An Adventure in Standards Based Calculus

Today was the first day of our new semester. This spring, I’ll be teaching two sections of “Calculus I” and one section of “Calculus II.” I feel like “Calculus I” is basically on autopilot; I’ve taught the class every semester for the last couple years and so I’m very comfortable with the course content. But this will be my first time teaching “Calculus II” in many years. (I think the last time I taught it was 2006 or so, at the University of South Carolina, using an entirely different textbook.) I’ve decided that I want to try something different & I am embarking on my first attempt at Standards Based Grading (SBG) — or as someone suggested today on twitter, maybe Standards Based Learning (SBL) is more appropriate?

Why Am I Doing This?
For the last few years, I’ve noticed a few things about traditional grading (TG) that I did not like. One thing that has bothered me is that a student can go the entire semester without ever solving a problem 100% correctly, yet still do very well in the course. For example, it is entirely possible to earn a “B+” grade, by performing pretty well on everything, but never really and truly mastering a single topic or problem type. I hope that Standards Based Grading helps me motivate my students to really try to master specific sorts of problems, rather than try to bounce around, hoping they can earn enough “partial credit” points to propel them to success. Really, I want to reward a student who gets four problems absolutely correct (and skips two problems) more than a student who just writes jumbled stuff down on every page. I think SBG will allow me to do this.

Another (related) thing that has bothered me: The point of calculus class is not to earn as many points as possible, doing the least effort possible. I will admit that I have used a TG scheme for years and years; I have no idea how many college-level courses I’ve taught. And I am pretty sure that I can look at a calculus quiz question, assign it a score between 0 and 10, and accurately give a number close to what my colleagues would give for that same problem. We might all agree, “Okay, this solution is worth 7 out of 10 points for these reasons.” But I think this gives the students the idea that the reason they should study is to earn points on the quiz — after all, 9 points is better than 7 points! Instead, I think the reason they should study is to understand the material deeper than they presently do now, and I think by assigning X points out of 100 sends them the wrong message.

Something that has really bothered me recently is that when a student is struggling with the course, I am never entirely sure what to tell them. I look up their grades in my gradebook; I see that they have an average of 62%; and then I try to give them advice. But what advice should I give? The 62% in my gradebook does not tell me very much: I do not know if this student is struggling because they need more practice in trigonometry. Or maybe they were doing very well, but bombed our last test because they got some bad news the night before. Or maybe they got L’Hopital’s Rule confused with the Quotient Rule. I want to be able to tell a student exactly what they can do to improve their understanding. By tracking each student’s mastery of particular standards, if a student comes to my office for extra help, I can tell that student, “Okay, it looks like you need extra help with [insert specific topic].”

Lastly, I would like to give students more low-stakes feedback about their understanding: That is, feedback without the worry that it will negatively affect their grade in the class. I will be giving a weekly quiz, and I will grade it, offer feedback, and return it to my students; then (eventually) their score on that standard can be replaced with a newer [hopefully better!] score. I will constantly replace their previous score on a standard with their current score on a standard. This way, if they are really struggling with (say) Taylor polynomials, I can communicate this to them early, they can seek extra help and resources, and then they can be re-assessed without penalty for their original lack of understanding.

What Worries Me?
I have lots of different things worrying me about this system! For example, since this is my first time teaching Calculus II in many years, I don’t know all the “common pitfalls” that my students will encounter, so I don’t feel like I’m going to see them coming until they’re already here. Also, I am worried that students will struggle to understand this method of assessment & won’t really “get it” about how they are doing in the course — or won’t take the opportunity to re-assess when they need it. Lastly, despite reading online that “before a course begins, start by making a list of what you want them to master (a.k.a, the standards)” I was unable to do this. I have the first half (or so), but I don’t know how good they are. Am I being too vague? Am I being too specific? Do I have too many? Too few? How difficult will they be to assess?

Some Resources
In my own course planning, here are links to resources I found helpful:

Wish me luck!


10 thoughts on “An Adventure in Standards Based Calculus

    • We have a departmental-wide cumulative final exam in Calculus I, and we require that the final exam account for at least 25% of the course grade in Calculus I, and there is a very detailed, specific grading rubric that goes with the exam itself. So I couldn’t quite figure out how to teach the entire course in an SBG-style and then have a very traditional Final Exam. Also, I have many more students in Calculus I (the enrollment cap is 40 as opposed to 27) so I worried about being swamped with that many students wanting re-assessment opportunities all at once. And since this is my first time through SBG, what if I hate it? Better to do a small pilot run and see what I think at the end!

      Also, hi Bryan, we miss seeing you! Hope things are splendid 🙂

  1. Whenever some says something like, “…rather than try to bounce around, hoping they can earn enough “partial credit” points…” I know that hundreds of students somewhere are about to win life. Good luck, and have fun!

  2. Good luck! Keep us posted on how it goes. Sounds like you’ve thought everything through and I’m sure your students will catch on quickly. (I haven’t done SBG, just watching from the sidelines.)

  3. Hi Kate,

    I think that you are going to love this (modulo a couple of details). I would never think about going back to TR after using SBG.

    Here is one of the things I have noticed about SBG: at the beginning of every semester under both TG and SBG, I can usually identity several really weak students. They usually are not very good with algebra, they lack confidence, and they have some bad misconceptions.

    Under TG, these students always—ALWAYS—did very poorly. Under SBG, some number of these students end up flourishing. It is truly heart-warming to see them improve.

    Also, if you wish to use SBG in Calc I in the future, I would recommend just doing SBG as you wish, and then calculating the semester grade by doing 0.75*SBG+0.25*Final Exam Grade (I understand that there might be some other constraints that I am not aware of).

    Keep us posted on how this goes!

    • Thanks, Bret! I am excited to see how it goes. For now, doing a new course prep & trying to figure out this SBG thing seems to take a lot of my time! My hope is that in subsequent semesters, I can SBG-ify (is that a verb?) my other courses when I don’t have so many things to juggle at once.

  4. Kate, I’ve done a modified version of SBG for years now, allowing re-assessment, but using the standard grading scale. Since I switched, I give way fewer problems on each test, and care much less about partial credit. (Tests under 50% just get an x on top usually.)

    Do you know if he intends the Apprentice level to include those who show no understanding whatsoever? (I’m wondering if Mastery is like an A, Journey like B or C, and Apprentice like D or lower.) I like his idea of splitting the content into core and non-core topics, though I might split it differently, and use different problems. (Not sure why 5b would be a core problem, among others.)

    I might be interested in trying something like this with Calc II also. If you’d like to chat about topics today, tomorrow, or Saturday, I’d be very interested in that. I’ve never taught polar well, so I’m moving it earlier in the semester to force myself to do a better job. (It usually gets squeezed into the few days.) My current plan is:
    1. Applications
    2. Polar, Parametric, …
    3. Techniques
    4. Infinite Series

    I think this class could benefit (more than others) from never seeing points.

    • My recollection is that Mastery is like an A, Journeyman is more like a C (passing and acceptable; room for growth; not great), and Apprentice is more like an F/D (just getting started; can’t work alone; growth necessary). Actually, he uses a +/- system too. So somehow “Journeyman+” might be a regular B- and “mastery-” might be a regular A- or B+.

      I’ll send you an email later! I’d love to exchange strategies and ideas.

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  6. Since I found SBG resources out there are mostly targeted at pre-college levels, I’m attempting to crowdsource some college math level SBG resources on the new Math Ed Stack Exchange site. Maybe you would like to contribute your favorites?

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