Quarter II on SBG

We’re at the twilight of the second quarter in my calculus class. Standards Based Grading has become normal. The most exciting thing about SBG is seeing students who are traditionally unsuccessful turn that around. They can get it, but they realize they have to conquer their weaknesses. The Giant Specter that Haunts All Calculus Teachers is the deficiencies we see with our kids’ algebra abilities.)

Students will use the quotient rule to get something like \frac{(x+1)(2\cos(x))-(2\sin(x))(1)}{(x+1)^2}. And then, then, *shudder*: \frac{2\cos(x)-2\sin(x)}{x+1} because, you know Mr. Shah, you can just cancel the x+1.

Students simply can’t get by without fixing their algebra deficiencies. But they have lots of opportunities to fix them. It’s really hard to unlearn bad algebra, but many are doing it.

The flip side is possibly the MOST FRUSTRATING THING ABOUT SBG. Yes, all caps means I’m yelling. It’s the students who just sit there, don’t reassess, and *hope* everything will turn around. I encourage (of course I encourage!), but I am only going to go so far. They’re not freshman. They’re seniors. They know what they’re doing. They’re making choices. It saddens me that students who have been given the opportunity to learn would rather languish.

It simply highlights my biggest pet peeve. I really really dislike it when I am confronted with a student with SO MUCH POTENTIAL and SO MUCH ABILITY but they flounder because they don’t want to work. They don’t want to put in the effort it takes. It angers me because they don’t realize that THEY ARE SO LUCKY TO HAVE THE OPPORTUNITY TO LEARN. They’re squandering opportunities and closing doors and that saddens me.

However, those students are few and far between.

In terms of the number of kids reassessing this quarter:

Week 1: 6
Week 2:  8
Week 3:  11
Week 4:  15
Week 5:  15
Week 6:  17

TOTAL:  72 reassessments

Making the change this quarter that students can only reassess on Fridays (and they have to send me their form email demonstrating they’ve remediated by Tuesday at 5pm) has been amazing, in terms of my own self-preservation. I generally spend (closer to the end of the quarter) an extra 4 hours/week writing, grading, and recording the reassessments. It feels worth it, so I do it.

I was hoping that the number of reassessments would decrease in the 2nd quarter, once students began to recognize what was required of them to do well on the assessments. That isn’t the case (Quarter 1 had 70 assessments). I have two conjectures about this:

1. The material is harder, and way more algebra heavy, so students are struggling more.
2. Students have started to view the reassessments as their safety net (or their crutch, depending on the student), so they aren’t adequately preparing for assessments

I also wonder how senioritis will affect things in the 3rd and 4th quarters.



  1. >because, you know Mr. Shah, you can just cancel the x+1.

    In an attempt to help students with this mistake I’ve banished the word “cancel” from my classroom, and now I insist on talking about “factoring fractions.” This has led to a lot of “OOOOOHHHHHHH”s from my Alg II students, and I’m going to teach my freshmen how to deal with fractions in this way instead of talking about when you can cancel.

  2. > The Giant Specter that Haunts All Calculus Teachers is the deficiencies we see with our kids’ algebra abilities.

    I don’t teach calculus, but I run into the same problem with my (college-level) students all the time. Such as the time that they were all doing a proof in pairs on the board and EVERY SINGLE PAIR immediately “simplified” the subexpression n-(k-1) to n-k-1. When I went around pointing out that these were not the same, several people did not believe me until I forced them to plug in numbers.

    I’m sure everybody here has a story like this.

    Over time though, my view has shifted from “they can’t do algebra” to “they can’t do symbolic manipulation” to “they can’t recognize when/where to apply known abstractions, and even when they do, they frequently apply them incorrectly”. For example, they know the associative/commutative/distributive laws (although perhaps not by name), but don’t recognize the opportunity to apply these laws when that opportunity is buried inside a subexpression or when the context is lacking explicit instructions to use this or that law.

    I can’t claim that this shift in view has magically fixed the problem, but I do feel like it helps me recognize when various kinds of struggles, both mathematical and non-mathematical, are really instances of this same underlying phenomenon.

  3. I was the kid in highschool with high skill / talent / potential levels but low motivation. I spent my evenings reading novels and learning to program my computer from the internet (which was more interesting than my calculus class and WAY more interesting than my history class) and spent class playing tetris on my calculator (which I was learning to program). Then, in college, I did the same thing (though I did get a degree in math). It wasn’t until I started teaching precalc that I learned to love algebra and to really get to KNOW things like the law of cosines, various factor theorems, etc. Now, I’m really glad to be so well read and to have such refined computer skills and to be a good writer. Admittedly, conversations about history these days can be downright embarrassing for me.

