Trying to find math inside everything else

Posts tagged ‘standards based grading’

The Spirit of the Rules

I just read the book One Man Guy by Michael Barakiva. (Pretty good, but has some problems). I wanted to share a scene from the book. (Emphasis mine.)

“Does that mean your absence last Friday, unlike your earlier absences this semester, was unexcused?” Mr. Weedin asked.

“It does,” Alek admitted.

“Mr. Khederian, you clearly have a strong grip on this material, and if you hadn’t cut, I would’ve considered recommending you for the Honor Track next year. But I’m afraid that I can’t go around making exceptions for students, regardless of how bright they appear.” Mr. Weedin’s picked up his paper and continued reading.

His teacher’s resolution almost made Alek give up. But he knew how important this was for his parents. And, he had to admit, for himself as well.

“Mr. Weedin, don’t you think failing me in a class when you think I’m capable of delivering Honor Track material is counterproductive?” Alek cleared his throat. ” ‘Let us once lose our oaths to find ourselves, / Or else we lose ourselves to keep our oaths.’ ”

“Is that Shakespeare?” Mr. Weedin asked, intrigued.

“Yeah, it’s from Love’s Labour’s Lost. I just wrote an essay comparing and contrasting that play to Romeo and Juliet in English, and that quote really stuck in my head.”

“Why?” Mr. Weeding leaned back and slid his glasses down so he could peer at Alek unobstructed.

“I guess I feel like we spend so much time trying to keep the promises we make, or the rules we set up, but it’s also important to look at those promises and rules and make sure they’re actually doing what we want them to do, and not the other way around.”

“Well, Mr. Khederian, you make a persuasive case.” Mr. Weedin tapped his pencil against his desk three times. “I’m not going to make it easy for you. For the remainder of this class, I’m going to double your homework load. If you complete it all satisfactorily, then I will reduce the penalty from failing to dropping your grade one full letter. So the highest grade you could receive would be a B.”

Alek had to stop himself from hugging Mr. Weeding. “Thank you, Mr. Weedin, thank you so, so much. I promise that I’ll do my best.”

“What is your best, I wonder?”

“I don’t know, Mr. Weeding, but I’m looking forward to finding out.”

“Me too, Alek.”

This was a major theme of the book and one I appreciated (it reminds me of Fiddler on the Roof in a way, especially the climax of the book). This isn’t the most moving scene but as this is ostensibly a teaching blog, I thought I would share it.

This seems especially relevant given the two articles I saw earlier today – one about the student who passed because of admin pressure even though she “deserved to fail” and the other about the student who passed because her teacher felt she should, despite her parents thinking she “deserved to fail.”

It’s interesting on its own to contrast the two articles. But now look at it through the lens of the quotation above. What does it mean to pass or fail a student, and why do we do it?  What is the goal of the grades that we give? Often teachers set rules in their classrooms, or grading policies, and stick to them rigidly, thinking that is what is right. But it is easy to lose sight of why we made these rules in the first place – because we want our students to be the best they can be. Most of the time those rules will help that happen – but sometimes they don’t, and so we need to be willing to change when that occurs. It is the spirit of the law that matters, so try not to get lost in the letter.

Rubrics for Standards

So my grading experiment has been going on for a month now, and so far I think it’s going well. But I was pretty stressed about getting it up and running, because a lot of the work was front-loaded. The thing I was particularly working to get done was my mega-rubric. I wanted to make a rubric that showed what exactly students needed to prove they understand to move up a level in a particular learning goal.

So here’s what I made (I call it the SPELS Book to go along with the students’ SPELS sheet):

I started by making the proficient categories, and for the first 8 (The Habits of Mind/Standards of Practice) it was pretty easy to scale them down to Novice, and then to add an additional high-level habit to become masters.

I was stuck, though, on the more Skill-Based Standards. I had all the things I wanted the students to show in each category, but how do I denote if they “sometimes” show me they can graph a linear equation? If I was doing quizzes all the time, like in the past, I could say something like “70% correct shows Apprentice levels.” But I wasn’t, and it seemed like a nightmare to keep track of across varying assignments.

So instead, my co-teacher had the idea that, if each topic had 4 sub-skills that I wanted them to know, we could rank them from easiest to hardest and just have that be the levels. So my system inadvertently became a binary SBG system, but still with the SBG and Level Up shell. Now if a student shows they understand a sub-skill, they level up. If they don’t, I write a comment on their assignment giving advice on what they should do in the future. What remains to be seen is how much they take me up on that advice. We’ll see.

Also, I’d LOVE any feedback you have on the rubric, and how I can improve it. Thanks!

Downloads

SPELS Book (pdf)

Updated Student Character Sheet (pdf)

Updated Student Character Sheet (pages)

Level Up! +1 to Exponents, +2 to Equations

Previously on The Roots of the Equation: You All Have “A”s, You All Have “0”s, and Grade Out of 10? This One Goes to 11.

I like games. All kinds of games: video, board, tabletop, role playing. And so I often think about how games and teaching align. One thing (good) games really do well is provide a sense of progress (especially role-playing games). You start off with not many skills, but as you advance you build them up, learn new things, and can conquer tougher tasks. By the time you reach the end of the game, those things that were hard from the beginning ain’t nothing to you now.

Games don’t usually score you on every little thing that you do. What they do is take a more holistic view and then, at some point, say that you’ve done enough to go up a level. And I say, why can’t I grade that way?

Many people have lamented that the best grading system would have no grades, just feedback that students respond to to improve their learning. But grades are required from external factors: school districts, colleges, parents, principals. But maybe there’s a way around that.

