Standards Based Grading 2011-2012

I gave my kids a google form to fill out with their thoughts on Standards Based Grading this year in calculus. My instinct is to interpret them for you before presenting them, but I’ll hold off. For context, I teach at an independent school where most kids are motivated to do well, partly because of internal motivation and partly because of grades for college. I teach the non-AP calculus course, which means I get a wide variety of students… from those who really really don’t like math but feel they need calculus on their transcripts to those who kinda like math (and maybe a few who really like math, but those are the exception). My calculus classes have on average 12 students in them. The students at my school do learn to speak up for themselves, so I think for the most part, the comments are probably fairly accurate representations of what they are thinking.

First, I asked what they felt about the grading system after the 1st quarter, and after the 3rd quarter. Then I asked about what they took away from it.

Then I asked for some numerical information on: how the grading philosophy worked, and if they collaborated outside of class more or less than other math classes. (Promoting a culture where I am not the sole authority in the classroom — and outside of the classroom — was important for me.)

Finally I asked for what they had to do differently in this class than in others, whether they think they would have done similarly if they had a traditional grading system, and what they think I should keep and what I should change.

And for some basic stats…

In the first quarter, I wrote 64 reassessments
In the second quarter, I wrote  54 reassessments
In the third quarter, I wrote  55 reassessments
In the fourth quarter, I wrote  40 reassessments

… and compared to last year, things went so so so much more smoothly logistically. Writing the reassessments didn’t take as long, I felt the work I was putting in was paying off.

In any case, I could analyze things, but I’ve already done that in my mind. My conclusion: although not perfect, this was a wildly successful year for Standards Based Grading in calculus.

PS. As I always say to the students on the disciplinary committee I run, “we do the best we can with what we have, and then we move on.”



  1. What did you think of this comment?

    Maybe be a bit easier on gradingwhen it comes to small errors. Itseemed like if I demonstrated aclear understanding of the topic,but made a small sign error orsomething similar, I still dropped toa 4 immediately. It seemed toslightly undermine a system whoseprimary goal was to ensure that weknew what we were doing.

    I had a number students complain about this to me too. I wonder what your thoughts are.

  2. You know, I got this comment last year also. I changed my grading system from 4 to 5, and I include a 4.5 for when a student makes a small error.

    But you know, I’m fine with it this year. I have the 4.5. Math is about precision, and it’s about knowing how to do the basics. Yes, students have to demonstrate a full understanding, and that includes precision.

    But the main argument I have is that many times students think what they did was a “small sign error or something similar.” I don’t know if that’s because a student had a misunderstanding (e.g. that the derivative of cos(x) is sin(x)) or because they forgot to include the sign. I do not give the benefit of the doubt. I tell my kids that they aren’t graded on their understanding, but their ability to demonstrate their understanding. If they make an error like add 2+3=4 and it doesn’t affect the outcome of the problem, I usually will give that a 4.5 (or sometimes a 5).

    My feeling is that if a student makes a sign error a couple times throughout the quarter and they get a slightly lower score, they’ll still end up with a solid A. And if it happens a lot, it’s more than “small errors” but indicates a larger issue.

    So yeah, I get where they are coming from. And since we break things up, it’s more noticeable for them than in a traditional grading structure. But I value precision. And heck, if it happens once or twice and they know the stuff, just reassess! (In my short experience with SBG, the kids who normally make this comment are not the kids for whom this happens rarely, but the kids for whom this happens a lot.)

    In other words, I know this is going to be a perennial comment from students, but I’m at peace with it.

    1. Yes, yes, yes. It is so difficult (especially if the student is hovering over you or if you have a lot to grade) to be 100% sure that they have made an arithmetic error vs a conceptual error that just looks like an arithmetic error.

      So many kids tell me that they are “bad at taking tests”—in my experience, that isn’t a very real ailment (and if it is, it cannot possibly apply to the number of kids who think it applies to them). What is really happening is that they don’t 100% understand the material, so they do poorly on tests even though they are working hard and feel like they get it. I think the half-point type thing that they’ve experienced forever in math class (I mean—taking off a half point or something for a sign problem or arithmetic problem, etc) really contributes heavily to that. The half point deduction very clearly means, “Don’t spend any more time trying to figure out what went wrong here. You made a silly mistake that I don’t expect you to keep making.” And yet, they keep and keep and keep making those mistakes.

      I would say that by the end of the year in my class (where poor arithmetic or algebra will keep them from getting a mastery score on any “I can solve problems…” objectives), my students are much more consistent in their math skills. And also I don’t have those students anymore who “really get it” but “can’t take tests well.” The mysterious ailment has disappeared!

