Grading for Equity: Reflection Questions (Ch 9 + Ch 10)

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 9: Practices That Value Knowledge, Not Environment or Behavior and...

Chapter 10: Practices That Value Knowledge, Not Environment or Behavior (continued)

I combined these two chapters b/c Ch 9 was pretty light, and these two chapters were basically the same big idea.

Initial Reactions:

• Judge? Or coach? At one point, Feldman discusses the difference between "feedback" and "grading" as the difference between what a "coach" does, and what a "judge" does. I won't go into it, but I think that's a really meaningful way to think about it. And I'm pretty sure that I'm trying to go the way of "teacher-as-coach." And then I only engage in "teacher-as-judge" to the extent that I'm required to engage in the system of grades by external factors. This feeling is a big part of why I increasingly consider myself a grade-abolitionist, and hope to learn more in the future about "un-grading."
• Healing from grading. I am expecting many of my students to come to me with many of the complexes forced upon them by their 8+ years-long journey through an education system where most teachers (myself included) have been enacting a problematic grading practice. With this book study and my commitment to equitable grading, and my commitment to CBG/SBG, I will be trying to disrupt that pattern of harm. So there will need to be a meaningful degree of time and effort invested in helping them to understand my (hopefully less oppressive) grading system. This process will also need to help students to understand, and heal from, the way that my profession has frequently traumatized students with our unfortunate enactment of problematic grading systems.
• Choice isn't always bad. At one point, Feldman discusses out extra credit provides students with an "out" for some content--they can drop the content, and replace it with extra credit, perhaps also consisting of content related to the course. Feldman disparages this option, is it creates a "Choose-Your-Own-Adventure" structure. I get why Feldman thinks that this is an undesirable outcome. But...
• If I'm teaching a one-year high school course on Number Theory, there are literally SO MANY COOL THINGS that it would be meaningful for students to learn in a year. Who said they all had to learn the same one-year of content? I can put out *years* of content to learn, and if the course design is clever/structured enough, students could theoretically pick the year's-worth of content that's most interesting to them. This was one of the big ideas behind my discovery-based math elective (which I wrote about here).
• I think that extra credit would be a lousy way to manage this. I'm just saying that Feldman seems to assume that this kind of course design is obviously undesirable, and I disagree. But I do get the point that Feldman is trying to make here.
• Well it worked for me... One of the most embarrassing moments for me as a student was in a grad-level seminar I took in college. It was about the history of math curriculum in the U.S., and we were discussing the issues with how math curriculum was presently constructed. I remember saying at one point, "How bad can it be? I mean, it worked for me, right?" The other students were thoughtful, kind, and prompt in their response, essentially saying, "Well yeah, but like...what about *everyone else* who isn't a straight white able-bodied born-in-the-U.S. cis-man on full scholarship at a private university?" They didn't use as many words, but I was so embarrassed that I dropped the course (there were other reasons I dropped the course too, but this was like...40% of the reasons). I've since learned a bunch, and am much more aware of why my comment isn't great, or even accurate.
• I connected this personal story with a point that Feldman made. He pointed out how teachers often use "what worked for them" in order to determine what behaviors and attitudes to reward/validate with grades. But "what worked for us" as teachers, a bunch of years ago, might not actually be that helpful today, for students who *aren't* us. Moreover, what "worked for us" also worked in the context of an educational system that I have come to understand as a fundamentally oppressive system.
• There's something to be said for allowing our personal experiences to inform how we coach students on navigating an oppressive system. But we need to make sure we understand was we are doing as *that,* and not as "It worked for me, so it must be 'good.'"
• Yes, and it's more complicated still. As I read more and more of this book, there's been a growing unease, even as I continue to learn and grow from it. And I can finally put it into words here after chapter 10.
• This book generally adds value, and I have found it helpful. But it feels elementary, and perhaps naive, in its failure to fully position itself in the broader context of the oppressive society in which it exists. I'm not saying that it never does this--it certainly does to a great extent. But it falls short in places.
• Here's the idea in the book that finally pushed me to put this feeling into words. Feldman's second pillar of equitable grading is that our grades should be bias-resistant (great). A driving principle of this pillar is, "Grades should be based on valid evidence of a student's content knowledge, and not based on evidence that is likely to be corrupted by a teacher's implicit bias or that reflects a student's environment." (Makes sense). For example, one way to violate this principle is to "inflate grades" with other things that don't actually have much to do with a student's level of understanding--like extra credit for bringing in supplies, or counting points for participation or effort.
• At one point, Feldman claims that violating this principle "is inequitable and deprives the student of important elements of equity: honesty and dignity." And I get it. But I think that there's more to it, because we aren't just teaching individuals in the context of our solitary school. And the grades we assign are part of a much larger system of oppression. There are schools full of privileged children getting their grades inflated in all these ways we've read not to do. And there is also my classroom, mostly full of students at the intersection of multiple oppressed identities. Who "needs" the privilege boost? Who "deserves" it? Who will ultimately *take* it?
• In the grand scheme of things, I recognize that the privilege of "grade inflation" is ultimately toxic to all who engage in it, specifically our students. And the matrices of oppression impacting my students can not meaningfully be deconstructed by me simply inflating my students' grades. But I am almost certain there is a non-zero degree to which we can leverage our teacher-capital to recapture some of that privilege for our students.
• For example, I can say with absolute certainty that it was harder to *get into* my college than it was to succeed in my college. And that's because there's an incentive to gatekeep colleges for a lot of very shitty reasons I won't go into here. But succeeding in college is an *enormous* access point for privilege. As a high school teacher, I can help my students side-step oppressive gatekeeping mechanisms. In doing so, I can help them access pools of privilege that they would otherwise have access to were it not for the active oppression they face by virtue of their identity and context.
• And honestly, I wouldn't lose a wink of sleep over it. I certainly wouldn't hope my students feel a loss of "dignity" for it. Meritocracy in postsecondary options is basically a myth. My students aren't the people who should be feeling moral decay for their efforts to accumulate enough privilege to *survive.*
• [Insert the counter-analysis that claims that my opinion here supports a race-to-the-bottom.] Yes, *and* the alternative to my strategy is just sitting back, allowing the privileged to continue to play *their* games and accumulate as much privilege as they can. Because let's be clear--they will.
• I can play The Game here to maximize short-term benefits for my students. At the same time, I then need to continually engage in a long-term plan that is working to construct a new, independent education system that is *actually* rooted in justice and equity. One that will slowly expand, and render the present oppressive system obsolete, left to wither, shrink, and ultimately disappear.