Last time, I said grades should just be a sum of the levels of the learning goals. So now I’m picturing students having a “character sheet” that looks something like this.

I maybe have created that name just so I could tell students to take out their SPELS sheet.

I maybe have created that name just so I could tell students to take out their SPELS sheet.

Student Character Sheet 2

The N/A/J/P/M are my current grading system, Novice –> Apprentice –> Journeyman –> Proficient –> Master

At the beginning of the year we can do a pre-assessment to determine their “starting stats and skills.” Then as the year moves in, we do our work in class. But none of that worked is graded in the usual sense. We would write feedback on the assignment, giving areas for improvement, but the only time a grade is mentioned is when a standard improves. Even then, we don’t focus on what they are (“You now have a 3 in Exponent Rules”), but rather in how they’ve grown (“You gained one level in Exponent Rules!”). The former just highlights that they are not the best they could be. The latter highlights their constant growth and improving.

(Then, at the end, based on what I said in the last post, their grade is literally how many boxes are shaded on the sheet. Have 75 boxes shaded? That’s a 75.)

In order to do this effectively, what we really need to have are rubrics for each standard. That way we know what counts as evidence of a certain level in a standard across all assignments, so it doesn’t matter which assignment provides the evidence. The upside to this is that you do not need to then have a rubric for each assignment! You only need your standards rubrics, because that is all you are using. (The collection of these rubrics, then, in the hands of the students, are a road map to success.)

I’m pretty excited by this idea, and can’t wait to try it next year. This is my idea from the last two posts taken to the next level, with a clear focus on growth, and not deficit. We can’t get rid of grading, and I’m not 100% convinced that we should. But we can definitely minimize the damage that it does and use it to actually promote students’ learning. All we need to do is focus on how we always get better.

Grade Them Out of 10? This One Goes to 11

Previously on The Roots of the Equation: You All Have “A”s, followed by You All Have “0”s.

I talked about how I currently grade (or, more specifically, how I tabulate grades) in my last post, but I don’t want to give the impression that I’m totally satisfied with the system. It was a great core idea, but is missing something.

When I first started student teaching, my mentor teacher’s school has just adopted a grading system called EASE (Equity and Access in Student Evaluation), essentially introducing me to SBG from the get-go, before I really knew what it was. Because the whole school used EASE (which had a 3-point scale: not yet proficient, proficient, and highly proficient), the report card could just display the list of standards and the proficiency level. But when it came time to send transcripts to colleges, they still needed to have final grades. So those were calculated based on the percentage of standards with a P or a HP.

However, you did not need to be highly proficient at every single standard in order to get a 100. That goal was achieved by earning HP for half the standards and P for the other half. But my current system (and possibly many SBG systems? Let me know) requires mastery of all learning goals for that A+. And that’s really hard to do! Why so we expect a student to be perfect at everything? No one is.

One way to deal with this is to weight mastery (5 on a 5-point scale) as worth more than it is. But that seems like a sloppy way of doing it. There must be something more elegant. And then I had the following thought:

Why average the standards, and then scale up to 100? Why not just add up the score? And then, if the problem is requiring all 5s to get to 100, why not just have more than 20 standards?

This requires thoughtful choices, but I think it has a lot of potential. Let’s walk through an example. Say I grade on a 5-point scale. If I have 20 standards, a 5 on each gets me a grade of 100. But what if I have 22 standards (sat, 8 standards of practice and 14 content)? Then someone who gets a 4 on every standard gets an 88, a B+. If then they turn half of those into 5s, that’s a 99, A+. Someone who has a 3 on everything, so some fatal flaw in all of their knowledge, but decent understanding, gets a 66, a D. This seems reasonable to me.

If you grade on a 4-point scale, you could have 28 standards. Unless your 4-point scale is 0-3 instead of 1-4, then you could have 40! The choice is yours exactly how you break it down. But I think the idea have potential. Am I totally off?

(To be clear, I’m not letting my grading system determine what standards I teach. I already break down complex standards and combine simple ones, until I find ones that fit my class best. Now I’m just having a target number of standards for that process.)

You All Have “A”s

So I was thinking about grading a little bit, and how grading works in my classroom. I tried to ask people about grading on Twitter, but perhaps the medium is not the best for talking about it, because only one person responded. (Thanks, @algebraniac.) I wanted to get a feel for how people out there calculated grades, before I wrote about it, but I figure, what the hell! Just write about it anyway! (Maybe channeling Hedge a little bit here.)

So, like, I’m imagining the typical first day of class that happens. The teacher tells all the students, “As of right now, you all have ‘A’s.” With the intention being, of course, encouragement, because despite how bad they might have done in that subject in the past, right now, they have an A.

But when you think about it a little more…it’s really kind of terrible, isn’t it? “Right now, you have an ‘A’…and the only way to go is down.” So then the grades don’t reward good work, they only penalize bad. Your grade tracks every mistake you make, every little fuck-up, dropping in a downward spiral. And we talk about students “slipping” and “dropping the ball” and “not doing as well as they used to.” The whole terminology is pretty terrible.

On the surface, it might seem like Standards-Based Grading can help with this, like it helps with so many others. Students have standards, and if they are low they reassess and go up. At the end of the marking period or term, that certainly seems like a good system. For each individual standard, it works, but as a collective whole? Let me ask you this:

It is halfway through the (quarter/marking period/term), so report card grades are not due for another few weeks. A student comes up to you and asks what their grade is. What do you tell them? What is it calculated from? And how will the future work they do affect that grade, if they do well? What about if they do poorly?

I’d really like to know. Drop a line in the comments and tell me. I’ll follow up with people’s responses and what I do in another post.