I’m jumping into the SBG waters! Hope there aren’t any sharks!

Guess what, ma? It’s taken me half a year of mulling, some cajoling from the “inspiring ideological cult”, and the realization that even though I think I’m teaching responsibility, I could be doing way better. So here I am, naked, standing before you… wait, no, that’s not right at all. I have clothes on. Scout’s honor.

Here I am, standing before you, newly self-inducted member of the Standards Based Grading (SBG) cult.

I can’t roll it out for Algebra II next year, but I am plunging — head first — into standard based grading in Calculus.

I made a list of skills that I taught last year — maybe it’ll be of some use to someone out there:

This ordering and skill set probably won’t be changing much for the upcoming year. But it will definitely have to be rewritten for the SBG skill/topic list.

I wasn’t going to blog about my SBG system until it was done, but someone (forgive me, for my mind is weak, and I have forgotten who) mentioned that it might be useful to watch the process unfold. Plus, I have a bunch of questions.

Here’s what I’ve definitely figured out:

1. I am going to assess most skills/topics twice.

2. The skills/topics I won’t assess twice are mainly “explain this idea, statement, or claim (using words, diagrams, tables, graphs)” questions. (Students can reassess those questions on their own, if they want.)

3. Students will have to email me by Sunday night to be able to reassess during study hall on Tuesday, and students will have to email me by Wednesday night to be able to reassess during study hall on Friday. This way I have time to prepare for these individualized reassessments, and students won’t have to individually work on tracking me down.

4. I am not going to be including homework in their final grade.

5. Students keep a binder with all their assessments in it — so students can have them to study from, and I can ask them to see them if I need to.

Here are where I still have to make decisions:

1. Do I want my gradebook to have skills listed, or topics listed? This is a big one! David Cox says this is a false dichotomy, and I can buy that — because skills and topics are really part of the same tangled net. Or two sides of the same coin. Or some other cliched metaphor. But I guess I still think in these different terms. A list of skills, and a list of topics, seems very different to me. Skills tend to be more specific, while topics tend to be more “umbrella”-y. I am leaning towards skills, because that’s where I’m comfortable.

2. Do I want a bunch of short assessments given frequently, or regular (longer) assessments? I think I’m going to go with the shorter assessments, even though it is going to be harder for me to do because I usually have a plethora of students (read: more than 50%) with extended time. I have to figure out a way to not spend too much class time on these assessments.

3. When I give assessments, I might have a few problems testing various cases of something. For example, I might put four problems asking for the limit of rational functions at infinity. Or eight derivative problems asking to apply various skills (e.g. product, quotient, sum, difference). How do I combine these multiple problems into one score? I’m leaning towards a holistic approach, using the rubric, and a lot of feedback.

4. Do I require students to demonstrate/explain to me what they have done to fix gaps in their understanding, in order to be able to reassess? Would setting up the expectation that they need to have done something before they reassess, and then having a place on the reassessment for them to write what they’ve done to fix gaps in their knowledge, be enough?

5. A student’s grade on a topic/skill will either be the average of the last two scores they earned, or the average of the top two of the last three attempts. I’m leaning towards average of the last two scores they earned.

6. Do I allow myself to throw “old” skills on assessments? Like, if students are taking an assessment on derivatives, and I throw on a limit question, is that kosher? This rubs me the wrong way. When I did this in Algebra II in previous years, I told my kids I when I would be including older skills, and I would give them a general idea of what the problem would be on (e.g. absolute value equations and inequalities).  Does that seem like a fair compromise, or is that spoon-feeding too much? I am leaning towards including older material, but with a general warning. It just rubs me as being fair and clear. And I do want students to know that retention is important.

7. Should some skills/topics be worth more than others? I’m thinking of making almost all skills/topics worth 5 points, but I think I might highlight a few and make them worth 10 points. Specifically, I’m considering something like: “Apply the sum, difference, product, and quotient rules for derivatives.” Alternatively, I can break it into two 5 point skills, making one “Apply the sum, difference, product, and quotient rules for derivatives of basic functions” and “Apply the sum, difference, product, and quotient rules for derivatives of more complex functions.”