Questions to Consider

1) In the professional world, what are some difference consequences when something misses a deadline? Do those consequences exempt the person from ultimately performing the task? (Ch 9)

• At my job, I am typically given grace, and opportunity to get the job done eventually. But in no occasion I remember, have I ever just been disbanded from completing the task.

2) Some consider cheating on an assignment not an act of disobedience, but as a signal that though she is stuffling, she is still engaged and cares about her success. Why is cheating arguable a reflection of greater engagement than if the student simply skipped the assessment? (Ch 9)

• If the student *actually* didn't care...they wouldn't do it! So they care about doing well in the class! Which should really be the only thing a student needs to walk through the door with.

3) Look back at Tangela and Isabel in chapter 4. If summative assessments were the only element in the grade, what grade would each receive? What are the implications? What messages do we send each of them? How might it change how they and their caregivers think about each student's progress? How might it change how each would respond moving forward?

• Tangela (a hard worker, compliant, and dutiful) doesn't actually have that much content knowledge, and so doesn't do well on assessments. She would get a 60%, because she understands about that portion of the content.
• Tangela and her family should be counselled by the teacher on how to help Tangela get more support in learning the content. Her energies and focus could be reallocated from being a "good" student, to actually being able to learn more.
• Isabel (not a "good student", but a quick and thorough understander of the content) would get a 90%.
• It would be important for the teacher to provide a context for Isabel's grades, so that Isabel and her family understand the degree to which her disruptive behaviors impact others, and Isabel's future, even if they don't immediately result in low grades in the short-term. But I think we would also generally expect to have fewer negative behaviors, as Isabel would feel her recognition in the class (as captured by her grade) would match her self-assessment.

4) Ask some middle or high school students about why they copy homework, or what gets in the way of students completing homework. What is more important to you--that students do as much homework (and presumably, learning) as they can themselves, or that they copy it so that they get the points? What would need to change to explicitly communicate this priority?

• No students around right now, but I can share my own experience. I copied a ton of homework in college, specifically in my more advanced math classes I took for my major. I won't go super into it, but I did it because I had to, and I hated it, and it made me hate math and myself. It's taken me a while to recover from that, and it still impacts me in courses I take to this day. I think that I copied as a part of a broader issue of asking too much of myself, volume-wise, during my time in college. I had simply over-burdened myself, and something had to give, and that was it. (And also my back, lol RIP).
• I think that, as teachers, we often feel pressure to "get" students to a certain point in the curriculum, to certain benchmarks. And we do our best, but those benchmarks are set by people who are 1) ignorant of my students and their context, and 2) are seeking to service the broader [insert anti-capitalist, anti-racist rant]. And I think that we sometimes justify this practice, thinking that "at least if they're copying it, they're thinking about it, kinda..." But that's not really that true. And what's even more true, is the detrimental effect it can have on a student's self-perception (which was the biggest negative impact that copying had on me).

5) For Teachers: Look at the grade book for one of your classes. Compare students' test or summative assessment scores with their homework scores. For which students are their summative assessments higher than their homework scores? If a student learned the materials, how much does it matter if the students turned in homework? For which students is it reversed (homework scores are higher than summative assessment scores?) If a student turned in homework but did poorly on assessments, what does it suggest about whether homework served it purpose (or who might have done that student's homework)?

• I didn't do "homework" last year because it was virtual. And I haven't even really done "homework" in general for the last few years. So...

6) For Teachers: Try this simple, risk-free experiment: Print out a copy of the gradebook for one class of students. (Do this in the evening or when you're confident that students will not be accessing their grades.) Change the percentage weights, lowering the weight for homework and participation categories, and raising it for summative assessments. Print out the altered version, and then return the weights to their earlier percentages. Compare the final grades. Under which weighting system do final grades describe students' levels of content mastery more accurately? Which systems final grades describe students' content knowledge less accurately? For which students (or what kinds of students)? Does this change your opinion about how much to weight summative assessments?

• I'm not going to dwell too much on either this or the previous question for a couple of reasons:
• Feldman doesn't really need to convince me of anything--I'm totally down for weighting summative assessments at 100%, and can already see the practical value, which is reasonable, and *still* dwarfed by the philosophical/theoretical value.
• Last year sucked, and I spent so much time sunk into data analysis because I was looking for a way to interpret what happened last year as anything but public education getting totally [insert anti-capitalist, anti-racist rant]. I'm not going to beat myself up over last year in any way.

Plan To Do

• So many of my "plans" here are centered around how "practice tasks" are going to be a part of my grading system. And that's because it's the super mandatory (?) and super weighted part of my gradebook that is least-aligned to the actual principle of competency-based grading (or standards-based grading) that my school and I are working towards. But what if...
• Each standard will have two entries in the gradebook: one for practice, and one for performance. That way students can analyze (and hopefully see a positive correlation between) their performance and practice grades together. Something like this:

• This wouldn't be that tough to do, but it would require two things of me, specifically:
• To be able to tag practice tasks to standards. This is a little messy, but probably fine. I've generally valued the way that sometimes practice can integrate content from multiple standards, even if they're ultimately assessed separately at the end.
• Would I need to be able to disaggregate the parts of each practice task into their respective standards, so that they could get possibly multiple practice grades for a single task? This feels worth it for performance assessments, but *not* for practice tasks.
• Instead, I could tag a task with whatever standards come up meaningfully, and then that grade gets counted in each of the "buckets" of practice grades that get tagged to that assignment. One interesting consequence of this would be that tasks that cover tons of standards would have more impact. This is good, in the sense that it's honest, but bad in the sense that it makes different tasks have different weights, which makes things a little more complicated in general.
• Or, most simply, I could just assign it to the standard that shows up the most. Which is fine, right?
• This would also require me to have a meaningful way of grading practice tasks. On one hand, I don't want to grade based on completion, because that's inaccurate for reasons explained in these chapters. And on the other hand, I don't want to grade them based on correctness, because I don't want to penalize students for not having a full understanding of the content on the work that is literally designed to help them practice and build understanding *before* the assessment.
• If I was able to weight practice with 0% of the grade, the practice grade becomes a matter of simple data presentation, without an actual impact on students' grades. But I don't think this is going to be easy to do because the 50/50 practice/performance weights is a school-wide policy, and even if they let me do something separate, I think students would still interpret the practice grade as impactful, because it's that way for literally all of their other classes.

