A Reflection on Grading

I recently had a conversation about student grades with an administrator at my school and it got me thinking about my attitude towards grades. I am writing this post to force myself to evaluate my approach. The very first thought I have with respect to grades is a quote from George Couros: "Is this going to be on the test? is not a question of curiosity, but a question of compliance." If our kids are only worried about grades, then our job is meaningless and can be replaced by computers. I actually found out how many students failed my class first marking period from my supervisor. In that discussion, I explained that I can tell you what each one of my students knows, doesn't know, and needs work on, and can do the same for my class as a whole, but I can't tell you how anyone but the absolute highest performers are doing grade-wise. At first glance, this may seem like I cherry-pick or only worry about the “best” students, but that is far from the case. In fact, they are the ones who get the least attention from me. (I'm glad I'm writing this because that needs to change.)

I decided a few years ago that if my kids could stop worrying about their GPA and worry about learning math, then my job and their experience would be much more enjoyable. I approached this through my tests (which are 73% of the grade). I made my tests incredibly difficult, but "curved" them a lot. Technically, what I do isn't curving, more shifting, but that isn't the point of this post. I put some computational questions on the test that I expect everyone to get correct, but I feel like I know all of my students can plug in numbers into the formulas by the time the test rolls around. I have found that the biggest problem is that students do not realize WHY they are plugging in the numbers because they do not understand the underlying concepts. They only focus on the “how” because that has gotten them good grades in math class up until now. So I put a lot of conceptual and multi-conceptual questions on the test to see who really understands the math. I also make all of my tests cumulative, meaning they're like a rolling final exam. Every test covers material from day 1, but the majority of the material is from the newest concepts. So instead of calling a test the "Chapter 3 Test," it is called the "Test through Chapter 3." I want my kids to know that everything matters, everything builds on previous material, and that nothing goes away. They need to know that they’re not just learning this for a test, but for mathematical understanding. I regularly tell my kids that if they choose an applied math career, they will probably never take a derivative, evaluate an integral, or perform almost any other computation without using a computer. They have to know what to tell the computer to find/calculate, what that value means, and how to use it. So all of my tests involve problems with very easy computations, if you know what computation to perform. Throughout their years of school, they have been provided with numerous mathematical tools for their toolbox. On my tests, they have to read the problem and decide which tool or tools work best for that situation. Since the problems are so difficult and most are of situations they are seeing for the first time, they are provided with a lot of room for error. If someone earns every possible point, their score is anywhere from a 120-140%. Earning about 75% of the possible points will get a student an A on the test. I have mainly used this method in my AP Calculus classes and have found that about half of my students have an A in the class. I have also noticed that most of these students, the same ones that know their exact average in everyone of their other classes, do not worry about their grade in my class because they know the grade will take care of itself if they learn the math. The students that struggle the most are the ones who cannot shake the habit of memorizing formulas and asking if “questions like this will be on the test.”

My concerns stem from the following questions:

1. Do I give them too much room for error? Most math people will argue that you take the number of points a student earns and divide by the number of possible points and that should be the student’s grade. Why should my kids get to miss 1 out of every 4 points and still get an A?

2. Is it fair that half of the kids in my AP class get A’s while a much lower percentage get A’s in other AP classes? I am the only calculus teacher, so every kid that takes calculus is in the same situation, but what about other kids? Does a kid that takes AP Calculus have an advantage over a kid that takes AP Lit and Comp?

3. Do I baby the kids too much? I address every mistake they make and question most of the correct decisions they make just to make sure they’re not getting lucky. I constantly send them reminders and involve their parents and counselors the second I see a potential problem. I am available everyday before and after school as well as during my lunch. I answer e-mails immediately and provide more resources than they can possibly use. As long as the student listens to my suggestions and works hard, they are very successful in my class. They will most likely not get that kind of support in a college class or in the workplace. Am I being a good teacher or setting them up for a shock when they move on?

4. Do the ends justify the means? The scores my students have gotten on the AP exams over the last few years have been outstanding compared to their peers and students that graduated long ago. If I am trying to get my kids not to worry about tests by de-valuing (not sure if that is a word, but spellcheck didn’t underline it) the tests, does it make sense that their score on one national test be the basis for the justification of my strategy?

5. Has the success of my former students had a negative impact on my current and future students? Last year was the first year my students’ results on the AP exam weren’t better than the year before. Regardless of whether or not AP scores justify my methods, they are a pretty good measure of how my students and me are doing each year. Our school does a great job of celebrating student success each year and AP exams are no exception. Over the last few years, Calculus has had the most success on AP exams and I fear that has caused some confusion with students. I think some students come into class and think that since they have always been successful in math, that all they have to do is show up to class and pay attention and they will have the same success as all of the students on our “Wall of Fame.” They don’t realize that every student on our wall worked their butt off to get there. It was easy to convince the first few groups of students to work hard because they were trying to achieve something that very few had at our school, but I have to work harder motivating now than I do teaching because current students think success in calculus is a right of passage, not a reward for hard work.

My short answers to these questions are:

1. No, I look at it as room for growth.

2. Yes. My kids that get A’s really know math, and that is what the grade should reflect.

3. Maybe, but if they leave knowing math, then they will be in a better position to adapt when push comes to shove.

4. Probably. I happen to be a proponent of standardized tests, especially the AP Calculus exam. I think it really separates those who understand the math from the ones who are good at memorizing formulas and plugging in numbers.

5. Yes, but that is my problem, and a good problem to have. I need to find ways to engage and motivate my students from day 1, regardless of their preconceived notions of the course.