Grading For Equity: Reflection Questions (Ch 7)

As part of a summer professional reading group, some colleagues and I elected to read Grading for Equity, by Joe Feldman. It's a big topic, so I wanted an excuse to do some reflective writing on it, so I can try to understand it more deeply. Fortunately, Feldman wrote some "Questions to Consider" at the end of each chapter, and so I hope to use those to guide regular reflections.

Chapter 7: Practices That Are Mathematically Accurate

Initial Reactions:

• Math is So Important. This chapter had a bit more math than the others, which was important. Grades are one of many applications where I can feel the positive impact that my math education has had on my ability to do my job. I think that it has always empowered me to have an extra level of ownership over my grades, and I want to work harder to include it as actual content in my Algebra 1 class. Because for as long as we're going to engage in this typically-problematic practice of grading, I ought to empower my students to play the game as well.
• Frequency of Grading. One thing that I think about often, however, is the idea that our "summary grades," like our overall grades, should be "representative." But there is noise in our grade data, since student performance depends on countless variables, not all of which are actually reflective of student understanding. So if we want to "cancel out" that unwanted noise, I have felt the pressure to increase the number of assessments. The more data points I have indicating a student's level of understanding of some topic, the more comfortable and precise I can be in my assessment. But I also don't want to spend an untoward amount of time on assessments.
• Option 1: fewer, more sophisticated assessments, that are more resistant to the random-ish impact of external variables unrelated to the student's understanding. These kinds of assessments are harder to design and grade. (This seems to be my school's general default approach to assessment with competency-based grading).
• Option 2: more, less sophisticated independent assessments, that *in sum* converge on the student's true level of understanding. These kinds of assessments typically result in more time spent on assessment, and result in grades that are given individually, but aren't quite as meaningful individually. (This has been my own general default approach to assessment with standards-based grading).
• I suspect that a good practice is to do a combination of both. This is my plan for the coming year. I see "Option 1" as bigger projects, potentially in groups. The grade is determined both through what I can see in the product, and also what I can observe during the process, having taken observation notes. I see "Option 2" as smaller quizzes, done individually, where I'm grading just on what I can see in the work. That's my thinking, and I'm hoping to think more about it as I go through this book.
• An important point, which I think this book will get to, is that I won't separate my grade categories as "projects" and "quizzes." Instead, I'll still have my list of standards for the year, and then each standard will have multiple data points, some taken from quizzes, and others taken from projects. Then will combine those data points to create a single summary statistic somehow (Max? Average of top two? Other? Hoping to learn more about that in this book.)
• The Purpose of Grades. One thing I think I learned well from my teacher education program was this--when you feel yourself falling down the rabbit hole, just stop, zoom out, and ask yourself, "What is the *purpose* of what I'm trying to do?" If we zoom out far enough and look at the problem on a scale where we can simply make sense of things, that makes it easier to understand what the "right" answer is.
• Part of why it's so difficult to talk about grades, is because there is no real "big picture" vision for grades, broadly speaking. There used to be, which Feldman discusses in the early chapters (social reproduction, efficient sorting of students into the capitalistic labor force). But over time, we've gotten further from that, or at least tried to, in name at least.
• I feel like a major position we've taken as teachers is using grades to communicate expectations with students and their families. Given that teacher caseloads are too big as a rule, more humanizing methods of communication are much less feasible at large scale, and the efficiency of using numerical omnibus grades to communicate feels necessary.
• So I need to make sure I'm crystal clear on what my own purpose is. And so far, the one that makes the most sense to me is grades as a "mirror" for students. Grades are essentially an abstract dataset used to efficiently help a student understand the course of their own development.
• It would be naive of me to just ignore external agents that read my grades, and likely harmful to my students. I need to figure out all the other expectations held by my school, district, and students' future options, who all use the grades I assign for their own purposes, for better or worse. In society, grades are an important (if fundamentally oppressive) form of capital, and I need to make sure that my students have access to it.
• As a person with some institutional power as a teacher, I can leverage my understanding of those external systems, as well as my understanding of my students. Thus, I can attempt to both fulfill my purpose for grades (grades as a "mirror"), and society's purpose for grades (grades as "capital").

Questions to Consider

1) For Teachers: If you've assigned a zero, was it intended primarily to affect students mathematically or psychologically? Knowing that it is mathematically unsound as well as inaccurate, does that change your opinion of it? Would it chant your opinion if you discovered that there is no evidence that receiving a zero motivates students, but in fact it often demotivates them?