Grading for Equity: Reflection Questions (Ch 8)

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 8: Practices That Are Mathematically Accurate (continued)

Initial Reactions:

• If you can... The downside of using a single "maximum" score in order to represent a full set of grades is that it makes it possible for students to "not try" or "not engage" in the learning period before the assessment, and then just do well on the assessment. But I don't think that means we need to adjust our grading system to directly pressure students to engage in every single lesson. If students can pass the assessment at the end, without going through all of our stuff we made to prepare them...that's kind of on us, right?
• Like, if we have our set of external standards, and students meet them, who cares if they didn't do all the other work leading up to it? And if they're wrong, and they show up on test day, and don't perform? Then they learned something...as long as we are quick enough in our grading turnaround, and maybe nudge them to reflect on that and grow from their failure, so they actually connect "not preparing" to "not performing."
• This is a thought that's always in the back of my mind. And I've got tons of little reasons why it's not that simple, but it's always in the back of my mind, and I'm not sure how I feel about it? Because it somehow *feels* right, and also *feels* wrong at the same time. It feels right because it's simple, respectful, and realistic. It feels wrong because it devalues the way that our own (dis)engagement can help/harm others. It also can lead us to accidentally not perform at the level we could, if we worked harder, earlier. But then *that* feeling in and of itself...is that good because it's about us pushing ourselves to develop and realize our potential? Or is that a habit of thought that leads to us feeling that we're never enough?
• Long story short, this is a weirdly fraught cluster of thoughts and feelings around this idea, and I'm not totally sure where the resolution is, if there is one at all!
• Mathematically "Accurate." There is no fundamental mathematical definition of "accurate" or "right." It is possible, if we think about things mathematically, for us to make a set of pre-conditions (or axioms), that define what "accurate" would mean. And once we have done that, we can start to look at statements or calculations as "accurate." And I think Feldman does a decent job of surfacing that just because some of the calculations we are are "mathematical," that doesn't mean that they're "accurate" for our context. This is a super important point that I'm glad he brings up.
• But I also can't help but notice that there are multiple moments where he asserts that some calculations are "accurate" while others aren't, but he doesn't do a sufficient job of defining the underlying pre-conditions that I think he is assuming.
• For example, when describing the shortcomings of the arithmetic mean, when it comes to determining grades, he claims "when there are outliers in a student's performance, [median and mode] are mathematically accurate than the average." And maybe it's the smartass mathematician in me that makes me immediately seek a counterexample when I hear an absolute statement like his. Consider the following student, with the following grades that all need to be combined into a single, final grade:
• Student A: 10, 60, 60, 100, 100
• The mean here is 66, and the median is 60. And if we disclude the outlier of 10, as Feldman suggests, then we're basically just looking at the subset 60, 60, 100, 100. And 66 feels more accurate than 60, because 60 is the minimum value, and ignores the 100's. I'm not sure 66 is even the best grade to give, but it's better than 60.
• Student B: 10, 70, 70, 100, 100
• There is definitely an outlier, so the median should give a more accurate measure. But both the mean and the median are 70, so they are either equally equally accurate or equally inaccurate.
• Student C: 1, 1, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100
• Nevermind the fact that the mode is almost never the best measure of central tendency, given that it straight up often doesn't exist, or there are multiple modes.
• Also, given that the goals of Industrial Revolution era education were to sort students along lines of privilege and access...then all of the problematic traditional calculations of 120 years ago were perfectly "accurate," in that they very reliably converged on the same lines of privilege and access they were trying to replicate. So it's important to say out loud what our underlying values are about the role that grades can and should play, and then create our mathematical definitions from there.
• I get that this feels a little nitpicky, and it kind of is. But Feldman rightly warns us of making mathematical assertions without interrogating the underlying assumptions, and then he seems to do that on his own at various times in this chapter.
• The most recent score. I'll be honest, I was pretty dissatisfied, if not surprised, by the lack of resolution on how best to distill a full set of grades into a single summary statistic. The arithmetic mean was soundly defeated, and he kept talking about the value of "most recent performance." But then there wasn't really enough explanation of how to actually execute "most recent." There was some quick discussion of what to do when the "most recent" and "maximum" don't agree, but it was cursory at best. Which was frustrating, because that's literally the biggest issue with "most recent."
• I've seen models where there's a time-weighted average. So more recent scores are weighted more heavily, perhaps *much* more heavily, and the weight of older assignments decreases. Which is a cool math problem, and not that hard to program, mathematically. But that's a great way to quickly turn your gradebook into a mysterious black box, which is not good.

Questions to Consider

1) For Teachers: Many of us give students a grade "bump" when they have shown improvement or growth over a term. By allowing (and encouraging) students to demonstrate growth over time through improved performance, and recording that most recent performance, do we still need to include a separate bump for growth, or does the improved score itself recognizes and reward growth?

• I'll be honest, these questions in the last couple chapters have gotten a little more "leading," than reflective? It really seems like Feldman wants to say: "We don't need to give a grade bump for growth, because the improved score itself recognizes and rewards growth." Like, he should have just spent a couple paragraphs talking about that, and then asked a better follow up question so that we actually need to reflect on our values and thinking, instead of just feeling like we have to agree with what he's saying.
• That said, I totally agree with what he's saying, lol.

2) For teachers: How easy should it be for a student to be able to calculate her own grade? How could we use a student's own grade as an opportunity to teach mathematical principles of median, mean, mode, scale, and percentages, and thereby empower students to be more critical consumers of statistics?

• See above critique, lol.
• I definitely agree that students should need *at most* 6th grade math skills to calculate their grade. How sick are you, as a teacher, of hearing: "What would I have to do to get X grade? If I get a Y on assignment Z, what will my grade be then?" And yes, if we just did away with this reductive economy of grade-as-commodity, then it wouldn't be an issue. But also, if students were actually able to sit down, and just play around with numbers, see how changing some things affects other things...I think that would have a serious impact on helping students to deeply understand the economy of grades, in a way that many students (and teachers!) kind of don't.

3) Think of an example in the professional workplace in which group work (or more likely, called "collaboration" is expected. What is the rationale, and how is the effectiveness of that collaboration determined?

