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I taught Calculus 2 at my institution the past two semesters and several students have left comments in their course evaluations that advocate grading homework problems based on whether they were completed, not whether they were correct. For instance, when asked, "What changes to the course would you recommend?", one student wrote:

grade homework on completeness and not correctness because we are putting in the effort even if we don't necessarily understand it yet

I think they have a good point here. I view homework as required practice of the course material. Furthermore, I've realized that grading every problem carefully for correctness is prohibitively time-consuming for me!

I would like to implement a new grading scheme next year wherein homework problems will be assigned and I will give a grade based on whether they were done, and add some helpful comments about what students should work on. Ideally, everyone will get just about full credit on this component of their grade. (Perhaps someone will skip an assignment during a busy week, but if someone actually puts in effort, they will get credit.)

However, I'm not sure how to synthesize this new idea with the overall grading scheme. Previously, I made homework assignments were 15-20% of a student's final grade. It feels strange, though, to essentially make this a "gimme" portion of their grade just for doing the problems. But if I lower this to 10%, what should I do ... Have another in-class exam? That eats up class meeting time. Have regular quizzes? That also takes up some time, and should I grade those carefully on correctness, even though the students are not used to that? Should I have a once-a-month "take home exam" that amounts to being a difficult homework assignment of sorts?

Essentially, my question boils down to this: I fully intend to take these students' suggestion and assign regular homework problems to be graded solely on completion, and not correctness. I am curious about how to modify the rest of my grading scheme so that the students' final grades are still accurate and fair, and without too much extra class time taken away.

I am interested in personal suggestions/anecdotes here, as well as any education research (if there is any). I am particularly interested if you have made a similar change and can explain some observed differences in the two schemes.

(Note: There is a great answer here to the question, "Is it worth grading calculus homework?". My question is not the same; I have already decided to implement this "grade for completion and add suggestive comments" method, partly based on that answer I linked to. I am curious about adjusting other components of the course to account for this decision.)

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I would find it unacceptable to give a 100% mark to a solution which is incorrect. An utter gibberish submission should get a lower score independent of students efforts. Where's the line between hard work with errors and lorem ipsum with a note "I don't understand it"? If you distinguish between these two, then you do include correctness in your grading. –  dtldarek Jun 5 at 22:53
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@dtldarek: I would consider gibberish to be equivalent to a non-submission. I won't just be reading to see that they wrote something but rather that they wrote something relevant. –  brendansullivan07 Jun 6 at 2:12
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If you do not assign grades based on correctness, then this necessarily makes your grades less accurate and fair as measures of performance in the class. I think a better way to address the student's objection would be note that effort will be correlated with correctness, so it will be rewarded even if grading is based on correctness rather than effort. –  Trevor Wilson Jun 6 at 6:31
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@TrevorWilson: That's circular---it assumes that how correct their answers are on the homework is part of their performance. One could instead decide that homework correctness isn't meaningful (it may reflect people who learn quickly rather than people who ultimately learn the mateiral), and that performance on the class means how much they can do on exams or other assignments which come later when they've had more time to absorb the material. –  Henry Towsner Jun 6 at 14:05

4 Answers 4

There's a compromise between "correctness" and "completion" called "Standards-based grading". Here's a few links about it with various people who have tried using it for Calculus: http://blogs.cofc.edu/owensks/2014/01/08/sbg-calculus2/, http://alwaysformative.blogspot.com/p/standards-based-grading-implementation.html, http://speced.fivetowns.net/lcs/content/Standards%20Based.pdf, http://www.computer.org/csdl/proceedings/fie/2012/1353/00/06462211-abs.html

You can implement it in a variety of ways, but the general idea is that associate all problems you give in the course with one or more "standard(s)" that you expect students who pass to achieve, and you give students (effectively) infinite attempts to "pass" each standard. In general, this means that, for students who don't need the extra practice, they can do very few problems, but for the students who need significant practice, they can keep on trying until they're solid.