      So anyway, yes. It is super annoying to not get the mastery grade when you think you’ve mastered it and made a silly mistake. If it really was a silly mistake, you’ll easily be able to do it correctly next time. If it wasn’t a silly mistake, then you’re welcome. I just made sure you actually learned this instead of thinking you learned it and failing later.

      And honestly, even if it was a silly mistake, you’re welcome, too. Let’s do things all the way right, not just mostly or sort of right. Especially when your final grade isn’t on the line.

      1. It is good to hear teachers other than engineering professors saying “let’s do things all the way right.” We’re tired of being the last ones insisting that correctness matters.

  3. any insight on the one kid that seemed to hate it? i had one of those this year (and he had a 60% in the class… but still didn’t do any reassessments) and i couldn’t figure out why he would be against it. i think he didn’t like it because of his bad grade, but without SBG, his grade would have been 60% too. so it didn’t affect him at all that other students were improving themselves, learning things and improving their grades. i didn’t understand his hostility (and this kid’s hostility too).

  4. I can’t talk about this year, because honestly I didn’t even know anyone hated it as I went along (I didn’t get hostility from anyone). I figured (as I always do) that some kids get tired of constantly reassessing because they either just don’t get things the first time or they aren’t learning things as we go because they figure they have an out… but that is always going to happen.

    But last year I had a few kids who were against it and didn’t do any of the reassessments without being forced to by their dean/parents/whoever. These kids happened to be the kids who were totally unprepared for calculus, and instead of stepping up and working through that (as some of the other unprepared kids did, who ended up doing so so so amazingly), they just gave up. *They weren’t willing to put in the effort. And SBG highlighted that fact about them. So I think they railed against the system.* (As opposed to a traditional class… they could do poorly and just say “the material is too hard” and not have the onus placed on them… they could blame the material…)

    That’s my conjecture, anyway.

    But this year I didn’t have those problems, and I think it was probably because those who were unprepared for calculus stepped up to the plate.

    At least those are my thoughts.

  5. Love the post. I also use the 0-5 grading system that includes the 4.5. How do you tally the total score for each skill? I often get complaints that a 1 and 4.5 tallies to a 5.5 which is still failing that particular skill. I am thinking of taking the most current grade and making that the overall skill grade. This seems to be fair to me. The only problem I can predict is procrastination. Will students not try during the first attempt at that skill? I wish I had a personal SBG consultant at my school who I could bounce the ideas off of! A few teachers have started to use it though which is good.

    1. I only take the most current grade (mainly because I don’t have time to retest skills in calculus because they are more involved … as opposed to something like Algebra I where solving a problem doesn’t take very long)

  6. Sam
    How do you feel about the kids who admit that they might not take assessments as seriously the first time around? Is this a problem with the grading system? I used to see situations where I would allow a lowest quiz score to drop from a grade and have kids routinely bomb the last quiz of a grading period because they knew there was a loophole. The situations aren’t quite the same, I know but it is something that worries me a bit. I dabbled this year and allowed/required retakes when grades were below a 70% but after a while I became frustrated that the same kids were falling into a reassessment rut and I wonder whether they would have stepped up a bit more seriously the first time around without that safety net.

    1. There are two issues here.

      1. Hopefully SBG will show students that always reassessing is annoying… and through that and conversations conmigo, they might recognize and fix the follies of their ways. This works to some degree.

      2. The bigger issue (for me) is that doing SBG while kids are taking traditionally graded classes, SBG is easier for kids to put on the backburner. Because when it’s the night before a calculus assessment and a Spanish test, and it’s 11pm, kids are going to focus on Spanish. And you know what, I don’t blame them. It’s human nature. I don’t have a good way of dealing with this, except in the first semester to talk about it a lot. Talk about making good decisions, and learning from poor decisions. Talk with them about not using SBG as a pair of crutches but instead as a safety net. Talk to them about how SBG can show them how to learn better, and be independent, and organize themselves — so that when they don’t have someone checking their homework each night (a la college, when homework usually takes a different form and doesn’t get checked) that they can do it, and do it well. But yeah, honestly, as much as I like to think of my calc classes as a bastion of learning without the total stress of grades, the fact is I am in a sea of traditionally graded classes, and I will always lose in the short run. But I think in the long run, I think I win.