• Sometimes projects are collaborative because it's more fun! I love teaming up with other teachers on fun little projects, just because it's fun to hang out with my colleagues and chill. Especially if it's something that's not that important/difficult--staffing the cotton candy machine at the field day comes to mind!
• Sometimes the goal of collaboration is peer-instruction. Sometimes because the product is *ourselves* and the resources is *them.* Lots of learning can happen when you let people just talk to each other, share their perspectives, and just learn from each other.
• But more often than not, we collaborate because the product becomes better (or even just possible) when you have a bunch of people. In this case, the objective is to create a product, not necessarily develop us individually, so we aren't really assessed individually on the group project.

Plan To Do

• In the last post I said that I wanted to have both PROJECTS and QUIZZES assessing the same standards, independently, hoping that they combine to converge on a dataset that makes for more accurate grades. Which sounds legit. But I also feel like it's pretty important for most projects (at least as I'm thinking of them) to be collaborative in the activity, if not also collaborative in the product.
• So what if I just make projects like practice tasks? Not graded with respect to demonstrating individual independent understanding of a specific content standard. But instead just graded however I grade practice tasks (TBD). Then *after* they do the practice task project, I give them the quiz, where they can be assessed individually.
• I'm just not sure how often I want to do these projects, but I would want to make sure I have enough so I can do one at least as often as quizzes (performance assessments). I need to look through my stuff to make sure I have enough of these. Because I want a very simple separation of task identity, like "projects <=> practice grade" and "quizzes <=> performance." And then everything else is ungraded classwork. That's easy for students to understand, easy for me to think about, and just generally simplifies the course structure for students.

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.

Grading for Equity: Reflection Questions (Ch 6)

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 6: A New Vision of Grading

Initial Reactions:

• Verb choice. I feel like there is, or could be, a meaningful difference between a "grade," "rating," and "score." Whichever noun/verb carries the least sense of "valuation," that's the one I want to use. I don't think it matters, but that's just something I've thought about for a while, and I haven't really ever gotten any kind of resolution.

Questions to Consider

1) Review your classroom's current grading policies through the pillars of our vision: How accurate are they? How bias-resistant? How motivation?

• Standard Disclaimer: I do want to make the point that I'm basically just sharing *my experience* with my school's grading system, which is largely determined by the network my school is a part of. The perspectives shared are my own, and not reflective of my colleagues, school, or anyone else who isn't me.
• Important context: my school uses competency-based grades (CBG). The way my school does CBG is pretty cool, and I don't understand the ins-and-outs of it that well, because the math department uses standards-based grades (SBG). This is because we haven't exactly figured out a way to apply CBG to math content yet. This is a bit of a loss for coherence, given that the rest of the school is on the CBG, but it's something we're working on.
• Brief summary of how we do SBG: each of the courses has a list of 30-40 "standards" that are considered the 30-40 biggest and most important ideas in the course. For example, in my Algebra I course, one standard is called "Graphing Linear Functions from an Equation." Any given assessment might have between 1 and 5 different standards attached to it, but they are each assessed, scored, and entered into the gradebook independently.
• For me, more than anything, disaggregating student assessment by a relatively short list of "big ideas" is useful. I suppose this is a feature that supports student motivation, because it helps make it clear what students need to work on. A student looks at their gradebook, sees that they have a lower rating in "Construction Linear Equations from Context," and know what they need to learn more about. It's empowering because students can do this kind of self-assessment, at least given their grades, independently.
• One thing I've done to further support this is to have a file system in the back of the room, organized by standard, where a student can go get supplemental or missing work related to the standard. This facilitates some independence in them knowing how exactly to "shore up" their understanding, and improve their performance.
• This process of disaggregating scores by standards allows for more accurate grading, because students have precise information about what content they have performed at what level in. It's not one big "omnibus" grade saying they need to generally do better in class, or just "pay attention on the classwork."

• When scoring student work, we look at the student work with respect to the standard, and use the following flowchart. (There's a more detailed rubric, but this is the actual thought process I go through.)

• I think that sorting work into one of just four buckets allows for a higher degree of accuracy. If there were say...10 different levels of performance on each standard, that would require me to have a much more precise assessment of student work. I would need to be able to clearly justify that a student's work should be rated a 5 and not a 6 or a 4. The more granular the rating, the more likely it is that I engage in biased assessment, especially in the pressured context of having to grade 100 student quizzes, typically with multiple standards on each.
• I do still think that this work is less bias-resistant than, say, having a list of "criteria for meeting the objective." In that way, anybody really could make an accurate assessment of whether they met the objective or not. But, as we do it now, without that specific criteria for meeting the objective" outlined, students (and others) really just have to trust me when I say, "yeah, you met the objective" or not.
• I toyed around with creating a pretty specific list of "criteria for meeting the objective" for each standard. For example, for the standard "Solving Linear Inequalities," I made the following list of criteria for meeting the objective:
• Choose a series of algebraic moves that can simplify a linear inequality, with the ultimate goal of solving it.
• Prove or checks the solution to an inequality by showing a series of valid algebraic moves, or by substituting the proposed solution into the original inequality.
• Respect the direction of the inequality, recognizing that some algebraic moves seem to reverse its direction.
• Recognize the solution to an inequality is typically an infinite set of numbers that satisfy the inequality.
• Identifies the boundary points of the inequality, determining if it is a solution itself (closed) or not (open).
• But that's really just a description of solving linear inequalities algebraically. Which means I could expand the list of criteria to include non-algebraic approaches ("Uses graphing technology, or guess-and-check to represent the solution on a numberline"). Or I could simply make the standard more specific, and call it "Solving Linear Inequalities Algebraically." But this brings up an issue I have with cooking up a list of specific content standards can calling their union "Algebra I..."
• Defining "content standards," and rating them with an exhaustive list of criteria, runs into trouble with accuracy. These standards we've cooked up to describe "Algebra I" can't possibly partition the entirety of what we have come to understand as the set of things we want to learn when we study 9th grade Algebra I. We tried to make sure the standards didn't overlap in any way, so standards were fully independent. Which is useful for assessment, but not entirely authentic to how mathematical knowledge is organized.

