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.