  7. Is your grading scale 100% SBG? Or is there any “one and done” parts of their grades? Do you think adding in some percentage of the grade as a “one and done” part will help solve some of the problems? A sort of hybrid system? I know the very premise of “one and done” goes against the very foundation of SBG, but perhaps splitting the difference between the two in a hybrid system might alleviate some problems. Just thinking about things for some changes to my own Calc class next year…

    1. For three quarters, I had 20% of their grade based on a problem set, or a poster project. But I don’t actually think I had many problems :) Almost none, actually, this year. So I hope next year I’m just tweaking.

      I can see doing projects/problemsets and having them be “one and done” but other than that, I’m fine. I see the advantages of a hybrid system, but as you said, it goes against the foundation of SBG. And I am not willing to give that up. It’s what I think has made my calc class so much more fun/interesting/relaxing… and we’re learning more.

  8. Hi, I’m curious about your grading structure. Do you explain your standards based system in another email? (And if not, would you be willing to explain it to me :)) I’d like to tweak how I grade my non-AP calc class next year, and I’m very interested in learning more about what other calc teachers are trying out!

    1. There’s a whole lot of information about Standards Based Grading (SBG) here: (use the links on the right to navigate). I’m definitely not the only one doing this…

      I have a bunch of blogposts about standards based grading, starting 2 years ago, but I don’t have them tagged. A search on my blog for “SBG” or “Standards Based Grading” would probably give you what you need.

  9. Sam,
    I’ve followed your blog and used some of your ideas. Thanks!

    For “one and done”, I do that with Lab work write-ups– I explain to students that the logistics of re-doing or re-assessing a lab are quite different than for a quiz or test. Also, students are given sufficient time (up to a week) to complete a lab write-up, with the option of having me review it beforehand, time to ask questions, etc. So, if they choose to throw it together at the last minute and not take advantage of my “pre-assessments”, well, then, that’s on them.

    Does it go against the philosophy of SBG? Yes and no…. they have the opportunity to “formatively” assess their work with me before the final lab write up is due. And, as I said earlier, the logistics of re-doing a lab can be quite cumbersome. I suppose I could re-quiz them after their failed write-up, but I haven’t gone there yet.

    My SBG system isn’t perfect, and they don’t get to re-assess on a midterm or final exam, either. Still, flaws and all, I think that SBG is a more accurate reflection of their learning, and it puts the responsibility where it belongs — on the student. And I wouldn’t want go back to traditional grading.

  10. Sam,
    I am heading into my 3rd year of SBG. Very refreshing I must say. For some reason, I am thinking of checking hw again and incorporating it into their grade somehow. This goes against everything that SBG is. I guess I am just trying to get these students who struggle on their skills to practice their skills ahead of time. I also agree with you that I “lose out” to traditionally graded classes. When I used to check HW in traditional class, it was often incomplete, copied, and not a help at all. In fact, I think in most cases it was counterproductive. Thanks for all your insights. I will admit that you, Kate, Dan invigorated my teaching career 3 years ago.

    1. I don’t know if this helps, but what I do is check the HW, but I don’t grade it. But, I do record it on our computer grading system (as “ungraded”) so students, parents, and I can see a record of HW completion. It’s on the record, but doesn’t average into the grade.

      I find this more effective with my 9th graders — they don’t completely get that I’m just checking it, not grading it. So, they have more concern. My 11th and 12th graders will either do the HW or not, but when a parent calls wringing their hands about why their kid isn’t doing well, I point to the HW record — there is a definite correlation of not doing HW and not doing well in the class. I also point out that if I had actually given grades (zeroes) for HW, the grade would be even worse.

      I do occasionally have a student who is bright enough to do well without doing the HW, but they are rare.

      My first year of SBG, I did make HW a “standard” part-way through the year, when I saw that HW wasn’t getting done. I can’t say that I liked it, but that is one possible answer.

      And, a silly thing I do with my upperclassmen — a HW form that they get a stamp or sticker on when they demonstrate completed HW. I know it sounds stupid, but I have had students say that they completed HW to get a stamp! When the HW form is filled, I give a little reward (like making oreo truffles, or something). Yeah, I know…

      Having said all of that, for myself, I need to improve my formative assessments to be more than just a quiz here and there. Implementing SBG was a big task, and formative assessments, for me, need to be improved. Work in progress…

      1. Nancy,
        That makes a lot of sense about the HW….I’ve been delaying deciding what to do, but I have 2 really good choice now. I’m leaning towards just checking and having a record for parents but the “HW standard” is intriguing as well. How did that go? Which were you happier with? This is year 3 of SBG for me and really the only problem I have is when I see students struggling but not doing any of the daily practice that I think would benefit them. I feel they are more apt to skip my HW due to the fact they do their “traditionally” graded HW from other classes. Thanks for the insight.

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