• Furthermore, there are gaps in the standards--knowledge we value and seek to build in "Algebra I," which is not (and maybe *could not*) be captured in a discrete list of standards with criteria. I think that some objectives are so specific, and in their entirety are so numerous, that it's not feasible to try and cover all of "Algebra I" with non-overlapping standards. I guess that just means that a big portion of "Algebra I" course objectives aren't precisely captured in the standards? Which I guess is okay, right? Like...our goal isn't to hold students accountable to 100% of what we think Algebra I is...we just need to make sure they get the biggest, most impactful, most interesting/useful ideas. So maybe this isn't as big of as issue as I thought?
• In the name of accuracy though, I just need to make sure that I am only ever attaching grades to my assessment of student work done with respect to the stated objective. Maybe I provide some light feedback on the other stuff, but if I'm not articulating it in a standard, I shouldn't weigh it with a grade. It is tempting, however, to "reward" students with grades if they demonstrate an understanding of some unstated between-the-standards content knowledge, and I need to make sure I don't. But that's two different places where my only mechanism against bias is self-monitoring, which is where bias is at its strongest, especially implicit bias.
• And then there's the issue of the fact that these standards totally miss the idea that math education should focus more on "practices and dispositions," rather than discrete, if connected, tidbits of content knowledge. But that's for another summer reading project.
• Students will typically have three or more opportunities over the course of the class to demonstrate proficiency on each standard. And the grade that goes in the gradebook is the average of the top two scores they ever get.
• This is motivating, because students can "bump out" lower grades by improving their understanding, and then performing better at a later date. This also motivates risk-taking, because once you have two ratings in the gradebook, your grade for that standard can never go down, reducing performance anxiety.
• We opted for "average of the top two" instead of the much simpler "maximum score stays." This was because we wanted to ensure that we valued students demonstrating peak performance multiple times, and for two reasons. First, being able to demonstrate understanding on multiple occasions supports the accuracy of our grade, specifically with respect to test-retest-reliability. Second, if we just use the "max" score, we can no longer apply the pressure of grades to incentivize continued effort and performance of students who get it right on the first try. Clearly, our second reason was less noble, but definitely one we had to consider.
• In an effort to provide some grade-incentive for doing work that is not considered an official assessment, the other 50% of a student's grade is called "Practice." For tasks that are graded as "Practice Tasks," it's really the Wild Wild West. I can't speak for other teachers, but I tended to revert to more traditional grading practices, and all that goes with them, for better worse or worse.
• Since I was already applying "SBG" to all of our work for the class, I ended up using the "Practice Grade" as more of a "Completion/Effort Grade." Which is riddled with bias, de-motivating signals, and prone to inaccuracy. I think the original intent with "practice grades" was to be able to grade-value the often-significant amount of work that students need to do before being "ready" to demonstrate performance on an assessment. Which makes sense. I also suspect it was originally intended to take the performance-anxiety-impact-edge off of what could otherwise be a performance-heavy grading system. (Before I got there, I think my school did something like 70% standards + 30% practice, but we changed it for reasons I only partly understand.)

2) How much does this book's vision for equitable grading align with your own, personal vision for grading? What concerns do you have about this vision? What are your hopes? How much does this vision match against your school's overall vision? How likely is it that your school community could agree on this vision?

• Accurate, Bias-resistant, and Motivating are three great places to start, objectively, right? I do think that there is a question of "Authenticity" that should be considered. As a mathematician teacher, I am responsible for inducting my students further into the community of mathematicians. How can I make sure that I am assessing my students in a way that is consistent with the way that mathematicians are assessed more broadly, outside of schools?
• I literally chose to work at my school because they were one of the few (only?) schools that use competency-based grading. And CBG is pretty close to the frontier of equitable grading, as near as I can tell. And they're committed to CBG for all the right reasons (equity, authenticity, inclusivity). So I was excited to join a team that had similar understandings and values associated with grades. Of course, having a school-wide commitment to CBG (modulo the math team) is not easy at all, and we're definitely still figuring it out. But it's a refreshingly radical starting point, and I love it. I think that moving the math team from SBG to CBG, in the name of coherence is the biggest next-step for us. And I'm so pumped to be a math teacher in the school when this is happening.
• The focus of this book seems to be 1) understanding how grades can be oppressive, and 2) figuring out ways to make grades more equitable, and less oppressive. But that gives me very "best worst option" vibes, which I think sells all of us short. I think I've mentioned this in earlier reflections, but I am increasingly interested in abolishing grades as a whole. I don't know much about it, but I understand that more and more teachers are stepping in that direction. I'm not sure I'm ready for that shift yet, and I'm definitely not sure I've got the capital in my new building/district yet to pull it off. But I am very interested in it. There are just so so so many ways that "grading" in the traditional (or even modern?) sense are oppressive and harmful. So why not just bail on them entirely?
• Of course, there would still need to be some complicated "patchwork" to cohere my students' experience with that of everyone else who is doing grades. Because improperly done, I can definitely see how just throwing the switch on "grades" as a whole could lead to issues. But I *have* to have a longer-term plan moving away from grades right? And don't we have to as a whole? Yes, it's going to be harder, and yes, it's going to cause some major systems to have to change, but that's a good thing.
• And yes, we could say that it's the external market of jobs, scholarships, and colleges that force us as K12 schools to commit to grades, but why *should* those entities get to decide? They don't have our best interests at heart when they let kids take out $300K in loans to get a degree. They don't have our best interests at heart when these massive universities suck up community land and resources, hoard wealth in their enormous endowments, and feed their hosting neighborhoods *crumbs* in the name of giving back. Private universities, the labor market, and scholarships are diseased with capitalism, and for as long as we allow them to set the vision for public education in the U.S., we will continue to find ourselves throttled in the clutches of capitalism. [When I say "insert anti-capitalist rant," I usually mean something along these lines.]
• I'm not saying it's easy to abolish grades. But I'm saying that I believe it's important. And I'm not saying we have to do it right away--I know I certainly am not. But for as long as we don't, we are actively perpetuating the way that grades are used as another system of oppression. And yes, we can work to utilize principles of more equitable grading (which is kind of the whole point of this book study), but that *can't* be the end goal.

Grading for Equity: Reflection Questions (Ch 5)

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 4: Traditional Grading Demotivates and Disempowers

Performance goals vs. Mastery goals. Performance goals are goals that you have to perform at a certain level w/ respect to others. For example, a performance goal could be to be in the top 10% of your class. A mastery goal is a goal that you have to be able to do a specific task, which is defined by the task itself. For example, a mastery goal could be to be able to find the roots of any quadratic equation, given in any algebraic form. I think that this is a mostly-useful characterization, and it's not surprising that performance goals lead to much more problematic outcomes than mastery goals. But...