8. Even though I am not including homework in a grade, I do want students to keep their homework organized someplace, so we can refer to it together. I want it to be powerful — when a student doesn’t do well on a skill, and then we can look it up. If they haven’t done the problems, it will be clear what they need to do to improve. If they have, we can use that as a starting point for a discussion of why they didn’t do so well. So how do I get them to keep their homework, and keep it organized?

So there is where I am. Providing any and all advice and thoughts in the comments would be SUPER welcome!




  1. Welcome to the Borg. I’m going to multiple post this over the next couple of days. As always, just my opinion.

    1. Topics. But you know I’m an advocate for that. Assess the whole game, feedback on the parts.

    2. I prefer shorter because that way we can move on to doing something immediately after. Quick assessment, do something the rest of the period to remediate your weaknesses.

    3. You’re going to need a simpler example. My brain just passed gas. I defer to Cox or Cornally on this one.

    4. You know your kids best. I have them keep a log with specific learning goal on one side, plan to remediate, and evidence of completion. Evidence is loosely defined though.

    More later….

  2. re: #3, i think you should just put one question per topic per small assessment. i know it’s hard to do this, but realize that you are going to put the same topic (but a little bit harder/complex/different numbers/different operation, etc.) on a small assessment in the future, so they will have to do the different problem, just at a different time. no need to stuff every problem into one assessment, that’s what’s great about the smaller, more frequent assessments.

    the way i was thinking about integrating more SBG into my curriculum is doing weekly “skills quizzes” that are small and based on more practice/rote problems, and at the end of a unit, doing a more word-problem heavy test similar to a standardized test. they get practice for both types of assessments through their homework. hope that helps.

    congrats on jumping on the bandwagon! it’ll be easy with so much support from the blogosphere.

  3. I’m so glad you posted your questions, I am starting SBG this year and you’ve brought up some things I need to think about for myself (specifically #5).
    For #6, I’ve found that regularly bringing back old skills on assessments does wonders for retention. I agree, though, that this shouldn’t be done blindly. I would usually tell students about a week in advance the “spiraled” skills that would show up on their next test. For my freshmen in Algebra 1, I would include these old skills in their homework.
    I plan to start spiraling old skills for my precalc students this year, so I’m not sure how much help they will need (if any) to review. This might be good motivation for your students to keep their homework and have it organized. You could tell them what the old skills are that they need to review, but leave it up to them to look back at their old assignments to study.

  4. I have this nagging problem with involving any kind of averages in grading at all. Here’s why:
    If you are taking a bunch of trials of the same data point, it makes sense to average them all. Your assumption is that approximately the same thing happened every time, so you are decreasing your uncertainty about the measurement when you average a bunch of trials.

    BUT, if you are taking those trials days or even weeks apart, and the phenomenon might (or, in fact, probably did) change quite a bit in between, then these are no longer trials. They are separate data points. And it makes no sense to average all of your data points together. You’d want to make a graph instead and see what the function family is, and see if there is a relationship.

    So, unless all of the trials are taken in a short amount of time (like during the same test) when the understanding of the student hasn’t changed by much, it just doesn’t seem right to me for there to be an average involved. If the trials have any significant time between them (even a few days), it seems to be still rewarding the “fast learner”. Or more importantly, representing (in part) the speed at which mastery occurred (if at all) rather than the existence mastery itself.

  5. Sam, a pleasure to read, as per usual.

    re: #5. Why average at all? If the student messes up and then fixes it, why should their now remediated mess-up affect their grade in any way?

    re: #6. Yes, bring back old things. This is how you let SBG help kids who are scared to initiate reassessments. I usually bring back the standard with the lowest average score for the whole class.


  6. I’m not (yet?) in the SBG cult.

    I have, this summer, been making a list of what my students learned every day. It’s basically a skill list, though there are some topics. I’m not apologizing for that.

    Anyway, #3 is a familiar problem to me, at least in the version where it’s “Students should be able to take derivatives by appropriately applying product, quotient, sum, and difference rules.” Well, in its mirror image where I want them to be able to integrate things.

    I’ve been treating it like there are five skills here: one each for knowing each rule, and applying it correctly, and one for knowing what to do more generally. (As I type this, my system only makes sense with integration… I’m not sure what it would mean with differentiation. But you know, when you get an integral and you decide to try integration by parts rather than substitution. That skill.) Anyway, it turns out I tend to test each skill, as I’m thinking of it, at most once per test. Except the “know what to do” skill.

