Grading for Equity: Reflection Questions (Ch 14 + Epilogue)

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 14: Putting it All Together and...

Epilogue

Initial Reactions:

• If you wanna go fast, go alone. If you wanna go far, go together. I'm very glad that my school is already on board with a ton of this stuff. The tradeoff is that there is limited capacity for teachers to diverge from this shared set of practices. I am very glad that some colleagues and I read this book together, and will meet to discuss it over the course of the year.
• Be patient. There are some smaller adjustments I'll be able to make this year. There are a bunch of bigger, more complicated adjustments that I'll have to spend the next year planning for, to be enacted next year. That's just how it goes. I need to make sure I remain patient with myself and my work.

Questions to Consider

Note: I'm going to paraphrase questions, because as we get further and further into the book, Feldman seems to make the questions longer, more loaded, and kind of embed the "suggested answers" into the follow up questions. So for each of these there's more to the question in the book, but this is the big idea. Also, the rest of the questions are poised "For Teachers," as opposed to the non-teachers who were also invited to read the book.

1) Which equitable practice will you try first? How will you know whether it was successful?

• Practice Tasks, for Algebra I
• I will try to pilot a new grade weighting, with 100% Performance Tasks and 0% Practice tasks
• If that doesn't work, I'll see if I can swing not having any graded practice tasks at all
• If that doesn't work, I'll try to have "bigger projects" as practice tasks, and have them be approximately as frequent as quizzes (which I talked about here)
• I will grade important "Practice Tasks" will be graded 50-100, and they will be graded on completion/accuracy. I will give either 50 (incomplete), 75 (mostly complete), or 100 (fully complete), based on accuracy/completion. The vision I am grading "towards" is that I want practice grades to be highly predictive of performance grades
• I will create disaggregate/track practice tasks by standard, so that students will be able to see compare their performance and practice w/ respect to individual standards (which I talked about here)
• I will aim for scoring Practice Tasks 1-2 per week per standard. But it feels like it's important for there to be multiple practice items graded before. (I'm still not confident that this is the best policy.)
• Other Algebra I
• I will run a "practice quiz" for our first assessment, which will include peer scoring (which I talked about here)
• I will run a "quiz bonanza" at the end of every quarter (which I talked about here)
• Performance Tasks, for Discrete Math
• I will create a rubric for assessing performance tasks. This will be a pilot/experiment in developing a rubric/continuum for practice-oriented competency-based math assessment. I'll start with this (which I've used in the past), and work from there.
• Big picture questions 
• These are some bigger picture question I have about how my school does grading, and I need to dive into them more deeply with my colleagues
• Minimum grading school-wide
• How to handle the "max" vs. "avg of top 2" vs. "two 4's > one 4"
• I'd like to work with the rest of the math team to actually develop a robust "rubric" or at least "criteria for success" for each of the Algebra I standards

2) As you try these practices, how will you apply a growth mindset and an embrace of mistakes to your own learning?

• I'm not worried!

3) Will you let students know about the new grading practices you are trying and why? Why and how?

• Fortunately, I just teach 9th graders, so this will be a lot easier. My goal is to discuss how grading works as each element of it comes up. (Talk about quizzes before the first quiz, talk about how retakes work when the first retake happens, etc.)

4) What would a partnership with students to make grading more equitable look like?

• I would like to give a quick survey at two points about 1/3rd and 2/3rds of the way through the school year, asking students to share how they feel about how grades work in our class. Specifically, w/ respect to the principles (fair, accurate, etc.)
• I also will plan on having "soft discussions" about grading, how it's gone for them, and how it is my intent to help grades *not* be as oppressive as they've likely experienced at times in the past (which I talked about here).

Grading for Equity: Reflection Questions (Ch 12 + Ch 13)

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 12: Practices That Lift the Veil and...

