Getting Ahead of the Curve
My school has recently begun an inquiry about how we assess. I have been struggling through the process for a number of reasons. I struggle most with trying to break away from assessing how I’ve been assessed. Mathematics lends itself to a certain type of grading – that where we think about the “skills” of the class. I’m very good at this game we call school, but many of my students are incredibly bad at the game, yet great at mathematical thinking.
The main question I go back on forth on: What does it mean to earn an 80% in a Geometry class? Does it mean that you’ve mastered 80% of each of the objectives? Does it mean that you tried really hard, but did not understand all of the concepts? Or does it mean that you know everything, but were kind of lazy and missed deadlines? Where do expectations fit in?
Just like the Fed is supposed to control inflation and stimulate the economy with one lever (setting interest rates), so too does a teacher try to represent too much with its lever: setting grades.
I’ve spoken with some of my students about this, and we’ve come to two general conclusions. Historically grades represent ability (think skillsets and applications) and work ethic (meeting deadlines, trying one’s best).
One Assessment Model
I tried to graphically represent a model of this historical assessment:
This two-dimensional graph has a number of implications:
First, when we think of skills, we tend to think of “hard skills” such as multiplying fractions or using the chain rule correctly. We lose the “soft skills”, such as the highly touted 4 C’s: communication, collaboration, creativity and critical thinking. Each of those is difficult in and of itself to assess
Second, how do we weigh these two dimensions?
Should we base grades solely on the content that students mastered? This brings up a few thoughts for me: If you were really great at Calculus, you might be able to walk into Calculus 2, listen to the lectures, try a couple problems and understand all the content. If we weigh only the objectives of the class, how can we justify giving a 0 for a missed deadline? The grade will artificially be lower – the student understands the material but their grade does not reflect it.
And what of work ethic? If a student is really trying, improving, busting her ass on every assignment but still only masters 79% of the material, we give her a C. That somehow feels cold and unfair. But standards/objectives-based grading would imply that she earned exactly that grade. The counter would be: multiple studies indicate that humans with higher work ethics are more successful than humans with solid skill sets. So perhaps we should prioritize work ethic…
Third, we can think about the mathematics behind this model. On a 1-100 point grading scale, lacking a work ethic will destroy any representation of skills. Miss a couple of assignments, ace all your tests, your grade could be interpreted as skill-deficient. You can get by more with good work ethic/poor skills than poor work ethic/good skills. Either mindset lends itself to gaming grading.
Trying to Give Weight
I began playing around with what weighing these dimensions with grades might look like, and I came up with…
Yes, yes, I know the proportions are not exact. Feel free to create a better one.
And just for fun, I put some hypothetical students on the original scale. I started thinking how I approach those students, and the results were delightful and frightening.
I’m so drawn to people with high work ethic, but become too skilled, and I’m flustered on how to keep you engaged… One class wanted me to put a point where I thought each of them landed. I don’t advise you to try it at home.
I’m still at a loss for how I want to approach grading philosophically. I had a great professor at Baylor tell me that he did not want to give out any grades, but write two sentences about each student. I think that mindset is powerful, but rarely feasible. Maybe I’m approaching this the wrong way and equivocating grading with assessment. I would love to know some other math teachers’ (or just teachers) thoughts on this particular model.