Teacher sensitivity, and the fallibility of self-assessment. One thing that I keep thinking about while reading this book is how really difficult teacher reflection and self-assessment is. Because we're professionals, right? Teachers typically have higher degrees, and some have been doing this work for decades and decades. And I think the classic issue with long-term professionals, in any field, is that they start to crystallize, and they are less and less inclined to make really radical changes, which looks like some combination of "stability" and "stagnation."

But I don't think it's for the "old dog, new tricks" reason that comes up so often. I think it's because we have actually convinced ourselves that we're doing the right things. We keep exhibiting the same practices and beliefs because we thought really hard about it, and came to a conclusion that what we are doing is the *right* thing to do. So for teachers to make major shifts in their practice, like modifying grading practices, there needs to be enough reflection, and enough self-analysis, for teachers to really identify and unseat understandings they've had from before.

For example, last year, I was adamant that I was doing the right thing in my classes, by grading every assignment I asked a student to do. I figured every minute of student engagement was so "expensive," I'd be loathe to waste an opportunity to give a student credit for demonstrating their understanding of the objective. Moreover, I figured that school-from-home in and of itself was such a demanding task that if I was making a kid do an assignment, they should be getting credit for it. I kind of understand better now why that's not a great policy in general (though again, I'm not beating myself up over anything that happened in remote teaching last year).

But I have the distinct memory of being SO CERTAIN that I was doing the best thing I could at the time. And this wasn't even the first time I've felt that kind of conviction with what I was doing. I feel this inside of myself ALL THE TIME. And I think it was even worse this past year because there was so little discourse with my colleagues. We were fully remote for basically the whole year. It was my 1st year in the district. It was my 1st year in the school. My school had not allowed time for content team meetings, and grade-level meetings were filled to the brim with discussing students and the constantly changing landscape.

In isolation, I think we retreat further and further into our own heads, both personally and professionally. At least I do. And so I think fostering rich and frequent teacher-to-teacher discourse time is critical. It's the key to keeping teachers open, flexible, curious, and self-critical to a healthy extent. And if that resource, teacher-teacher time, is both abundant and taken seriously, it's like fertilizer for professional growth. And I know this sounds like an obvious thing, but I just need to say it out loud here, because not all teachers have that. In fact, I'm willing to bet a decisive majority of teachers don't have that. And [insert anti-capitalist rant].

Questions to Consider

1) Interview some students. Are they motivates to achieve success or to avoid failure? What specific actions, policies, or words by teachers cause students to experience one type of motivation instead of the other?

• No students around this summer. RIP.

2) Do you think of your tasks at work as performance or mastery goals? What affects how you define the goal? How does this affect how you pursue the task?

• Let me say both, and why. When I'm clear on the goal, that's when I experience it as a mastery goal. But when I'm not clear on what the goal is, what the path forward is, or how I'm doing, that's when it becomes about performance.
• For example, from the end of my junior year in high school, I just wanted to be a great high school math teacher. And every question, doubt, path went through this lens. Is this going to help me be the great teacher my future students deserve? And when it was time to pick colleges, majors, and activities, that laser-focus made it clear, and it really didn't matter what other people were doing, and how I was doing with respect to them.
• But towards the end of college, and at various times throughout my first 4 years of teaching, what it means to "be a good teacher" is so much larger and amorphous than I initially understood. So I fell to looking at my professional growth as a "performance goal." It's simpler, I'll give it that. I'd look around at other people, seeing what they were doing, and thinking, "I just need to do better than them, right?" Which is awful. And still is awful, and is something I need to continually confront and mitigate in my practice. It fills me with self-doubt, anxiety, negative perspectives on others, and a generalized sense of insecurity.

3) In what ways do schools and classrooms send a message of competition for achievement? How does your school's treatment of awards and honors promote or undermine a growth or fixed mindset?

• I appreciate that my school doesn't do any awards based on relative performance (except for valedictorian/salutatorian). They're usually benchmark awards, like "these students are passing all their classes", "or these students have 95% attendance or better," and then I would say the majority of "award/honor capital" is attributed directly by teachers shouting out students. Which is cool. I think many of the teachers recognize the importance of picking students to "shout out" by more humanizing metrics than "the highest performing students." Which, again, is cool.
• But any time teachers compare students, like, "Be more like student X," you're creating a hierarchy of perceived status and achievement. There are tons of ways that teachers support class status hierarchies through patterns in how they call on people, intervene in discussions, interrupt students, provide certain kinds of feedback, and publish grades that are easy to compare.
• I think that the culture that administration projects towards teachers will basically always get reflected down to students. Sometimes directly through policies, and sometimes maybe it's just through vibes. But let me ask you: say there was one teacher on your team who only gave out A's and B's, year after year. Wouldn't their colleagues get suspicious? Wouldn't students get suspicious? Wouldn't administration be suspicious? If enough teachers at the school did it, wouldn't district administration get suspicious?
• If they're suspicious, it's because there is an expectation that student performance should kind of adhere to a general distribution, where there is a non-zero amount of students performing at a "below average" level. Moreover, that suggests that there is some expected "center" in the B to C range, and at least a small number of students should be getting below that center. And I would expect that teacher to feel some pressure to "curve" their class so that it matches the expected distribution. This is a very powerful, if quietly said, culture that *many* schools and districts subscribe to, and it is very an expression of regressive models of human intelligence (see: IQ tests, and eugenics).

Grading for Equity: Reflection Questions (Ch 4)

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 4: Traditional Grading Hides Information, Invites Biases

On the term "traditional grading". Throughout the book, Feldman refers to "traditional grading," and I *think* I know what he means, and I *think* a lot of teachers would. But I'm not sure I believe in it as a useful euphemism. The descriptor "traditional" feels like it's being used to mean "outdated" here, and I know few professionals who would be okay with someone describing their practice as such. But what makes it hard is that I'm not sure what other way to describe it? Like, we have "standards-based grading," and "competency-based grading." What is the more precise, accurate term? Or is that the point...that there is no central core "idea" after which to name the practice?