Chapter 13: Practices That Build "Soft Skills" Without Including Them in the Grade

Initial Reactions:

• Time maximization. Time maximization is a soft skill that Feldman mentions. When I hear "time maximization," I think of the times in my life where I was the most exhausted, most depleted, most exploited, and least "whole." Which isn't good. I connect it to what I have come to understand as an element of White supremacy culture, the "omnipresent sense of urgency." I have also come to conceptually group it with toxic features of capitalism like "time = money," glorifying profit maximization, grind culture. And [insert anti-capitalist rant].
• All of that said, I do think there are meaningful, important, humanizing applications of "time maximization." I also recognize that deconstructing capitalism has to be more complicated than just ignoring the reality of its toxic presence. As such, I think I generally need to do some learning around this topic, to understand how better to work with this idea, which is concurrently toxic and valuable.
• Peer assessment. I haven't done a lot of peer assessment. At my currently level of understanding, I do recognize it's value for building student understanding of the assessment process in general, facilitating student-student discourse, and building a culture of feedback.
• But it also runs counter to a value I have that student work is deeply private. Over time, I have slowly become more aware of the way that I have that value based on a general feeling of insecurity in my own work as a student. And that insecurity is itself rooted in an unhealthy relationship with competition in identity and the learning process that I have cultivated as a result of my own context, identity, and educational journey. I think I also have a lot to learn and reflect on here.
• Concerning this topic, there was a passage from Mcfarlane-Dick (2006), where it identifies one of the values of peer evaluation: "...by commenting on the work of peers, students develop detachment of judgement (about work in relation to standards) which is transferred to the assessment of their own work (e.g., 'I didn't do that either')." I had a really hard time making sense of this point, and how it connects to peer assessment.
• Adults as exclusive prophesizers of "the real world". Feldman talks a bunch about the negative impact of teachers citing "the real world" in defense of oppressive grading practices. And it's a *great* section--very relevant, and very insightful. There is another important point that he didn't make, or at least not in the way that I would have made it. I think that many adults often cite "the real world" as justification for their practices because it feels like a "trump card," because as children, students supposedly can't argue against it, because they're children who are almost by definition inexperienced in "the real world." In this way, it becomes a tool of ageism, used by adults to oppress children.

Questions to Consider

Note: I'm going to start to paraphrase questions, because as we get further and further into the book, Feldman seems to make the questions longer, more loaded, and kind of embed the "suggested answers" into the follow up questions. So for each of these there's more to the question in the book, but this is the big idea.

1) Think about your professional career. How have your supervisors made the evaluation of your work transparent, or opaque?  (Ch 12)

• At it's best, the evaluation process in my so-far-short career was based on a strong mentoring-grounded relationship between my evaluator and me. Very early on, my evaluator and I discussed the unfortunate reality of most teacher evaluation models. We both agreed that the process recommended by our district was primarily combination of bureaucracy and liability protection. But discussing this openly, we came to develop a partnership that was grounded in us bringing in actual lived experiences as they arose, processing them together, and problem solving from there. Importantly, the pace and content of my evaluation was largely set by me, with additions from my evaluator as they sought fit.
• By allowing me to set the pace and content of my evaluation and mentorship, my evaluator placed upon me the responsibility and opportunity of making sense of my evaluation. If I'm the one dictating it, I must fundamentally have a clearer understanding of where it's going, and why.
• It is very possible that my evaluator took a much more active, if subtle role in directing my professional growth. They often provided direction for my development by suggesting additional projects, or external opportunities I could take advantage of. In this way, they were able to direct my development by nudging me towards a series what were essentially "project-based learning" opportunities.
• At its worst, the evaluation is a process of my evaluator and I going through what is essentially a "checklist" of "important things to do." This list (usually some version of the Danielson Framework) isn't necessarily wrong--I think most teachers look at it and think, "Yeah, these are all good things you should be doing." So in that sense, it does provide a mediumly useful tasklist, I suppose. However, the process is devoid of any sense of me establishing a "vision" for my development and instruction, and assessing myself with respect to that vision.
• And that's something I think is generally missing from evaluation and growth--visioning. I think there is little value in practicing a deeply contextual practice (goal-setting) devoid of the actual context (a context-rich understanding of what we want our future to be).

