I have now been using a Standards Based Grading (SBG) system for one school year, and it seems like it is time to reflect on it.

I used SBG in three courses: Linear Algebra, two sections of Business Calculus, and two sections of Mathematics for Elementary School Teachers. Here are the basics of my implementation. Here are the things that were common to all classes:

- I listed the content of the course into “topics.” But topics tended to be broader than most SBG implementations. For example, for calculus included such things as “Second derivatives, concavity, and inflection points.” I would guess that the usual implementation would break these topics down into smaller, more specific actions: “Students will be able to take the second derivative of a polynomial;” “Students will be able to determine the intervals where a graph is concave up (or concave down).”
- The main way students could meet the standards was through weekly quizzes.
- Each quiz question is graded and recorded individually. There are only two possible grades: “Acceptable” and “Incomplete.”
- If a student gets an “Incomplete,” he/she must either get a similar problem correct on a later quiz. There is no limit on the number of redos (save for the time limit of “end of the semester”). There is no penalty for missing a quiz question (except that you have to make it up later).
- The students’ grades are determined by how many “Acceptables” they get for each topic. I made sure that students had a least twice as many chances on each topic as they needed to get an A (and sometimes as much as three or four times as much).

Here are a couple of variations on reassessing:

- For my linear algebra class, I allowed students to come to my office to take mini-quizzes—one per day.
- For my education course, students could create screencasts where they explain a topic.

Here are a couple of variations on grading:

- For linear algebra, I split each topic into two categories: “Skills” and “Concepts.” To get a C, students needed to get three “Acceptables” in every topic. To get a B, students needed to additionally average one “Acceptable” for every conceptual topic. To get an A, students additionally needed to get two “Acceptables” for every topic. For averaging purposes, students were not allowed more than two “Acceptables” for any single topic (so they couldn’t be really good in one topic but bad in all of the others).
- For Business Calculus, students needed to average two “Acceptables” in each topic for a C, average three for a B, and average four for an A. Similarly, they could only get four “Acceptables” in any one topic.
- For my Elementary Education course, students could get a maximum of five “Acceptables” in any topic. But their grade was calculated by the minimum number of “Acceptables” they had in any one topic. If the minimum was five, they got an A; a minimum of four was a B; and a minimum of three was a C. The theory for this is that teachers especially need to know all of the topics, and the grading system should reflect that.

Here are links to the topics for each course: Linear Algebra, Business Calculus, Math for Elementary Education Majors.

I think that SBG was a huge success in Linear Algebra and Business Calculus, but not great for the Elementary Education course. The main reason was that the first two courses included a large amount of computational-type assessment (take this derivative, find the determinant, etc), whereas the Elementary Education course was mainly a proof-based course (I didn’t use the word “proof” in the course, but that is what they are really doing). The computation parts of the course are pretty simple to implement because the assessment for them is cheap. The Conceptual questions for Linear Algebra were more of a challenge, but I could still create a lot of interesting questions for, say, eigenvectors that were not computational.

But this problem might have more to do with a quiz-based system, too. A different solution to make it work for proof-based courses: do something like Andy Rundquist does. He essentially does a series of oral quizzes (in various forms), which I think would allow me to figure out how well a student understands a topic. This has the advantage that I could repeatedly ask the same question, ask follow-up questions to probe the level of understanding; this kind of makes the assessments “cheap,” since I can ask the same question repeatedly (“Why do we invert and multiply when dividing fractions?”). The main problem with this solution: it seems like it would take a lot of time when you have 25-50 students.

All in all, I think that SBG is a huge improvement over the old “averaging system,” even for the Elementary Education course. I felt that I understood where my students are much better; this led to more accurate grades (in my opinion). But there is much room for improvement.

Tags: assessment, SBG

June 16, 2011 at 11:58 pm |

As I reflect on my past semester I realize that I most enjoyed the assessments that were more proof-like as opposed to mechanical. It was hard to get students to realize that just writing the right steps was not good enough. In the proof-like ones, especially the in-class oral assessment ones, were great because of the follow up questions.

June 20, 2011 at 10:14 pm |

Hi Andy,

I think that your method is great for proof-type problems. Do you have any ideas on how well your method is going to scale up to 15-20 students? Bret

June 20, 2011 at 10:24 pm

With 9 this past semester I think I was underworked. In fact, I think with more scasts coming in on the same or similar topic it will help me give better class-wide feedback. I’ve got 15 for the fall so we’ll see.

June 20, 2011 at 10:28 pm

Hi Andy,

Hmmm…I have 25 (total—17 in one class, and 8 in the other) this fall. Would I be completely foolish to consider trying something like what you do? Bret

June 20, 2011 at 10:34 pm

At what rate will they submit for you? For me I wanted 2-3 scasts/student/week. I never really got that so I can’t say what that feels like. I think I’ll get something more like that this fall.

I guess I compare it to what I used to do: 1 problem/student/class period. That’s easy to keep up with all the way up to 50 students, especially since the problem is the same for everyone. My scasts rate (that I want) definitely takes more time but you get a much better feel for where the students are at.

June 21, 2011 at 1:01 pm

Hi Andy,

I don’t really know the rate yet—I am only starting to consider it.

So you basically still want about 1 problem per student per class per week, the only difference is that you now want a screencast instead of written work. Of course, it takes longer to watch a screencast than it does to read a problem solution. Is this right?

I will have to sort through all of this, but I like your method. We will see… Bret

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