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.