• In general, I have come to use a 0 as a "missing" in situations where it would be difficult to just put an "M" for missing. So most of my discussion of the role of a "0" is going to be w/ respect to missing assignments, and how to handle that numerically.
• I agree that when we're grading a student's understanding, it is neither appropriate nor accurate to assign a 0. I'm less certain of the role of a 0 if we're grading for completion, and have come to use it as representing "missing" in that situation. Feldman has argued that grading for completion is generally an ineffective practice, and I'm inclined to agree, though I need to learn more about how to better handle the situations where I was doing it.
• Why not just put an "M" in the gradebook, and leave it like that? Well, imagine the student with the following five grades on practice assignments that have been graded on completion: 80, m, m, m, m. My grade calculation doesn't know how to numerically interpret the "m," so it will skip over that and say that the student has an 80. Which is not the message I want that student to receive.
• Before last year, I only assigned 0's in two situations. It is important to note that I was on a 0-4 scale for all assignments.
• For grades attached to standards, students would only get a 0 if they did not sit for *any* of the 2+ assessments for that standard that quarter. I would keep it as an "M" for missing in the gradebook, but would convert it to a 0 when posting quarter grades. But these 0's were not permanent, and I'd go back and change them as soon as they completed a assessment, even if it was in an earlier quarter.
• Given how many opportunities for assessments there were in a quarter, and that you only needed one assessment to ensure you never got a 0 for that standard, not many students ever had 0's. That usually meant that most students with 0's had 0's because there were large portions of time where they were totally missing from the class, for whatever reason. Given how most other teachers 0's were harder to come back from than mine, I can imagine that many students, already in a tough spot, saw so many 0's and lost motivation.
• When grading low-stakes practice problem sets. Students were graded 0-4 on completion, which was typically curved up anyways (never curved down). So students would get a 0 if the assignment was missing. Because there were ~20 such assignments in a quarter, and keeping up with week-to-week practice was more important, I felt comfortable with letting students feel the mathematical impact of missing assignments right away.
• In general, however, I assigned 0's out of an inability to come up with a better system for handling "missing" assignments. This is about where I've landed on the utility of 0's.
• This past year, at my new school, we've actually got a different system for handling "missing" assignments, which patches up my system quite well.
• Students get an "M" if an assignment is missing. Their overall grade is calculated with all the numbers available, essentially ignoring missing assignments. But then, if a student is missing 30% or more of their assessments, their grade automatically gets locked down to a 50 (our district's minimum course grade). And no matter what, their grade will remain locked at a 50 until their % M's is under 30%.
• I think this system honors the fact that a missing assignment is not accurately accounted for by a 0. It also creates some "space" in the grading system, allowing students to miss an assessment here or there, without too much issue. Given that all standards are going to have multiple assessments, and possibly very many, it doesn't actually seriously impact the overall "data snapshot" for the student.
• I'm not sure if students experience it as such, but it's kind of like "dropping" up to a small number of missing assessments. And if a student had a good enough idea of how many assessments of how many standards to expect, they might think, "I'd rather just take an M for this assessment, and as long as I stay under 30% missing, it won't affect my grade." Again, I'm not sure if this is actually a thought process students may have, but I suppose they could!
• One negative design feature of this 30% missing threshold, is that it hides some information. If I see that a student in my gradebook has a 50, it's not clear if that 50 is a 50 due to an actual lack of understanding, or if it's a result of missing things. I wonder what would happen if the grade defaulted to an "I" for "incomplete" or something like that? The good thing about reverting to a 50 is that if a student doesn't do anything...nothing changes. So if we were to do an "I" or something, that would mean that when final grades are calculated, the "I" has to convert to a 50.
• There is a caveat to my school's system for managing missing assignments--it only applies to assessments, which are 50% of a student's grade. The other 50% is determined by "practice" assignments, which are run largely like a traditional grading system. For practice assignments last year, I used a 0 to indicate that the assignment was not completed, since they were graded almost entirely on completion.
• Our practice assignments aren't attached to standards, like our assessments are. They are not graded with the intent to actually assess and communicate student understanding of a given topic. Instead, they're meant to provide "credit" (in the form of grade value) for students completing assignments leading up to the performance assessment. They also help us tease out (sometimes) whether low assessment grades are due to a lack of practice, or due to performance issues.
• In general, however, I'm not sure I totally understand how "practice" fits into my school's vision for competency-based grades. If I ruled the world, I might advocate for doing away with the "practice assignment", or at least walking them back to like...~20% of a final grade. Because it definitely makes this more complicated, and doesn't even feel that necessary.
• At least at the high school level, I think it's okay for us to have a small assessment every week or two, and if a student doesn't want to do the practice work to prepare for the assessment...well, they'll figure out what happens. And as long as we are deliberate in our reflection with students, and timely in our turnaround of grades, it shouldn't take long for students to attach value to work that's not directly impacting their grade.
• So here's my question: how do I handle "missing" practice assignments? I can put in an "M," but that means they're essentially "dropped" b/c our grading software doesn't use the 30% missing mechanism for practice assignments. From the perspective of the student looking at their overall grade, an "M" is a dropped assignment, neither positively nor negatively affecting their grade, directly anyways. Is a missing assignment as "bad" as doing the assignment with as little as possible understanding/completion?
• Feldman discusses the role of true accountability, and how making students do the missing assignment is the true accountability that just giving them a 0 just isn't. And for assessments, I agree. But that's a very taxing system for what are supposed to be quick, negligible-stakes practice assignments.

2) Because the zero is never an accurate description of a student's knowledge, some teachers use a 1-5 scale instead of a 0-4 scale. Would this scale make the grade more accurate? More equitable? More motivational?

• I'd say it's more accurate in the sense that, just as the question suggested, it avoids placing the value judgement of the number "0" on something which is not fundamentally "0," which is a student's level of understanding. But for me, I think I'd just as soon call it an "M" for missing. If a student sits down, looks at the quiz, writes literally nothing, and then turns it in...that's "missing"...right?
• Less complicated, is generally more equitable, because it returns the power of calculation to students. I suppose it could complicate (or simplify) the calculations supposing that there is some pressure to map your grading system to a traditional 0-100 scale, which is something we often have to do.
• I do think it is a "harder hit" to deliver a 0 instead of a 1. I think that some teachers think a "harder hit" is more motivational, and others don't. I don't think I do, and would rather give a 1 than a 0. But again.

Plan To Do

• Note: as we get into the chapters of the book that discuss more concrete practices, I'd like to spend some time articulating concrete adjustments to my grading practice. These will likely evolve over time, and are just drafts.
• Practice assignments will be graded 50 to 100, to avoid the outlier's impact that 0's have on an the average of a dataset, when the bulk of the data will be in the 50 to 100 range.
• Given that (as of right now), my school has mandated 50% of the grade being based on "practice assignments," which are not standards- or competency-based, I need to learn more about what my school's vision for those grades actually are, so I can understand better how to fit it into the much more meaningful and important broader system of standards-based grading.