I teach physics and grade with a standards-based grading system. We’ve been formatively assessing (and reassessing) all semester. In my view, the purpose of a summative assessment like the semester exam is to show (a) sustained mastery of the skills taught in the class and (b) synthesis and depth of understanding (that is, knowing both when and how to use each skill in a larger context).
My flavor of SBG
We (the physics teachers here) split the skills that we teach into two categories. ”A objectives” represent the most basic skills of the course; they often involve modeling a situation using diagrams. In order to pass the class (have a grade >= 70), students must demonstrate mastery on every A objective. “B objectives” are more complex skills and often involve solving problems. In order to earn a grade above 90, students must demonstrate mastery on every B objective.
Our system is essentially all-or-nothing. Throughout the semester, students received feedback on tests by getting a 0, 1, or 2 on each objective. 0 and 1 both mean “no” (but a 1 indicates developing mastery while a 0 indicates no mastery). 2 means yes. In the first semester, most reassessments were student-initiated, and most students took advantage of the breakfast and dinner time (boarding school) to do them. There were some in-class reassessments (both teacher and student initiated) as the semester drew to a close.
Format of the exam
My honors and “normal” classes had fairly similar formats, so I’ll mainly talk about the normal classes’ exam here. The exam was split into two sections. The first section (about 45 minutes worth) consisted of short, structured questions that aimed to isolate and assess all 15 of the first semester B objectives. The second section was a selection of 5 goal-less problems from which students chose two. Students had up to three hours to complete the test (I meant for them to finish in about 1.5 to 2 hours).
Goal-less problems were practiced throughout the year. They give the set-up of a situation, but they don’t ask any specific question. The general approach to these problems is supposed to be:
- Say which models apply and why
- Start to model the situation by drawing as many of the appropriate diagrams/graphs as you can
- Use your diagrams/graphs to do calculations and find as many quantities as possible
Here’s an example of a goal-less problem (click to make it a bit bigger) from our conservation of energy unit:
Mapping objectives to a final numerical grade
Of course, at the end of all of that demonstrating, I need to come up with a number on a scale (0 to 100) that is more precise than the instrument with which I’m taking the measurement. So. How do you go from scores on objectives to a number grade?
We decided that it wasn’t fair to “lose” an A objective on the exam (that is, to think you are passing the class before walking into the test and leave failing it). We also didn’t want to use one data point to completely determine the final grade. Any grade above 85 is supposed to be considered an “honors” grade at our school, and we decided that you couldn’t have done honors work without being able to show that level of mastery on the exam. Considering all of that, we came up with a pre-exam grade range for each kid that told them the minimum grade (something generally between 70 and 84) and the maximum grade (100 for everyone) that they would be getting for the semester. The only way they might get a grade below 70 was if they hadn’t shown mastery on every A objective before the exam (only one student had any A’s left, and he did show it on the exam, so everyone passed).
For each exam, I took a list of the B objectives and marked it up. I highlighted the ones they hadn’t shown before the exam, and I made + or – marks next to each based on their work on the exam. For any B that had any – marks, I looked back at their work and decided whether the + work outweighed the – work (for example: if they – had come from only a unit or calculation error rather than a major conceptual error). For any that they were still missing, I went back and looked at their history on that objective (I’ve been using https://activegrade.appspot.com/ since the start of the 2nd quarter) and decided whether this new evidence was enough to outweigh their history (assuming they had shown fairly consistent mastery before the exam). In the end, I circled any B objectives that they still didn’t have.
I used a simple linear interpolation to determine a grade between 70 and 90 based on the number of B objectives they had shown. If that number was less than their minimum grade (this applied to only 3 of my 42 students), then their grade for the semester was simply that minimum number.
The 90 to 100 range was determined through their work on the goal-less problems. We had a point system (not grade points, simply a way of quantifying what they had done on the goal-less problems without respect to any grade value) to judge the work that they had done.
Stating a model that applies AND WHY IT APPLIES = 1 pt
Drawing a diagram = 3 pts
–> annotating the diagram = +1 pt
–> using the diagram to calculate something = +2 pts
Stating a fundamental principle before you use it = 1pt
Doing a calculation = 1 pt
–> an especially clever or complicated calculation = +1 pt
A decent amount of points to get on a problem is usually around 25 to 30. An exceptional solution usually gets at least 50 or 60 points. So a sum of 50 to 60 would be good, and a sum over 100 would be excellent. One of my non-honors classes averaged a sum (over two problems) of 55 points, the other averaged 40 points (so an average of 47 points for both classes). My honors classes averaged a sum of 57 points. (More data: high/low for regular physics was 96/19. For honors it was 128/15.)
While I didn’t have a precise way to translate that score into a concrete part of their semester grade, I did make a cut-off: unless a student had a sum of at least 40 points, their goal-less problems did not improve their grade (outside of being able to gain a B objective from them).
Where do we go from here?
First, I should say that many (almost all in Honors) had the best exams that I’ve ever seen (in my 4 years of teaching physics). I think a good portion of the credit goes to the grading system. My students have been calm and interested all semester. Their course evaluations (a good subject for a future post) indicate that they almost universally LOVE this system and realize the benefits (being allowed to make mistakes, learning at their own pace, working on a skill until it is mastered). They also indicate that they were not completely happy with taking their progress on objectives and turning it into a number grade. I’m not completely happy with that one either, and I think we need to keep playing with how to do that.
One amazing moment was handing back the exams at the end of class early last week. In one of my sections the students were just stunned: “Woah… there’s a number on this. What does that mean?”