2) For Teachers: Draft a rubric for an upcoming assessment or select one you've already created and assess it against the "rubric for rubrics" at www.gradingforequity.org. What are ways that your rubric could be more transparent and equitable? (Ch 12)

• I'm going to spend some more time later this summer developing a rubric for my Discrete Math elective this year. I will be sure to share them, and link them here once I have.
• I think that developing rubrics is something I have done very very little of in the past. I very much have gone by the "I know it when I see it" assessment of student understanding. Feldman does a good job of outlining why this is inadequate, and is one of the places where I appreciate the way it feels like this book was written by someone who is pretty intimately aware of the lived teacher experience.
• One issue/question I have about rubrics is that they tend to place "skills" and "knowledge" in a hierarchy, with largely discrete and distinct "threads". But from an epistemological perspective, that reveals an assumption we have about how knowledge is constructed, and what it means to know something. I think that knowledge, skills, and dispositions (in math, and in general) are far more nebulous, interconnected, and often unobservant of our efforts to apply overly-simplistic hierarchical models. I've recently become interested in the difference between thinking of knowledge as rhizomatic or arborescent. But this feels like one of those situations where "all models are wrong, but some are useful" (credit to Dan Meyer for that saying). So I need to reflect more on how rubrics can/should (not) observe those different definitions of the structures of "knowledge."

3) For Teachers: This chapter has suggested that teachers need to be the creator of rubrics, but could students create them?  (Ch 12)

• This is actually super cool, and Feldman describes an introductory "constructivist" approach. Start by identifying the objective, and work with students to backwards-engineer a rubric against which to measure our performance. I think this can be valuable because:
• It builds student understanding of rubrics more broadly, which is good for "lifting the veil" on how they're being assessed, which is a move in the direction of equity
• It gives students an intimate understanding of whichever rubric they developed
• It allows me to calibrate my own understanding of what I have messaged is "important." If I have been teaching kids about how to graph a line from a linear equation, and all they do is talk about the components of a procedure to do the task, that's a sign that I must have emphasized that procedure in my instruction.
• It also deepens student content knowledge of whatever we're making a rubric about. They have to be able to verbalize knowledge, organize it, and negotiate the relative value of different parts of it.
• Building on that last point, it also provides students an opportunity to wrestle with the very big question of "How do you know that you know something?" It positions "knowing" as a fundamentally subjective, negotiable, and non-fixed thing, which is a healthier relationship to have with "knowing" than the assumption that some authority figure (teacher, politician, boss, etc.) has the authority (and even ability) to define truths and meaning objectively.

4) Do you believe each soft skill has an equal impact on a student's academic performance, or do some soft skills have more impact than others? (Ch 13)

• Different skills certainly must have different values and weights. And those things certainly vary depending on the context of the student, the teacher, and the assignment. Some deadlines matter, some don't. Sometimes it's important that you're "polite," others, it doesn't (and sometimes it's important to be actively not "polite").

5) How student-specific is the connection between any given soft skill and an academic performance? What are the implications of this? (Ch 13)

• I think generally, one value of not attaching abstract grades to performance on "soft skills" is that our valuation is allowed to expand or contract in context. For some students, it really *doesn't matter* if they do the homework. Some students are able to "get the job done" with or without the extra practice. But if I directly grade-penalize all students who don't turn in the homework, I'm telling the student, "Hey, that observable part of your human-ness that allows you to perform with less practice than average? I don't care about it, it's not valuable, and I wish you would be more like what *I* expect you to be like." Not a good look.

6) For Teachers: How might you pilot "student-led grade conferences" in your classroom for a specific project or performance? (Ch 13)

• I think that my school tries to emphasize the degree to which conferences are student-led, at least at times. I do love it when students come to teacher-family grade conferences. I like opening by asking students to start the meeting with how they things things are going. I like it because it increases the degree to which students need to reflect, and understand on their own how they're doing. I also like providing students with the chance to demonstrate their own self-understanding and capability. They also have a ton of perspective that I don't have, because they're the subject themselves. But students don't always come to their own conferences, and I understand that there are lots of reasons why, and a lot of them are legit.
• But I rarely do more than say, "It's good if you come to your own conference, because that allows you to have a bigger role in directing the narrative that's built around you." But just unpaching that statement is non-trivial. And understanding how to "control the narrative" is also a non-trivial set of skills and understandings.
• In order to support students in the leading of their own conferences, in the class before teacher-family grade conferences, I could lead students in doing some like preparation for the conferences. I could help them go over their grades, overall performance, and recent and long-term changes in it.
• One of the most impactful "soft skills" I've learned in my profession is, "The person who best prepares for the meeting, wins the meeting." Or in less problematic, conflict-oriented language, "If you prepare for the meeting properly, you're more likely to get your agenda met." And that is certainly a "soft skill" worth surfacing for students, as it can empower them long-term.