    Summary: it sounds to me like some of your skills are really several skills lumped together. Breaking them up might help you not test them in so many places on one assessment. Or might not.

  7. Sam, it looks like you’re thinking deeply on SBG, which is great!

    #4. I didn’t see it explicitly stated, but I think it’s a good idea to have the student re-do the problems they got wrong on the original assessment. If they can’t solve them correctly with their notes and the textbook in front of them, then they’re not ready to reassess. Unfortunately, some students will view reassessment as “what do I have to lose by trying again?” and will take the reassessment before they’re ready. I also don’t want to have to explain to a parent why their child did WORSE on the reassessment in that scenario.

    #5. For similar pragmatic reasons, I tend to agree with averaging scores over using the last assessment taken as the final grade. Yes, in theory, the last assessment is the best reflection of the student’s level of mastery. However, if you DON’T average test scores, then you have to come up with a method to ensure that your students don’t develop the mindset of “why bother studying for the test when I can just re-take it until I get the grade I want?” Because I don’t think that’s an attitude we want to encourage.

    My two cents, anyway.

  8. I was initially confused by your topic/skill distinction, since it is so different from mine. What you listed were bigger or smaller groupings of the same thing, rather than orthogonal ways of viewing the course. For me “skills” are fairly broad things (can structure and debug a computer program, solve a system of equations, write a paper, prepare a presentation, …) while topics can be quite narrow (hidden Markov models, Smith-Waterman alignment algorithm). Skills tend to be assessable, while topics are groupings of information that need to be conveyed, but are not directly assessable.

    I also had an immediate reaction to you “sum, difference, product, and quotient rules” standard as being 2 or 3 quite different things. Sum and difference rules are identical, so that’s one thing, but the product rule is a totally separate standard. The quotient rule can be combined with the product rule, but that is probably too advanced for your students, who will probably need to learn product and quotient rules as separate things. It is quite common for kids at that level to have the product rule solidly and not have the quotient rule at all. That means that they *must* be different standards if SBG is to mean anything.

  9. Sam, re: question #6, I think if you tell them what old standards are coming you will continue to support the cram-and-dump style and not be looking at true retention. Now, I am also jumping into SBG this year, so I may be eating my words in a few months, but I plan on being clear with my students: any standard can show up on any assessment. Retention is my goal.

  10. Thanks all for the comments! You’ve given me a lot to think about.

    The list I posted will be revamped for next year – to make it work for SBG. I will be definitely breaking apart some things and combining some others.

    I think I will go for the “last grade is your grade” approach. I want to encourage reassessment, though, and I’m afraid that some students will be too scared to reassess if their grade can go down (which it can!). However, since I’ll be asking on later assessments topics that whole class tends to struggle on, I guess this will be “forced” reassessment.

    I am convinced to give questions about previous topics throughout. Retention is part of this. I’m on board. It still feels weird to not say “there will be a question on limits on this derivative assessment”… I have to think about it a little more.

    I’m so unused to shorter assessments that I’m going to have to think a bit more about how to do them effectively.

    Thanks all for your thoughts. Keep ’em coming!

    1. re: scared to reassess because the grade can go down…

      I should preface by saying that I’m doing SBG this year for the first time, so these are just thought experiments until a few weeks from now. Anyway, here’s how I think I’m combating that with my system.
      0 – no mastery shown
      1 – developing mastery
      2 – mastery
      3 – sustained mastery
      You can’t get a 3 on the first time you assess (you also have to wait for another scheduled assessment to get your 2 up to a 3 on a standard… you can’t come in for individual reassessment unless you have a 0 or a 1). A 1 cannot go down to a 0 (but neither count for anything anyway). A 3 can go down to a 2. A 2 can go down to a 1.

      There are A, B, and C standards. To get a 70 for the marking period, you have to have 2 or 3 on every single A objective. To get in the 90s, you have to have 2 or 3 on every single A and B objective.

      So, I don’t see a lot resistance to reassessing… if you have a 1 or a 0 on an A objective, you HAVE to reassess. It doesn’t matter if your grade “goes down” because you haven’t mastered the objective yet. They might be a little nervous about dropping on future scheduled (in-class) assessments if they have forgotten something or lucked out on the question that I asked the first time, but they can always reassess and bring that one back up.