Teacher-to-teacher variance. Feldman also talked about how problematic it is that for most teachers in most schools (at least in the U.S.), grading policies changes from teacher to teacher. I think students typically understand that this is the norm (at least by the time they get to high school), and just figure out how to deal with it. But also, Feldman points out that this extra layer of complexity, in an already complex system, is yet another barrier to students understanding and owning their grades.

But forcing all teachers in the same district, or even just the same school, to have identical grading policies in all respects...on one hand, that sounds utopian, and on the other, it sounds horrifying. This is the classic "autonomy" vs. "uniformity" conflict, which has no real solution I think? But it *can* be mitigated by investing heavily in teacher-teacher collaboration, co-developement (as opposed to individual development), effective coordination, and an abundance of resources. But that's not easy to make happen because [insert anti-capitalist rant].

Complexity in grading systems. My school is working to be competency-based, and I think that what we're doing is super cool. But it's also pretty complicated at times, especially for 9th graders who have spent the last 8+ years in schools that likely have "traditional grades." Over the years, students eventually get used to it, and it's fine (or so I'm told--I've only had one year of teaching remotely with 9th graders). And more often than not, in order to make the grading system accessible for students and families, we end up focusing students on just the final "overall grade." That's because it looks like a regular 0-100 grade, with all the associated feelings and expectations behind it. So on the surface, the grades contribute to many of the unhealthy and oppressive practices that "traditional" grades do. But there is technically some underlying theory that goes into the the calculation of that "overall grade" using out principles of competency-based grading. So...that's better, right? Right?

I do think that being a math teacher has seriously benefited my ability to understand the math underlying grade calculations. Even as a student, I remember doing tons of calculations along the lines of "if I get X% on this assignment, which is in category Y, which has an associated weighting of Z%..." Which is good high school level math, but I'll be the first to admit that I don't think every high schooler can do it. Heck, I don't think every teacher can do it. And that's not great. The more complicated the grading calculation, the further it removes students from owning and understanding their grades, and the more it feels like an arbitrary system purely run on bias.

So how complex should grading systems be? We definitely want to avoid what Feldman identifies as the "Omnibus" grade--a barrel-ful of information in a thimble-size container. But if we make it super complicated, that becomes its own possibly not-better system. So why not just invest in taking the time to teach students and families how the system works? That takes a lot of time that might not be worth it, especially if you need to get your own grading "orientation" for every different teacher you have. I guess and important distinction is that of "sophisticated" vs. "complicated." A sophisticated grading system can do "what we need grades to do" (whatever that is?), and can do it with nuance, sensitivity, and accuracy.

How simple should grades be? I don't think we need to come up with a better way to calculate a better summary statistic of the right combination of the right things, so we can all have one, perfect "score." I don't think it should even be *possible* to boil down all your learning into one score. Yeah, that's useful for quickly sorting students, and efficiently assigning privilege and access, and for pressuring students to perform. But like...who wants to do *any* of those things?

If we can't do grades "right," should we do them at all? In this chapter, Feldman also talks about bias, implicit and otherwise. And maybe he's just getting us fired up before delivering some strong, effective, bias-free systems in the last part of the book. If the goal is to create a system that abolishes implicit bias, and systems of oppression...what do we do if we *can't*? What if the idea of summarizing growth and learning with just a few statistics that we would recognize as "grades" is inextricably rooted in oppression and contrary to how "learning" happens? Is it then our responsibility to abolish the concept of grades?

I know some would say that grades are the "lesser evil," but lesser for whom? When we resign ourselves to "surviving" a lesser evil, we are essentially saying that some should be expected to suffer because...we can't find another way? Who has the right, the power, to decide who gets to suffer?

Questions to Consider

1) What confidence or uncertainty do you have that two teachers in your school would assign the same grade to a student?

• Within my department, at least, given the grading structures in place for us as a whole department...assuming we when through the same "volume" of content at the same pace and students received the same instruction...I'm 90% sure that our final grades would be within 10% of each other. Which doesn't sound that good, but I actually do think that's better than the industry average, so to speak. It helps that one of my school's big thing is their grading system, so there is some meaningful investment in allowing us to talk through things together, and connect.

2) Are there teachers with reputations as "hard" or "easy" graders? What, specifically, defines them as that? How does this categorization make you feel? How does it make that teacher feel? How do students react?

• Certainly. And here are some responses I can imagine teachers having, either because I've had them myself, or have seen them in other teachers:
• The "easy" grader might feel...
• "I am being sensitive to students' needs."
• "Grading isn't so surgically precise that it's worth making students feel bad about them."
• "Grades don't actually matter."
• "Giving low grades restricts student access to critical resources like scholarships, in-school prestige, and access to post-secondary options."
• The "hard" grader might feel...
• "I have high expectations for students."
• "If I grade harder, they'll work harder."
• "Other teachers coddle students, which is unfair to them and the teachers that don't want to coddle them."
• "Students have it easy in school. Try having a boss!"
• I think that the vast majority of teachers would consider themselves as "warm demanders" (Lisa Delpit, 2013), and as "tough but fair." I think that students are much more likely to categorize teachers as "easy/hard" graders, than teachers are themselves. I think that there is a general teacher culture to prefer being viewed as "too hard" rather than "too easy," or at least that's the perception that feels like it gets rewarded/validated by leadership. Which feels contrary to "err on the side of doing the less harmful thing"? But then again, I think I just revealed to you a bit of my internal vibes re: "hard" vs. "easy" graders.

Grading for Equity: Reflection Questions (Ch 3)

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 3: How Traditional Grading Stifles Risk-Taking and Supports the "Commodity of Grades"

Initial Reactions. It really is amazing how every teacher, every school, every district, is so very different, but we all seem to land on some of a handful of the same conflicts. At one point, when describing (in very thorough detail) the "commodity of grades," Feldman quoted the student who asked, "Can I erase the board for 10 points?" It was easy to see the student in my mind's eye, in my classroom, asking that question. And it was easy because that experience is sooooooooo real. It's disturbing, really.

This whole chapter was filled with disturbing moments like that. One particularly uncomfortable passage detailed the negative impact of counting every single assignment towards grades. I thought this was an effective practice, because I figured that a student demonstrated proficiency with the standard at any point in the arc of learning, they should get some kind of "credit" for it. Also, given that it was the middle of full-year remote learning, it was arguably the worst school year ever (citation *not* needed). I knew how much it meant that students were still logging into class, and I wanted them to feel like they were getting something out of it.

