In the high school math classroom, grading is more complicated than correct responses divided by the total number of questions. What is effort or persistence worth? How many points for improvement? What’s the penalty for late work? How late? When students work collaboratively, how is that graded? How much is getting the right answer actually worth?
Essentially, how is each grade (A+/-, B+/-, etc.) defined in terms of math ability, which is what the grade is supposed to represent? Is it the progress of math ability or the level of math ability? Should anything else besides math ability go into the grade? What does ‘math ability’ mean again? With students being so different from one another, it is quite difficult to grade them all on the same scale with consistency and fairness.
Students come into class at varying levels math ability. Depending on how old the students are and how inclusive the classroom is, the range of ability could be quite wide. If the goal was to get every student to the same particular level of math ability, the results would be a disaster for most everyone. Those with lower initial ability would be lost almost immediately and those with the higher initial ability would be bored almost immediately. The highest level goal of every high school math class should be to get every student to learn more math than they knew on the first day of class. This is the goal of differentiation, which is solely focused meeting the student where they are and making progress from there.
This does not say anything about where the student has progressed to, which seems like it should matter too. Let’s use a metaphor for a moment. Imagine if the entire 9th grade class was running a marathon. Some students are at mile 25 on the first day and other students are at mile 0 and everyone else is spread out in between. If we set the standard that you have to get to mile 26 to get an ‘A’, it might be completely unreasonable for the students at or near mile 0 to get there by the time the grading period ends. This means right from the start, some students have almost no chance to get a high grade in the class. For the students at or near mile 25, getting to mile 26 in the grading period is hardly any challenge at all. It is not a good thing to leave students in a math classroom unchallenged and bored. If we set the minimum for a passing grade to the 10, 12, or 15 mile mark, this still means that the students with the lowest initial ability have the most to do to not fail.
Conversely, if we set the standard that an ‘A’ grade means that every student must go 10 miles from their current position, the lowest initial ability students might end up performing below what many consider is appropriate for their age level. This also means that the teacher must create a wide range of classroom activities that attend to the needs of each student. On any given day, two students sitting next to each other in the same class might be at mile 7 while the other is at mile 32. This is a lot of work for the teacher, especially when most class activities are geared towards a very narrow range of student ability.
So, the dilemma when grading is between valuing the level of math ability throughout the grading period and the growth in math ability throughout the grading period.
Grading the Ability to Learn
I favor valuing progress in math ability much more than raw math ability. I strive to challenge every one of my students just beyond their level of competency every day. That is to say I don’t want to challenge them too much so that I run the risk of them giving up and not too little so that very little progress is made. What actually happens is that some days I don’t push my students enough and some days I push them too far. I very rarely get it just right for everyone, but when I do it is pure magic. I would never have that magic moment if I was simply trying to get every student to the same level of ability. Although, it would take a lot less time to plan class activities.
Students’ grades mean something different when they represent progress of their math ability instead of their raw math ability. A high grade means the student demonstrated a strong ability to learn math, not necessarily a strong ability to do math. It would not be uncommon then to have a student with higher math ability who is quite reluctant to learn new things get a lower final grade than a lower math ability student who is eager to learn new things. To be clear, those new things might be concepts that the higher ability student with the lower grade is already familiar with.
Why Does This Matter?
The most important reason is that despite what they might say, all students care about their grades. They at least start out caring about their grades with some of them becoming jaded (for good reason!) over time. Student look at their grades, they question them, they are proud of them, and they are ashamed of them. If the message to my students tells them their final grade is strongly dependent upon where they are at before they even enter my class, the message does not bring with it a growth mentality. This is not a message I want to send to my students, nor should any teacher.
The message I want to send to my students is that every student in class is held to the same standard regardless of what they are currently capable of. Achieving that standard requires similar effort, perseverance, frustration, success, and, ultimately, growth from each student. I want to teach them that what really matters is not just being good, its about always trying to be better. This what deserves and ‘A’ in my book.