# Assessment in Math

## 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.

## Conclusions

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.

## 6 thoughts on “Assessment in Math”

1. Like you, I feel very constrained to give each student a single letter to reflect his/her content mastery, participation, behavior, class citizenship, etc. One lone letter don’t convey enough information! I’m tempted to give a letter grade (via report cards) solely for content mastery, but also send home another evaluation that includes scores for organizational skills, homework, class assignments, citizenship, and teamwork. It would be a lot more work, but I think detailed feedback would be more meaningful.

• Our school started heading that direction: sending home a narrative evaluation with the report card to address work ethic, organizational skills, communication, and so forth. All of the classes get addressed in one evaluation, and it seems data is being lost. I am thinking about how my mechanic evaluates my car or better yet how my doctor evaluates my health. She doesn’t give me a single “health” number. She tells me my weight, temperature, pulse, blood pressure, cholesterol levels, etc. All of those numbers paint a landscape of my physiological well-being. Maybe this approach would work for assessing my students. They would still get a number attempting to communicate how much math they know, but they would also get numbers indicating their socio-academic well-being.

• Echoing what both of you have said – I’m starting to wonder if grades are like Nike Fuelbands? Sometimes flashy, sometimes pretentious, but people are really willing to pay a lot for a single number, no matter how much it is reflecting an actual truth.

2. I am divided on this issue. I taught in an extremely high-need school where we bent over backwards to create a grading policy that rewarded effort and compliance. The result? Students graduating high school and getting to college without the proper background or academic tools for success in that arena. Now I am in a school where the departmental policy dictates that 80% of the students grade is based on their performance on tests and quizzes.

What does a grade mean? Does it represent mastery of material? If a student takes my honors Geometry class, and even though they attend every day, take notes, and attempt homework, they still cannot demonstrate that they understand the material on either a traditional assessment (aka test) or some type of structured task, shouldn’t their grade reflect that lack of understanding? When a [high school] transcript is sent out, doesn’t an A or B in a math class signify that the student is performing at an above average level? On the other hand, how do modify the school environment so that the student who is putting in superhuman effort can succeed in proportion to that effort? In other words, I don’t know…..

• To tack on one more idea Wendy – “mastery of content” might look a lot different in your room than mine. Where your students might know how to write formal proofs, where (I hope) we have focused on what it means to prove a statement true and false.

Just the quality control within my own school is extremely difficult… and we only have about 200 kids from grades 6-12. I have no idea why colleges realistically care what transcripts say at this point. This might lend to the notion of emphasizing of percentiles for acceptance conditions… which just turns schools into competitions… This debate gets complicated very quickly…