    All this to say that I wouldn’t worry too much about those smart kids that aren’t choosing to do your class to their best ability. They may be squandering opportunities, but they may not be – they may just not be ready to be interested in your class. I think it’s ok for them to choose something else, even though they’re lucky enough to go to your school.

  4. Sam, you said, “They’re not freshman. They’re seniors. They know what they’re doing. They’re making choices. It saddens me that students who have been given the opportunity to learn would rather languish.”

    I agree that the SBG philosophy gives students more opportunities to re-assess and in turn demonstrate understanding of concepts when compared with the traditional system. It also levels the playing field a bit between students who “get it” early and those who “get it” later. For these two (among others) reasons, I can’t imagine teaching/assessing/grading in any other way. You recognized there’s a difference between seniors and freshmen and I couldn’t agree more. I wonder if re-assessments should be “forced” rather than optional for some grade levels (not necessarily seniors). At what point do we release 100% of the responsibility to the student? The intent of this comment is not to criticize what you’re doing, Sam, but rather to stir up a conversation amongst the SBGers here in the edublogosphere. How much of the re-assessment should be left up to the student? If a sixth grade teacher tells me he/she leaves it all up to the student, I think I’d question that practice a bit. What are your thoughts? It may be the topic for a future post.

    1. Along these lines…

      One of my grad school professors had that attitude (probably still has it!) that all papers not only should be rewritten, but they MUST be rewritten. To move this process along, every first draft was returned without a grade. Instead, he simply marked next to each line or passage where he thought there was an issue that needed to be addressed. It was up to me to decide whether I needed to strengthen an argument, fix a grammar problem, move a sentence, etc. I never thought more deeply about my writing than I did that semester. How applicable is that idea to our discipline?

  5. I really want my students to take the second attempt in class but the majority do not. Will limiting re-assessments make the second attempt more important? I really don’t want to limit total re-assessments though? I am limiting them to 3 per week to make it more manageable for me, but not a total for the quarter.

  6. Keep fighting the good fight, Sam. You are doing exactly what you need to do to reach students half way. I’m proud of you for jumping into this!

    I’ll bite on Townsley’s prompt. SBG is about clarity in grading and reporting. SBG is about not punishing students with arbitrary timelines. The reassessment component is what makes most teachers shy away from SBG, and I think we’ve all put too much emphasis on it. I’ve taken almost all of the reassessment control from my students (GIANT classes, ahem, Matt), and things are still working fantastically. I just have to write better quizzes and quizzing schedules. (for Math, that is)

    Good luck, man. Don’t get caught up in systems and rules. Just remember that this is better than the penal colony we were all warden of before.

  7. I once told my students (not as sharp as yours, perhaps…) who absolutely were not giving me even the minimum effort to pass my class what my best friend had told me about poverty in the Philippines (where he had spent all of his life up till 22): Many kids in the Philippines live in shacks with no roof and they have to dig through trash for food. And yet they still go to school everyday. Why?? Because education is deeply valued.

    American kids don’t know how good they have it, so they just throw away learning opportunities. It’s truly such a shame. In El Salvador, many kids don’t even get to go to school. They have to sell Chiclets and cigarettes on the street with their parents all day/night, just to make enough money to buy food.

  8. Sam and all –
    I am more and more intrigued as I read about your adventures into SBG. I want to convince my administrators to free up some PD funds to send me (and hopefully some others at my school) to a nearby conference discussing SBG. My question is this – Is there a concise reading I can find to present to my colleagues and administrators that really summarizes SBG ideas and benefits neatly?

    I thank you all in advance!

    Jim D

  9. I believe there are seasons of hard work and seasons of slacking off in all students’ lives–even among the most motivated. You definitely seem to be experiencing a fallow period with your Calculus students, and I can understand your feelings of discouragement and frustration. Still, I think it may be premature to catapult all the way to sadness because they are, in fact, still adolescents. Plus it’s February. Nobody is at their best in February. I haven’t finished analyzing all the data — because there’ve sure been a lot of Februaries since the institution of the current calendar! — but I’m pretty sure about this.

    Also, as a teacher, parent, or mentor, there always comes a point when you have to just allow a student to experience what happens when they stop acting impeccably in their own best interests. Many of these students, especially the ones who make it to Calculus, have never experienced failure or even a significant setback. But that is part of their development process too.