I won't review all the reasons why grading every single assignment generally harms student learning (even if you are able to make it a feasible undertaking). Nor will I self-flagellate for anything I tried last year. But I am definitely clearer than ever on the degree to which I as a teacher can harm student learning by over-applying grading. Which isn't even surprising to me, but important to be reminded of. The degree to which things are graded is almost perfectly negatively correlated with the amount of joy, healthy teacher-student relationships, and general positive vibes of the classroom. And that is as both a teacher, and a student.

Any time I do a math or teaching course as professional development, and the instructor starts to talk about passing grades, weights, and all that, my trust in the course and instructor immediately starts to decay. It makes me feel like they care more about the products I'm creating (the assignments) than my learning. And I wonder--did I always feel like that? Or is this an attitude I've developed as a result of just getting older? Or because of my work as a teacher? I certainly don't remember caring as a student.

Another thing that Feldman discussed was how it is the teacher's "burden of proof" to show that they, and their class, can be trusted as a safe, supportive, and worthwhile space. As a student, I don't think I believed that, but as a teacher now, I think I do. And this is because I see schools, more and more, as services created to serve. More or less, a community gets together, pools resources, and invests time, money, and faith in the school, expecting that their (typically, but not exclusively) children are going to be nurtured and educated.

So imagine being a child, forced to go to this school that your community has paid so dearly for...and some random adult says that you have to "prove" that you care about your learning? That your family cares? Asking you to "meet them halfway," after everything that had to happen to lead to you being there in class that day?

I think that teachers often feel this pressure to ask students to "meet them halfway," implying that students and families aren't working hard enough. But I don't think that pressure actually comes from teachers believing that students and families don't care (at least not most of the time). I think it comes from the teachers feeling exploited by the exploitive capitalistic conditions of their employment and positioning in society. But capitalism, somehow always able to position itself as the hero, pushes us to direct blame in the wrong directions, toward students and families.

Questions to Consider

1) How have different supervisors (or those whose opinions you care about) responded to your mistakes? How have helpful responses impacted you and your effectiveness? How have unhelpful responses impacted you and your effectiveness?

• I rowed in college, and at one point there was a part of my technique that was ineffective. My coach basically stopped practice, and took the opportunity to provide me direct, explicit feedback on what I was doing that wasn't productive. I won't go into the details, but he basically said, "Look Bear, this is what you're doing. I know X about you, so this is probably why. Now that we *both* understand what you're doing and why, this is what you should do instead, and why."
• I definitely still had to keep working to break that bad habit in my technique, but there was a intellectual switch from that point on. Instead of him fighting me to make a change I didn't understand, I was able to own that development myself, because I knew what I needed to work on and why.
• Moreover, he didn't present my mistake as a character flaw. I wasn't just lazy or stupid because I had a bad habit. I felt seen and understood, because he was able to help me better understand a part of myself that I hadn't before. And that built my trust in him as a coach and a leader--trust that he actually understood what I needed, that he wanted to help, and that he knew how to help.
• That's something I've been thinking about all year--the importance of us, as feedback providers, to make clear that we understand why students make certain mistakes, have certain misconceptions, or have problematic behaviors. Instead of just problematizing a behavior, if we can make clear we understand why that happens, I expect that *alone* will lead to an improvement. Sometimes all students need is support in understanding themselves better. The danger here is that it's important for the teacher to be accurate in their assessment, instead of just assuming. An inaccurate assumption will betray a lack of mutual understanding, and reduce trust that students have in the teacher (with reason). And so truly listening and understanding students and their thought process is again highlighted as an essential practice in all assessment. And this is so hard to do.

2) Recall something you learned to do outside of the school context. What motivated you to learn and to continue learning when you struggled?

• My go-to example here is spreadsheets. I have never done any formal training in spreadsheets, but at this point I would say I have pretty advanced proficiency (at least for my field). When I think about being in a "flow state," where I'm just cruising through problems, fully absorbed, right in the heart of my Zone of Proximal Development...I imagine myself doing spreadsheet projects. I was motivated to learn because the only time I ever learned spreadsheet techniques was when I needed them for a project I already wanted to do.
• All of the best projects I've had started with me not knowing how to do it, but believing deep in my heart that it was possible. Throw in a dash of some useful background math ideas, and increasingly capable Googling skills, and I really do feel unstoppable when I'm spreadsheeting. This is also, incidentally, my go-to example for thinking about what "problem-based learning" can be.
• Over time, my motivation to learn has extended further and further beyond the immediate practical motive of needing this spreadsheet to do something for me in my work. More and more, I want to dive into spreadsheet challenges just because...it's fun! Each new project is like solving a puzzle every time. What do I want to do? What do I already know how to do? What else do I wish I could do? Where can I figure out how to do that? Is this the best way to do it? Yes, there is often some extrinsic motivation from my job, but it can really be paper-thin. Because once that intrinsic passion kicks in...love it.

3) Some teachers think, "If I motivate students to learn with points now, they'll realize success and become internally motivated." If you believe this, how could you test this theory?

• If that's true, then we should be able to "wean" students off of points and grades...right? So over the course of the year, have fewer and fewer assignments worth points, and we should see performance remain at least level, if not improve. But it never feels that way (to me, at least). It always feels like we get trapped, and once you start giving points, you have to keep doing it.
• On the contrary, I actually think it's easier to start by *not* assuming things are graded. At the beginning of the year, students arrive eager to do well for the most part. That's when we can establish policies based on trust, on faith, and on mutual understanding (and the expectation that those three things will grow over the course of the year).

4) How effective are the use of points for students who are the least motivated and engaged? How might the use of points--the addition and subtraction throughout a student's day--affect those students' relationships with adults and their self-concept about whether school is "for" them?

• Imagine if your boss walked around and overtly deducted and attributed wages for individual tasks. It'd be demoralizing. Dehumanizing. It shows that you can't be trusted to "get the job done" on your own. Then, imagine you go look at your grades salaries posted on the wall in the back of the room...and you see that you're making the least. Would *you* be motivated by that? And even if they don't post grades salaries in the back of the room, your peers still talk about them. They still give out awards, and you and everyone knows that you're nowhere close to getting one of them.
• Maybe you're just at the wrong school job. So maybe you try another school. And imagine how terrible it must feel to see that they do the same thing. Makes you wonder what you're even going to work school for?