I’ve been thinking and talking with my co-teacher in Algebra II honors about grading. What follows are some general principles that I think are beginning to form some semblance of an overall grading policy.

First, we love standards based grading. In particular, we really like the approach Dan Goldner has taken in his Advanced Algebra class—you really should check out the link to his very impressive course document.

Dan has organized his course around the theme of “Using functions to make predictions”, and he’s determining grades by measuring student’s ability to do the following things:

The basic idea is that a student must show proficiency in each technique (e.g. making a prediction from a table, or make a presentation) across all six function families.

We like this, but we’re covering a few more function families in our course. We also think we want to keep grading presentations and reviewing student papers out of the grading process (but still make them a vital part of the course). Finally, making predictions from words and interpretation seem like similar techniques, so we’ve created the following table of concepts:

We will grade each concept on a 0-2 scale, with the following interpretation:

0- you’ve shown no understanding.
1- you show mastery of the skill in isolation.
2- you show mastery of the skill in a problem, when the concept is required implicity.

This isn’t a strictly binary scale—one doesn’t have to earn a 2 on the objective to get any credit at all, showing mastery of the skill in isolation will give students half credit for that standard.

This leaves me with two remaining things to think about in grading, and one novel solution I’ve come up with. I love Kelly O’Shea’s approach to grading the exam in honors physics. I want students to be preparing to do their best work on the most challenging assessment of the year. But we aren’t going to be defining our standards as core and intermediate, all standards will be equal in value, and grades will be some sort of interpolation on how many standards a student masters overall, with demonstrating mastery on all of the standards earning a 90%.

How will students earn grades above 90? We aren’t likely to have a lot of goalless problems in math for now, so we can’t take the approach that my physics class does. But, this is also an honors course, where students really are setting out on the path to become sophisticated mathematical thinkers, so I think there’s room to incorporate capstones into this course, which I’ve written about previously . These capstones are very similar to the papers Dan Goldner’s students complete.

One other caveat from my first go-round with capstones. You might recall that the way I did capstones previously was that if a student completed one, they connoted as 3 points on the pre exam average if the student had mastered all of the concepts, but only as 1 point if they had not. Obviously, this put a lot of pressure on the student and me when they were trying to master one or two remaining concepts and had 2 completed capstones—they felt like they had 6 points on their pre-exam average on the line (if they failed to master the 2 concepts, they’d have a 90 [88+2 capstone pts], but if they mastered them, they’d have a 96 [90+6capstone pts]).

So here’s an alternative that I think could work. Students submit and revise papers/capstones until they are accepted by me as demonstrated sophisticated mathematical thought, and completing at least paper/capstone of these should be a requirement to earn an A (90). This leads me to think I can reframe capstones as unlocking higher maximum possible grades, roughly as follows:

• Complete one capstone: maximum grade: 93
• Complete two capstones: maximum grade 96
• Complete three capstones: maximum grade: 100

Students still must show mastery on the exam—capstones don’t add points to a student’s grade, instead they allow a student who shows sufficient mastery on the exam to earn grades above 90, and a exam that showed complete mastery of all of the concepts above would earn either a 93, 96 or 100 depending on how many capstones the student had completed.

So these are my preliminary thoughts. I think the idea of having capstones “unlock” higher grades, rather than “give points” seems more appropriate and less likely to cause stress. I’d love any thoughts you may have about these ideas and how to make them better.

1. August 29, 2012 12:56 pm

I think there are a lot of good things in your plan. I really like the idea of capstones unlocking grades. I’ve always found it difficult to assign specific grades to projects that vary between students. Last year I resorted to pass/fail. In some ways that was too easy because a fail can drastically change a grade.

I’m still confused about how the exam affects objective score or overall grade. Are the exam questions simply more problems like quiz and tests, such that a wrong answer can drop a standard from mastered to not mastered? Does this cause a problem where a student’s history of mastery can easily be nullified?

One suggestion is to maybe do a mock/draft set of instructions that you give the students to explain the marking. If you can concisely and clearly do this on a single page, you probably have a winner. Some sbg schemes, while well thought out, get pretty complicated.

2. August 30, 2012 11:10 am

One other thought. If a student is sitting at 80% for example, do they get any marks or credit for completing a capstone?

3. September 7, 2012 2:56 pm

Hi! My name is Brittany Leavitt, and I attend the University of South Alabama in Mobile, AL. I am currently in Dr. Strange’s EDM310 class, and I was assigned to your blog to follow for the next few weeks! I am a secondary education major and also love math. I will be teaching history, but math was also one of my favorite subjects. I enjoyed reading this blog about finding a different way to get your students more involved in physics! I also went back and read the blog you posted initially about the capstone idea. I think it is fascinating that you are using this, and I really hope it is working for you! I think that students in this day and age slide by in school without ever really being challenged! The idea of capstones helping their grade but also helping them deepen their education is great! Thank you so much for sharing this! I read that you teach at a boarding school; what grade(s) do you teach?