      The 3’s are nice to get because they give them that psychological safety zone. Really, though, once they have a 3, I doubt they would be getting that skill wrong very often in the future.

  11. I am not on the SBG bandwagon yet, since I just really learned about it this spring/summer. I love it though.
    One question, let’s say I have the skill I’m testing be, oh I don’t know, graphing an inequality. Do you normally teach it and then two or three days later give an assessment (quiz) ? If so, do they ever take a “test” on it later? If they do, do you replace their original grade with that grade? Also, lets say you do spiraling and add a question from the topic much much later on. Is that score then the “last score” that gets put in the system?

    I know this is a lot of questions, but I really really really want to do this next year, maybe even second trimester, but I want to be able to explain it to the other teachers correctly.

  12. Re #6: Lots of people have talked about including old material to ensure retention, but I think the more important reason to do this is to reinforce connections. Sometimes harder to do, but I’d really try to create problems that address both the new skill and the skill/skills that the class has struggled with the most (versus having separate problems for each). For example, if your new skill you are assessing is “apply the product rule for differentiation” and the class struggled with “determining the derivative of exponential functions”, have them find the derivative of x^22^x.

  13. Hi Sam,

    Great post and I can’t wait to go home (I’m giving my final exam as I type) and come up with my own answers to your questions. A quick thing, though. I haven’t had one student express any concern about their grade going down when they reassess. However ill-founded, it seems students do not consider that fate. Better to be an optimist and a fool then a pessimist and right, eh?

  14. I’ll second the welcome to the collective! I’m about a cm away from not including homework in my grade as well and just need to take some deep breaths to get my logical brain to thwack my traditional-omgnooneelseatmyschooldoesthat brain into submission. That or talk to my Veep who is excellent at helping me think things out.

    A few thoughts on your decisions list:
    [note: I call the little bits I assess ‘skills’]

    2. The nice part of skill assessments for me has been the time. I do a hybrid version of sbg with my precalc (they have sbg quizzes and normal tests at the end of a unit), and the quizzes are fast to give and quick to grade so yay for fast feedback to boot. Even my students who have the option for more time rarely take it with the skill assessments, though perhaps yours are more aggressive with requesting theirs?

    3. Unless a problem has a ridiculous number of cases (like ‘solve for x’), if a student can do the problem twice perfectly, is that enough of a demonstration of mastery for you? If it’s not, can you break up the skill more? I would be interested to see what rubric you use.

    4. I have students walk me through general steps verbally as a quick check of their understanding. I usually pick out an assignment problem or something from the book for this and ask ‘why this step?’ After a month or so, I know my kids well enough that I can usually tell if they need to practice more or are ready for a retake.

    5. I take the last score with my current system, though this year I am thinking of using Nowak’s system where she carefully choses a harder level problem for the second round and adds up two scores so the kids with a 4/5 the first round don’t sit on their laurels. Need to think about it more.

    6. I did it all the time. I actually kept a log on the wall of class averages for each skill and would glance up at it to see if there was an older skill that could use an extra go. I would usually give them a heads up as for the students who still needed mastery it would help and for the ones who already had it they could do it for fun or skip it. For me the heads up comes back to what does ‘mastery’ mean. I feel I have mastery of calculus, but there are parts I would like to have 5 minutes to review before whipping out awesomeness on paper. If a student needs 5 minutes to review a problem and can then do it, I’m going to call that good. A bit of short term memory reliance on their part? Yes, but retention is a touchy word for me as I have an incredibly poor memory but relearn things pretty darn quick. Isn’t that what we do in life? Read the directions when we forget how to do stuff then go do it. Granted, that isn’t very helpful with standardized tests, but is that what we’re really worried about here? … I think I’m off topic. Back to the task at hand.

    7. Ooo, interesting thought. I would (and have) split up large skills (see ‘solve for x’ above). I’ve also had skills with the question “which method would you choose here and why? Do not solve.”

    8. Could you make homework mandatory to retake a skill? as in, ‘no retakes until you show me you have done these X problems’? And if you find the secrets to homework organization, let me know. I’ve never found a system I really liked.

    Lastly, thank you for the link to your fav twitter convos. My husband is worried I’m insane with all the cackling coming from the computer room this evening.