Plan To Do

• My school does use "Next Gen Standards" as a way of standardizing, and attaching a grade value, to soft skills. I haven't used or analyzed them yet. For reasons outlined in the book, I don't actually want to attach those standards to students' official grades, and would ideally track them as "practice standards" which are tracked, but with 0% grade weight.
• I'd like to at least start with the Next Gen standards, and go from there, since they already exist, other teachers and students are already familiar with them, and this is a pretty unfamiliar landscape for me. Starting with those, I need to generally reflect on the "soft skills" I care about, and think through how I want to surface them in the class. Lots of work to do here. Once I know what, and why, I can then start to ask, "How will I assess these?"

Grading For Equity: Reflection Questions (Ch 11)

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 11: Practices That Support Hope and a Growth Mindset

Initial Reactions:

• Public Reflection vs. Virtue Signalling or Unsolicited Peer Advice. This is less a reflection on this particular chapter. It's more of a meta-reflection on this book study reflection series, and general reflections made public by blogging or tweeting.
• There have been so many moments where I have had to stop myself from taking a point in the book that I already agree with and understand, and expounding upon it here. I believe that that instinct I have in that moment is more about me trying to virtue signal, or provide unsolicited advice to other teachers, neither of which are particularly helpful for anyone, myself included. 
• Like, if I'm not so clear on the topic, or need to figure out how to clearly articulate my thinking, sure, writing and reflecting on it can help me to clarify things for myself. But if I'm already pretty clear on my thinking, or my position, that particular thought process can remain internal!
• Max vs. Most Recent vs. Most Accurate. Given multiple performance assessments on a single standard, I need to find a way to deduce a single, accurate, number to represent the student's level of understanding. We've talked about why measures of "center" aren't great. In general, Feldman seems to advocate for a "most recent" metric. Though Feldman does mention how "most recent" isn't necessarily the "most accurate." That being the case, teachers might have to determine the "most accurate" score, while adding the caveat that any hard-fast rule will always result in some inequity for some students. I'll admit, it always feels like he gets a little..."hand-wavey" in this parts. This certainly doesn't feel bias-resistant. I wish Feldman discussed this issue more (hopefully it comes up in one of the later chapters).
• In general, even though Feldman doesn't bring it up, I think I want to stick with a "max score" metric, if only because it very much reduces performance anxiety, which is huge for me, and for many of my students for sure. I think I'm willing to complicate it a little bit, which I'll discuss below, but I *do* believe that the Max metric is best. That's also generally how my school handles the competency-based grading in all the other classes anyways, so there's value in being aligned in that respect as well.
• "Exceeding Standards." Feldman advocates for a 0-4 scale, that roughly looks like this:
• Exceeding Standards = 4 (roughly translates to an A)
• Meeting Standards = 3 (~B)
• Approaching Standards = 2 (~C)
• Not Yet Met Standards = 1 (~D)
• Insufficient Evidence = / (formerly an F)
• Getting rid of the letters (A-F) is helpful in the day-to-day because it's an attempt to divorce assessment from the world of problematic expectations that students may have about what certain grades imply. To take it one step even further, he advocates for replacing the numbers (0-4) with descriptors (Exceeding, Meeting, Approaching, Not Yet, Insufficient), which are actually more indicative of the level of student understanding. The numbers and letters then only exist for the purpose of allowing us to patch our data into the traditional grading system we will likely have to observe when reporting grades to the district at the end of each marking period. This is mostly great, because my school is generally down to get rid of the A-F denominations, and/but has fully committed to the numerical scale, for other reasons that also make sense.
• The thing that I'm not sure I totally agree with is the distinction between "meeting standards" and "exceeding standards." What does it *actually* mean to "exceed" the standard? Because here's how my school and I have come to understand my version of the 0-4 scale:

• Isn't the big goal to "meet the standard"? Or in other words, we should "set the bar" at "they can do the thing"? We can debate the definition of "proficiency" or "mastery" for sure. But I think that "proficient" = "meeting standards," and both of those mean that the student can definitely demonstrate a thorough understanding of the objective.
• The biggest caveat here is that I also generally agree that "total proficiency," something I've called "mastery" in the past, can't be sufficiently assessed in a single moment. We want to require multiple independent assessments, so that we can make sure that the student understood the objective more broadly, and didn't just "luckily" understand that one instance of the objective. We may also only want to say a student is "proficient" if they have demonstrated a "time-durable" understanding, which would also require at least a second assessment at a later date.
• In the past I've said that 4 = "proficiency" and 4.3 = "mastery", and the only way to get a 4.3 was to get a 4 on at least two separate occasions. I think that requiring two 4's before they can get a 5 is a slightly bigger jump than I'm willing to give. Because if our scale is a linear model, then that would imply that one 5 equals two 4's, which is 25% better than one 4. And I'm *not* sure that I agree with that? Also, the greater the grade impact of one 4 vs. two 4's, the more important it is that I provide at least like...4 separate meaningful assessment opportunities for each standard. And I usually only end up averaging ~3 in-class assessment opportunities, and even that is tough sometimes.
• This past year, we tried to do this by saying that a student's grade on that standard was the average of their top two grades for it. That way we didn't have to give anything higher than a 4, but students were still numerically incentivized to perform on multiple occasions. And if we're expecting students to hit an assessment 3, 4, 5+ times, students can definitely need a mathematical incentive to keep trying.
• An interesting implication of this metric is that your grade can *almost* never go down upon reassessment. It *can* go down if a student does worse on the 2nd assessment than the 1st. Once there are two entries in the gradebook, only then does a grade become non-decreasing.
• That said, this book has gone into pretty thorough analysis against this position, saying that just such a mechanism complicates/veils the grading system (which is bad) and relies on leveraging grades as commodity/incentive for behavior (which is bad). And I'm inclined to agree? IDK. At "my peak", I stuck with the 4 + 4 = 4.3 thing, and never had a student complain about an assessment, or skip it, because they already had a 4. Students just get used to taking whatever assessment is put in front of them, and doing as well on it as they can. Which I think is the best situation?
• I *do* think there's a difference between
• A: "we need multiple, independent demonstrations of proficiency before we give you the highest possible demarcation"
• B: "we need to give students a reason to keep trying on assessments, and preparing for them, and so we need to leverage grades to create an incentive to do so"
• The differences are more philosophical than anything, but that impacts how we talk to students about it, and how they experience it. Because if students receive the messaging of option (A), I can foresee students experiencing it like "we're moving the goalposts in order to keep you busy." Which does sound pretty disrespectful, I think.

Questions to Consider

1) When in your professional life have you been given a "redo"? Who offered it to you, and why do you think you got that second chance? What did it feel like to receive it? What happened before and during your second chance? How did it benefit you? Was there a time when you were asked to demonstrate competence and weren't given a second chance? Why weren't you given that chance? Did you ask for it, or believe that you could?

• I'm all for retakes, no problem. I generally have the policy of "no more than one retake of one standard on any day" (not including regularly scheduled in-class retakes). But this is more of a constraint I put in place in order to prevent students from trying to knock out a million retakes on the last day of the quarter.
• I also don't have a "retake procedure" in order to ensure that students go through some re-learning process before re-taking. But I think that limiting retakes pushes students to be a little more careful in their retaking, and put a little more thought into preparing, as opposed to just blasting through retake after retake, hoping to get lucky.

2) For Teacher: How much of a motivator is hope? How much do you notice a change in students behavior and motivation, particularly among lower-performing students, before the first assessment of the term compared to after they have received the scores of that first assessment? At the beginning of the term versus after the first progress report or report card (when they receive their first formal low grade)? How could offering redemption via retakes, weighing more recent performance, minimum grading, or 0-4 scales throughout the term affect motivation?

