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A friend of mine recently tried a standards-based grading (SBG) approach for her Calculus II course. (You can read about Kate's experience on her blog.) I find this approach to evaluation very interesting and, after seeing Kate's success, I am eager to learn more.

There are plenty of resources for SBG at pre-college levels, but it seems that college level resources are somewhat scarce and hard to sort from the giant haystack of pre-college resources. I'm hoping we can build a list here or that someone can point me to a list compiled elsewhere. I am especially interested in seeing other accounts and examples of using SBG in college math courses, especially for calculus courses.


SBG is based on a fine division of the course objectives into concepts, tasks, skills or other learning objectives, henceforth called standards for simplicity. Students are evaluated for each standard on a coarse scale, typically 0-4, indicating their level of mastery of the standard in question. Final course grades are assigned according to what portion of the standards that each student has mastered at an appropriate level.

Implementation details vary. In the course that my friend gave, students were regularly assessed and re-assessed for each standard using tests and quizzes to measure their current level of mastery as the course advanced. Students were also given some opportunities to ask for specific standards to be re-tested. In cases where a standard occurred on the final exam, the average of the latest course score and final exam score was used to compute the final score for that standard. For final course evaluations, letter grades A,B,C corresponded roughly to earning 4,3,2, respectively, on at least 85% of standards.

Two features of this scheme that I really like are that the meaning of each grade is perfectly clear and students are constantly aware of their strengths and weaknesses as the course progresses.

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    $\begingroup$ As just a comment: Kate Owens, mentioned by the OP, put up A Beginner's Guide to Standards Based Grading on the AMS Math Education blog today, Nov. 20, 2015. The post can be seen here. $\endgroup$ – Benjamin Dickman Nov 21 '15 at 2:46
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This is in response to the bit:

I am especially interested in seeing other accounts and examples of using SBG in college math courses

I've done SBG (aka "criterion based assessment") in an undergraduate mathematics course. I heartily recommend it. I've been trying to write up my experience with the course that I tried it in. Here's the part on SBG (warning: this is in draft form):


Criterion Based Assessment

I have never been a fan of numerical assessment in exams. (This might have something to do with the fact that my undergraduate university - Oxford - used no less than four different schemes for devising a final grade).

My reason for this is simple. Learning is not a continuous process; whilst it often proceeds in small increments there are definite leaps from one level to the next. It is these leaps that we should be focussing on measuring: has a student achieved the next level, or are they still at the previous one? Within those levels, there is not much to separate students. Grading a paper purely numerically paints a false picture. It says that learning is continuous, and that the student who got 68 points is better than the student who got 65 points. We then draw graphs showing a nice normal distribution and select cut-off points for the different grades.

So we take something discrete, namely the amount the student has learnt, force it into something continuous, their grade, and finally make it discrete again. As any topologist could tell, discretising a continuous function is a Bad Idea. Suppose we decide on 70 as a grade boundary. What about the student who got 69? Are they really qualitatively worse than the one who got 70? It was only one point! But by that argument, all students should get the same grade since each possible total of points differs by only one point from the next one and therefore should get the same grade as it.

Most likely, the grade boundaries are not as solid as that. We look carefully at students on the boundaries (well, we ought to; whether we do or not is another matter). But this is actually worse. Not only are we acknowledging that the original system is incorrect, we are fixing it in an ad hoc way that is completely opaque to the students.

Enter Criterion Based Assessment. The core of this is to avoid the false assumption of learning being a continuous function. Instead, the grades are aligned with specific stages of learning.

The exam is viewed in a different light. Instead of a slow accumulation of points, each unit is graded according to the rule "Is this evidence of a particular skill?". At the end, the question becomes "Has this student shown sufficient evidence to justify this grade?".

When grading, my imaginary scenario is the following. I imagine that I award a student a certain grade. Then I imagine that sometime after the lecturer for another course has marched into my office demanding to know why I awarded that grade (since clearly the student is as thick as two short planks). The exam is then my evidence for that grade. If I cannot use the exam to defend the grade, the student does not get it.

(This has a useful side effect. It so happens that I sometimes get asked to write references for students who have taken this course. However, it is a medium to large course - about 100 students - so there are very few that I can say too much about. But as my grades are knit to specific achievements, I can list those achievements and say that the student has demonstrated that ability.)

For this course, the levels of achievement were the following.

  1. Memorisation.

    This was the student's ability to remember things they had been told: such as definitions and statements of results.

  2. Utility.

    This was the student's ability to use things from the course in the manner in which they are intended.

  3. Adaptation.

    This was the student's ability to adapt what they had been told to new situations, or to join together ideas to build a bridge.

These three levels corresponded to grades E, C, and A. Not every part of every question could provide evidence for all three levels. In particular, one question simply asked for specific statements and so could only provide evidence for an E grade.

Thus at the end of grading an exam, the question was "Of those questions which could provide evidence for a grade, were enough done to that level?".

The intermediate grades (D and B) were very definitely low versions of the next grade up. Thus the qualitative leap was between E and D, and C and B. The distinction between D and C and between B and A was quantitative. So a C-grade student was very definitely C-grade.


In addition to the above, let me link to the scheme of work for the course where you can see what the specific learning outcomes were (together with how they translate in to grades). Exploring that site will tell you more about the course if that's useful to you. There are also links to exam papers (of both types).

I think it is also worth pointing out a couple of additional advantages. The exam was a doddle to write (comparatively), and the number of queries/complaints that I got about grades in that year was far fewer than any other year (with the same course). I have no proof of causation, but it's a very strong correlation!

Lastly, you say

There are plenty of resources for SBG at pre-college levels

so use them! I have the great benefit of being married to a(n excellent) teacher. Every time I hear about some innovation in university level education, I get the same line from her: "We've been doing that for years, it's called XYZ.". Then I get on my high horse and say that of course it's different in university because of ABC. Finally, when I actually try it then I realise that she was right all along and at heart, it really is the same.

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  • $\begingroup$ Thank you for sharing your experience Andrew! This is exactly what I was looking for. I completely agree with your final comment and I have found pre-university resources extremely useful and insightful. Of course, I still want to hear more about experiences like yours that are more closely related to mine. $\endgroup$ – François G. Dorais May 5 '14 at 11:10
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    $\begingroup$ @FrançoisG.Dorais Yes, the point of my final comment was that we shouldn't dismiss pre-college sources, although they often need a little translation to see how to apply them to college-level setups and that's where seeing what others have done (as you are trying to do) is extremely helpful. $\endgroup$ – Loop Space May 5 '14 at 11:36

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