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For many years, I've been an instructor for lower level undergraduate math classes (precalculus through calculus III). During that time, I've noticed that the vast majority of problems I assigned were mostly computations rather than proofs. I gained a lot of expereince teaching these classes and gained a sense of how to grade computationally focused problems.

However, now I'm teaching an advanced mathematics course (linear algebra) with both computation and proofs as significant components. I feel that proofs should be graded somewhat differently from how computations are graded, but I can't seem to put my finger on how.

What are some useful strategies for grading proofs and how do they compare to (or differ from) grading computational problems?

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  • $\begingroup$ I have some thoughts about the question posed in the actual body of your query, and will write up an answer later. But regarding the simple question posed in your title: "YES!" $\endgroup$ – Brendan W. Sullivan Sep 16 '14 at 18:46
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    $\begingroup$ Computational problems are easy to grade: with a little experience, one can scan the thing and assign an accurate grade. Proofs, by contrast, have to be actually read carefully, and if the students are to learn, one has to make detailed comments. I have not found a way to bypass this process and do a decent job. $\endgroup$ – André Nicolas Sep 17 '14 at 6:00
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I can't speak to linear algebra, but I did teach standard Euclidian geometry where it was almost all proofs. Many of the exercises were tantamount to the most recent proof, but drawn in a different way. Made for a horrendous marking load.

Basically I treated much like I would an essay. (I also taught lit in this school...)

I would do the proof myself.

My normal score for a problem was 1 point per line.

So I would look at the student proof.

Often there were several ways to go about it, and there was a certain amount of changes in order possible. All the stuff present and in the right order -- Full marks. Missing stuff -1 per line. Out of order -1/2 Correct step, but incorrect reference to justifying theorem -1/2 Clever alternative use +2. Clever use that was shorter too +3.

I would start by grading the 3 smartest kids in the class. That would catch my own mistakes.

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  • $\begingroup$ +1 for the last sentence. $\endgroup$ – Taladris Sep 17 '14 at 5:42
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When teaching Linear for engineers, I grade the proofs very similarly to the computations; the proofs are simple enough that there is only one reasonable way to prove it.

I write out a proof, break it in to 2-5 core ideas, and assign point values in a rubric.

Grading proofs in more complicated classes is very different, to me. It is not linear, but when grading the intro proofs class (and any class where serious mathematical students might have to write proper proofs for the first time), I placed a lot of emphasis on rigor, rather than problem solving. Students need to learn how to formally argue, which is a big mental shift for many of them.

But I have only been teaching for a few years.

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