• A major motivator! I feel pretty good about what I think this question is trying to get across, so I'm gonna skip this one?

3) For Teachers: How would the commitment to mandatory retakes align or conflict with your school's vision? What would have to change for your classroom or your school to commit to mandatory retakes? What would make it difficult? What could your school do to make it easier to make retakes mandatory?

• My school is big on re-assessment. They generally encourage spiraling back on older content, re-teaching, and providing multiple assessments on the same standard over the course of the year. And that's fundamentally mandatory retakes for all students (including those who already demonstrated "full" understanding).
• I think that anything's fair game, except it does get dicey when it comes to requiring students to spend time with me outside of regular school hours. I [insert anti-capitalist rant] so I don't like placing expectations for students time spent on my class, outside of my class.
• A fun one I've done in the past is a "quiz bonanza" where students go through and figure out which standards they need to retake the most, they spend some time studying for it, perhaps together, and then we end the class with everyone doing their retake. I don't do it that often, but the more I think about it, the more I want to do it more often.

Plan To Do

• Grading "practice"? I will probably write about this in every single post, because it's super unresolved in general, and I don't think the book will ultimately resolve it. But...if up to 50% of my students' grades are going to be "practice" assignments, how can/should I grade them? This came up again in this chapter, but from the perspective of hope/motivation.
• I technically don't want to grade on anything but demonstrated understanding of the objective (i.e., accuracy). But I honestly don't even want to grade on that, because these are *practice* assignments, and I don't want students to feel *any* grade risk from making mistakes in the normal course of learning.
• First quiz as a practice run. The first time I do a quiz this fall, I want to make the first one like a "practice quiz." This is because I want to remain sensitive to the fact that not many students may not taken an in-building quiz in literally over a year. Also, the way assessment and performance tasks in my class and building are likely pretty different from their previous schools.
• So after the first few weeks, when it's time to give the first quiz, I'm going to make it like a practice quiz. It'll look like a regular quiz, and maybe I'll "grade" it like a regular quiz. But it won't count as an actual performance assessment. That way they can get familiar with the quiz format, both as a task, but as a routine.
• In an effort to minimize how triggering it might be, I will make sure that in the lead up to the practice quiz, I am very clear that it is just a practice quiz. I usually only dedicate 25-30 minutes for a quiz, but am expecting to dedicate a full 75 mins on this first practice quiz.
• Part 0: in the week/days leading up to the quiz, tell them what it's going to be like.
• Part 1: As a intro to class on the day of the quiz, students talk about their experiences with quizzes, maybe writing individually first, and then sharing after.
• Part 2: I talk them through what the quiz is going to look like, and how it's going to go.
• Part 3: They take the quiz individually, with like...10-15 minutes on their own.
• Part 4: I "open it up" and they can collaborate on the quiz with other people at their table, sharing answers, strategies, sharing what they did that was helpful/right. I'll make sure to note that this is just a one-time thing, and not how quizzes will usually go.
• Part 5: I grab a couple quizzes where someone did something interesting or useful, and I throw it under the document camera, and surface it for the whole class. Things I could surface include:
• Annotations, writing questions to themselves, providing partial answers when the full answer eludes them...what else?
• I could also use this opportunity to talk about important parts of the quiz that really only make sense after trying it out. Things like the way I title quizzes (there is a system that is useful to understand, though I've never explicitly taught it to students).
• Part 6 (maybe?): They swap quizzes, and we kind of grade it together. In doing so, I show them how I think about grading quizzes, and how I assign grades.
• I think it's important that students had the chance to collaborate before swapping work. That way if a student was lost in the individual phase, they've got a chance to recover during the collaborative phase. We're going to be projecting non-anonymized student work on a performance task, which I usually keep as a pretty private thing.
• Part 7: the next day/week, we do the real quiz for real.
• I can actually combine this with the "Quiz Bonanza" I mentioned earlier, as a way to similarly model what a good retake process could look like. I would definitely want to do one early in the year, so students can experience how productive a thoughtful retake can be. But also do it a few times throughout the year, in order to minimize the extent to which students would need to come in outside of class time.

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.