Often, courses that use SBG do it on exams too, but you could probably only do it on the homework if you wanted. And you can still give students significant credit for attempting the problems, but this way, still making the homework a "gimme"--they still have to try, but only until they get it.

One clear concern here is the overhead of keeping all this information (since you now need to record which standards students are passing, possibly review more [but smaller!] batches of hw, etc.). In general, I think the benefits outweigh the extra overhead though, particularly, because there should be (a) fewer grading overall and (b) more significant learning overall.

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My standard breakdown for calculus courses is:

  • 10% total for homework outside of class (on a 0,1,2 scale: 0 means they didn't turn it in, 1 means they turned in a partially complete assignment and 2 means they turned in a complete one)
  • 15% total for two or three (depending on the size of the class) problem presentations on which I call pairs of students randomly to present a homework and they are given a few "I didn't get that one" kind of chances during the course of the semester
  • 15% for each of three midterms that are 90% based on homework or simple extensions of the homework and whose remaining 10% are somewhat different that what they've seen (e.g., more theoretical, repeated application of the same method)
  • 30% for a final exam

In the end, with this kind of break down, the median grade for a typical calculus course of mine is a B-, which is where my department would like it to be.

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How many students are in your course, on average? How do you assess/keep track of these "problem presentations"? –  brendansullivan07 Jun 5 at 19:14
    
Each section of calculus where I am has between 20 and 30 students. I assess the presentations using a rubric that they know about beforehand, part of which is peer evaluation (I hand out index cards and ask the students in the audience to answer three standard questions for each pair which then goes into the evaluation of the pair -- this could be done more quickly if you used clickers). You might think: this is so much work. But the homework is done via WebWork, so I've essentially replaced homework grading with presentation grading. –  ncr Jun 5 at 19:22
    
@ncr call on students randomly with or without replacement? I can see major pitfalls to both. With replacement - some students are never called on, without replacement - previously called on students stop working. –  MHH Jun 11 at 17:01
    
@ncr I created a new question for this, that you can see here matheducators.stackexchange.com/questions/2651/… –  MHH Jun 11 at 17:39

You should ask yourself what the homework is for (check they do work, check they can do the problems correctly, ...), and grade according to that.

In my Discrete Math class I give many (some 6 to 8) homework problems, which check if they know how to work carefully on problems related to what is seen in class. This is 30% of the grade. With the TAs, we select 3 problems each week. One is to be solved by the TA, asking for input from the class; one is solved by the class, perhaps asking the TA for guidance; and one is solved individually, graded as turned in or not. This is 5%. And a midterm (30%) and a final (35%).

In homework they have time, and can consult external sources and use whatever tools they want, grading is according to work done carefully and completely. What I want is that they understand what they turn in, even if they got it off MSE, so a "random" selection of students get their grade from explaining to the TA what they turned in, not by grading what was turned in. The sessions with the TAs are geared towards not having them cram the day before the exams (which has shown time and again leads to a masacre), the exams are meant so see if they understand the material (apply it in situations at most mildly ouside what was seen in class/homework, do not ask for careful development but e.g. just explain how to set up or solve a problem, or why something is done a specific way).

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I've had professors do a hybrid approach. A small set of problems would be graded and returned with detailed comments on errors. This was to help us know if we were understanding the material well enough for the exams.

A larger set of problems would be turned in and graded mainly on completeness. This was to encourage a lot of practice, which, despite everyone's best intentions, just doesn't happen unless the work has to be turned in. We knew in advance which set was which, and we received solutions after-the-fact for both sets.

To answer your main question, homework was still 15-20% of the grade. Each graded answer was a larger portion, but I didn't hear any of my fellow students complain about that. (Although, perhaps the ones who didn't do well on the homework didn't have the math skills to figure that out. evil grin)

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In a class I took we had weekly homework. Four questions, only one was graded (announced on turn-in), all solutions where published. Cuts down on grading, but requires equally hard/interesting problems. –  vonbrand Jun 6 at 11:27

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