being a good marker as a TA

I'm a new graduate student, and am currently TAing a calculus II class (which covers primarily integration). At my university this involves both marking assignments and leading tutoring sessions.

I feel like I have a pretty good grasp on most of how I should mark & tutor, but the one thing which I've heard opposing opinions on is the 'harshness' of marking, e.g. say a person misuses the De Morgan laws, but consistently, throughout an assignment. How should one mark this? I've seen two schools of thought:

1. hammer them each time they make the mistake so that they will (ideally) never make it again
2. mark off once the first time, but only point out their mistake each subsequent time (provided that their mistake does not make the problem too easy)

I can see advantages and faults in both approaches. I would love your thoughts on which is better, or to hear of a third way if you have come up with one.

cheers!

• You should really ask the instructor of the course how he/she wants you to do this. – ff524 Sep 21 '16 at 20:45
• I have, and I know what their opinion is (and I will follow it), but I want to form an opinion of my own. – C.Mac Sep 21 '16 at 21:01
• I generally agree, and I do try and provide helpful comments as much as my time allows given that I have more than 100 students to grade for. We have a tutoring centre that I also encourage students to go to for extra help. Generally, if a student does below average (which I calculate after I am done marking) on an assignment; I specifically write a comment suggesting they take advantage of the centre and the professor's office hours – C.Mac Sep 21 '16 at 22:17
• Even if you don't take off points each time, you should definitely mark each error. Students may not be reading their graded work linearly or completely and may be misled into thinking that the wrong work is correct. – Adam Sep 21 '16 at 23:53
• Relevant PhD comic (and the previous one too). – dtldarek Sep 28 '16 at 15:56

I personally give homework small weight for such courses. I encourage my TAs to grade fairly harshly, because I want students to be aware when they do not know something, to motivate them to learn the material well. Hopefully for them, that will lead them to study more and increase their subsequent exam performance.

So I would lean to instructing TAs to follow option (1). I'm not opposed to option (2) in cases such as the one you propose, but I find it ends up being a lot of work for minimal practical impact. Because my homework weights are so low, the difference in grades has little appreciable difference on the student's final average.

In your case, as @ff524 suggested, I would ask the lecturer how he wants the problems to be graded. On the other hand, if you would like to dwell on the topic for a few minutes more, here you can find some additional comments...

For a number of practical reasons I prefer the grading method to be composable, in particular, you should be able to use scores from different portions of the exam without the knowledge of what caused/produced those scores (this is similar to how abstractions in software engineering should not leak their implementation details).

This are some reasons why I think grades should be composable. Nevertheless, that doesn't mean you should cut points every time a student repeats the very same mistake. It means that, if your score for each task is represented by a single numerical value, say from $[0,1]$, then the total exam score should be calculated only using those numbers (it doesn't have to be plain sum).
If you want to count an error in some formula only once, then you should make it a part of the score, for example $[0,1]\times\{\mathtt{GoodFormulaForXYZ},\mathtt{BadFormulaForXYZ}\}$, and then you can calculate the total score of the exam using those two values, say sum of the first numbers and $-10$ if there was $\mathtt{BadFormulaForXYZ}$ in any second coordinate.
In practice I don't think I would keep a count for something so specific as De Morgan laws, unless it would be really important for that particular exam. I had used (in computer science course) scores like $(\mathrm{algorithm}, \mathrm{complexity}, \mathrm{proof}, \mathrm{clarity})$. One advantage of this is that I could tweak scoring to reflect hardness of the problems well (meaning each problem would still be worth, say 10 points, but each component could be scaled non-linearly, for example 0.2 alg would give you 1 point, while 0.3 alg could give you 4 points). In a regular math course I could use score with components representing students idea, its execution, and the overall clarity of the solution.