some of the research I’ve seen.
2. The other change I made was I separated “during semester scores” from “final exam scores.” So 70% of course grades will come from a letter grade assigned based on the scores on standards that were accumulated during the semester and 25% of course grades will come from a letter grade assigned based on scores on standards that will be accumulated on the final exam. This breakdown was in response to some conversations with students from last semester who felt that the old policy (“average of semester score and final exam score”) was too strict. We will see how this works out and if there is much movement in pre-final letter grades to post-final letter grades.

I’m teaching calculus II again in Spring 2015 and I plan to continue using this system. I am still entirely undecided about trying it in Pre-Calculus. I have several worries about trying it in that course.

Postscript: Here are some links to some older blog posts about my SBG Calculus adventure:

https://blogs.charleston.edu/owensks/2014/10/09/big-questions/

https://blogs.charleston.edu/owensks/2014/08/18/list-reboot/

https://blogs.charleston.edu/owensks/2014/02/25/on-the-purpose-of-examinations/

https://blogs.charleston.edu/owensks/2014/01/09/sbg-faq/

I spent some time over the last several days trying to track down documentation about SBG/SBL. I wanted to find something to pass along to my students to address some of their questions or concerns, like, “What’s this SBG thing?” or “How will this work in our course?” or “How is this going to be beneficial?”

Thankfully, Joshua Bowman came to the rescue and sent me something he gives out to his students. It addressed some of his students’ frequently asked questions and it was a great launchpad to write my own. I’ll post it below. I kept stole his format and questions, but re-wrote (most of?) the answers as the apply to my own course.

Introduction to Standards-Based Grading

How is standards-based grading different from traditional grading?

You are probably accustomed to the following system: You do an assignment (like for homework, a quiz, or a test) and give it to your instructor to grade. After grading, it is returned to you with a score like “14/15” or “93%”. In our course, I won’t keep track of how you do on particular assignments; instead, I will keep track of how well you master specific mathematical tasks or concepts that are called standards. Once I see your work, my goal is to give you meaningful feedback: I want my feedback to tell you what you have mastered, what you should practice, and how what you have mastered relates to the goals of our course.

There are three major advantages to this system:

• First, it rewards mastery instead of a “hunt for partial-credit” strategy. On an assignment with five problems, I believe it is better to do three problems extremely well (and leave two problems blank) than to just write stuff down on every page hoping you’ll earn enough points.
• Second, I hope that it will allow you to see how to improve your knowledge of our course material. This system will allow us to track what topics you understand well, and also what topics you should spend more time working on. This way, if you seek additional help, you will know exactly what you need help with! Since your grade on a standard is not a fixed number — it changes over time — it is always advantageous to go back and fill in any gaps in your knowledge.
• Third, it allows us to be clear about what the expectations of the course are (namely, demonstrating an understanding of topics in Calculus II) and how well you are meeting (or exceeding!) those expectations.

How will I know how well I did on a test?

Each assignment will probably look similar to those you have seen in prior courses. When I return them to you, you will be provided with a rubric. The rubric will give you two kinds of information. First, it will outline what standards correspond to each problem you solved. Second, it will outline the level of mastery you demonstrated on that problem, using a scale of 0-4. Apart from the rubric, my hope is to offer additional feedback on your solutions that will help you toward your goal of continued mastery.

How do I know which standards will be tested?

On each quiz, you can expect to see material we covered in the previous week. However, as you know, mathematics tends to build on itself. So although maybe we didn’t talk about the Quotient Rule last week, you will probably still have to know how to use it this week! Before each test, I will provide a list of all of the standards the test will cover. Since our course is cumulative, although a particular test might focus on recent standards, you might encounter problems that require knowledge of previous standards from earlier in our semester — or even prior mathematics courses.

How often will each standard be assessed?

It will depend on the particular standard. Standards that appear early in our course will be assessed multiple times, since we will be using them (either implicitly or explicitly) to solve problems later on. Toward the end of our course, you might only encounter a particular standard once or twice.

Why can my score on a standard go down?

It’s important that your score shows your current level of mastery. Your score on a standard may go down because you’ve forgotten some of the material, or you were unable to apply earlier techniques in solving problems later on.

In addition, some of our standards are quite broad: For instance, one of them deals with “techniques of integration.” We will see many of these techniques in our course. So your score may go down if you show mastery of the earlier techniques, but aren’t comfortable with techniques that show up later on.

How can I raise my score on a standard?

There are two ways to have a score on a standard raised.

First, you can wait for that standard to be re-assessed later on. For example, some standards assessed on quiz questions will be re-assessed on test problems. Especially early in the course, when there will be many opportunities to reassess standards, this may be the easiest way to raise your scores.

Second, it will be possible to “retest” a particular standard by making an appointment to meet with me. At this meeting, you will demonstrate your understanding by trying new problems and then answering questions I pose to you. You can make appointments to retest up to two standards each week. You choose which standards you would like to retest and when. You can retest any given standard more than once, as long as you only retest up to two each week. Each “retest” will take 10-15 minutes. Please request an appointment for re-assessment at least one class day in advance; this will allow me to prepare materials for you. You can request an appointment simply by e-mailing me and letting me know which standard you have chosen.

How many times can I ask for a standard to be reassessed?

You can ask for any standard to be reassessed as many times as you want, subject to the limitation that you may only retest two standards each week. If you require multiple attempts on a particular standard, I might ask you to work on some additional problems first (potentially with my help) so we can clear up any knowledge gap more quickly.

What about the final exam?

Our final exam will be cumulative and will have problems reflecting standards we have encountered throughout the course. Not every standard will be directly assessed on the final exam (after all, we don’t want to make it too lengthy!). Also, by the nature of final exams, you cannot re-assess any standard after the final exam. Your course score on each standard will be decided as follows:

• If a standard does not appear on the final exam, your course score for that standard will be your score as of Reading Day. For Spring 2014, the date is Thursday, April 24th.
• If a standard does appear on the final exam, your course score for that standard will be the average of [your score as of Reading Day] and [your score for that standard on the final exam].

How will my final grade be computed from my scores?

Your midterm grade and course grade will be the usual sorts of letter grades you are accustomed to. Here is how I will convert your mastery of the course standards into letter grades:

• In order to guarantee a grade of A, you should attain 4s (or 5s) on 85% of course standards and have no scores below 3.
• In order to guarantee a grade of B, you should attain 3s on 85% of course standards and have no scores below 2.
• In order to guarantee a grade of C, you should attain 2s on at least 85% of course standards.

Plus and minus grades will be given based on how closely your performance is to a full letter grade. (For example, if you earn 3s on only 80% of course standards, and 2s on the other 20% of course standards, a grade of “B-” may be more appropriate than a grade of “B.”)

If I don’t like this method of grading, can I tell you about it?

Please! This is my first time using standards-based grading, and there are bound to be hiccups. However, I truly believe it will provide more helpful feedback and give you a better chance to prove your mastery of the material, so I ask that you at least give it a try, even if it seems strange at first.

If I have questions about how I’m doing in the class, can I ask you about it?

Absolutely! One drawback of this system of assessment is that you may have questions about your performance in the class. If you have questions or concerns about this, feel free to come talk with me and I will try my best to give you an accurate picture of your progress with our course material.