    1. 8. I was about to say how much I like the idea of organizing homework and simply providing the structure that makes this feasible for the students. But I like what mythagon has to say about showing homework for retakes. I think I would personally ask that they show me at least one homework problem for a retake.

      Then again, in an ideal world I’m setting up my homework and assessments so I don’t need to set up hoops and ramps for the homework to be valuable.

  15. Thanks for posing these questions. I have been blog lurking on this topic for months and think I may join the cult for my geometry class this fall since I am not team teaching the course.
    One thing I am curious about is if you think you have more or less freedom to embark on this at an independent school.

  16. Sam – you just posted some great questions about standards-based grading AND received nearly 20 comments. No matter what you do, you’ve surrounded yourself with an outstanding group of individuals who are here to help you through this transition. Even if there are sharks, I don’t think they’re going to bite too hard for too long. Good luck.

    P.S. I agree with Shawn. There’s no need to average the scores in #5. Averaging is a step back in time for you. :)

  17. Hi, Sam – I’ll be the 20th comment :-)
    Just two short points. First regarding #5, only because I just read this part in Marzano’s Transforming Classroom Grading last night (yes, SBG borg rejoice over the fact that I was reading up on SBG on my Saturday night!). He specifically discusses whether or not to average the individual scores for multiple assessments of one topic/skill. As I understood it, Marzano recommends using the Power Law to calculate the final score for a topic/skill because learning occurs in large increments at the beginning and slowly tapers off as students develop more and more mastery.

    Therefore, you should need a few scores per topic/skill in order to use the Power Law, which could pose a problem if you intend to only have 2 assessments. However, if you keep bringing back old skills/topics, you will gradually accumulate more scores. Not sure if any of the more experienced SBGers have experience with using the Power Law or not.

    Regarding #8, I am planning on having my students keep math journals/notebook (something bound, not looseleaf) where they will do all their practice problems and homework (not sure yet if I’ll include notes in there). I’ll collect their journals weekly (but I’m sure you can do it less) and give feedback. Prior to submitting their journal to me, I’ll ask them to write a reflection on the week – what worked, what didn’t, what was easy, what was hard, what will you try (w.r.t. study skills) differently next week, what can I (as teacher) try differently. I’ll respond to that too.

    Just my confused, not as short as promised, Sunday morning thoughts. I’m new to the SBG cult as well and so appreciate reading how you are sussing out all the details. Cheers!

  18. Hey Sam — This course outline is very helpful for me, as I gear up to teach this class for the first time this year (as one of 4 preps). I’ve always used the concept check ala Dan Meyer as the overarching assessment structure in my classes, and I plan to do that for AP Calc too. I’m wondering if you or anyone else on this thread has examples of their skill quizzes from previous years. I’ve found that’s a very effective way for me to backwards plan for a new course. If anyone can help me out, I’d really appreciate it.

  19. Sam,
    It’s like looking over the platform of the high dive getting into this SBG thing for the first time. I loved your post on joining the cult. That’s what it feels like. I’m about to drink up the SBG Koolaid myself. Two things – 1.) Do all of your posts connect to something in your virtual filing cabinet, which seems unlikely? I thought you had a tag/categories column but don’t see it and think it’d be very useful for lurkers like me who remember seeing a post and want to return to it. 2.) I assume you pay for Scribd and you think it’s worth it, or does Scribd only charge the lookers who want to download documents?
    BTW, your blog is top notch!

    1. hihi-

      thanks! have fun with the SBG! it’s scary, but really powerful in terms of reorienting your thinking about why you’re teaching / what your role is / what your true goals are. at least it was for me.

      as for your questions:

      1a) no, sadly not. i’m terrible about remembering to put my posts in the filing cabinet – sometimes i do it but not often
      1b) i REALLY want to create and tag all my posts – i’ve thought about it a lot bc i myself have tons of problems finding things i know i’ve written about but can’t find it through searching. it’s dumb of me, and i’ll get it it… sometime. (i have hundreds of posts tho, so it’s daunting, which is why i’ve put it off)
      2) i don’t pay for scribd. i didn’t know they charge to download documents! is that true? AWFUL! if it is, i’ll post things on scribd AND post the docs in the post too…


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