    I find that again and again, I have to step back, let go, and simply say, “Wow, well, this is going to be interesting for me. I’ve never had a super-motivated student like you simply give up so early in the year. I’ll be curious to see how it all turns out. Good luck with this!”

    After all, if we are REALLY trying to get these students to take ownership of their own learning, we can’t just restrict our perspective to the positive parts of their experience. This too is part of SBG. It is also about respecting the adult-style boundaries students are demanding. By their senior years, kids need to be accountable to themselves for their own performance, and we actively do them a disservice by taking on more of the responsibility for their success than is appropriate.

    Some people need more time to experience the consequences of their own slacking off. I know that once *I* got to college and realized how seriously I had shortchanged myself by slacking off that last semester in high school, it put my choices into sharp relief for me. And at that point, I made major changes to my study habits that took me to a dramatically higher level of performance.

    Fortunately, I — like your students — had been given a terrific foundation that had just gone slightly dormant. So it was a lot easier for me to kick back into high gear than it was for those students who had always gotten along on the sheer easiness of classes.

    So be of good cheer, ye SBG teachers of 12th grade slackers. You have planted the seeds and given them everything they need for success. Now it’s up to them to decide whether (or when) to pick up where you’ve left off.

    Elizabeth (aka @cheesemonkeysf on Twitter)

    1. I agree with your statement, except for one thing: although it is the student who needs to take ownership of their learning (and I encourage them and show them ways to do so), I as their teacher get stuck with the aftermath of students who are underperforming (by parents, by higher ups, etc.). Logic about personal responsibility may go a long way in convincing *me* that I’m doing right by these students, but it doesn’t always convince those other adults who are involved with looking out for students who are underperforming.

      Which is all to say that I’ve found the “sink or swim” mentality (even when I’m throwing life preservers and rope and sending helicopters) of SBG to demand nuances that I did not anticipate before I started it.


      1. I can definitely understand what you are saying and I too go pretty far (life preservers, ropes, helicopters, trained rescue dolphins) for the students who are underperforming.

        In my comment, I was thinking primarily of the peculiar case of those high-achieving seniors who have actually made it to Calculus and are showing symptoms of acute senioritis. For myself, that is the moment at which my attitude shifts to the above.

        Also I would characterize this posture less as an insistence on “personal responsibility” and more as an implementation of Rudolf Dreikurs’ work on using “natural and logical consequences” with adolescents who are taking on more and more autonomy at this pivotal moment in their lives.

        When I have a 9th, 10th, or 11th grader fluffing off and squandering their educational opportunity, it’s a whole different situation, and my interventions are more direct and incessant.


  10. from a recent convert…

    I just started doing SBG (right after Thanksgiving in my Geometry classes and about 1 month ago in my Algebra classes. I have done very little reassessing because a lot of my students do not really care. I’m thinking it will pick up after conferences and the end of the trimester. Any student with a C or below is getting a phone call this week though.

    I am also quite discouraged by their prerequisite knowledge and using this type of assessment is making their deficiencies very clear. This “canceling out” phenonema Sam mentioned starts in middle school, they also like to cross multiply willy nilly.

    I am wondering what to do with my advanced 8th graders (taking Geometry) who cannot calculate slope or write the equation of a line or solve an equation with fractions. They are doing fine with concepts that are strictly Geometry (as long as they don’t contain fractions)!

    Because they are doing fine with most of the Geometry concepts, their grades are not too bad, so they are not motivated to fix it. I know that these are the students who won’t know their algebra in their high school classes and that is frustrating because I want to fix it but I don’t know how.

    Any ideas?

    1. @Anita: What I generally do with such a student is to have them come to my desk after the lesson and call the parent with the student present. I then put the student on the line to explain to their parent why I’m calling. You’d be amazed what a difference that often makes. Especially when I tell them afterward that I will be calling their parent again if they stop doing homework again. (Your mileage may vary, depending on the student.)

      I also subscribe to currency theory, which I recently blogged about how I use it in my classroom:


      The bottom line for me is that my honors students work hard because they already get something out of it: good grades, getting into college, they enjoy the subject, etc. For a lot of the students in my regular classes, they need to be “paid” in their own currency to get them to do what I want.

      Paul Hawking
      The Challenge of Teaching Math
      Latest post:

  11. How about if students have to demonstrate readiness prior to writing a quiz? Would this help negate the situation where students don’t take the first test seriously because they know they can remediate later? So perhaps they would have to show completion and some level of mastery prior to writing the initial quiz/test.

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