I am working as a teaching assistant in a course that first year mathematics students take. Some students who have maths as a minor also take it.
I run what is called a supervising session in the official translation - guidance session would be more literal translation. I help students who try to solve exercises similar to the ones they are to complete for the exercise sessions. There is no effect on grading or any other incentive besides learning for students to come to the guidance sessions. There are maybe 10 to 20 students (in maybe 6 to 13 groups, though some groups are singletons), and one tutor. I will visit the student groups, moving through them in order. Sometimes I will write a sample proof or discuss something several groups have problems with on the blackboard.
Often the students have several problems. Consider the following, which is very close to a real example, though most attempts are not quite this weak: The task is to prove that if $a \geq 4$ and $b \geq 2$, then $a+b \geq 6$. The student has written: $a \geq 4$, $b \geq 2$, $a+b \geq 6$. Antithesis: $a < 4$. After this the student has done calculations, some of them faulty, to get a contradiction with $a+b \geq 6$. The calculations are simply lines of inequalities without words or implication arrows joining them.
Some of the mistakes: Assumptions and the claim are not clearly separated. The antithesis is wrong. There are mistakes in the calculation. The writing is poor, as it only consists of formulae.
When encountering a student's proof attempt (or calculation) with several mistakes, should I focus on correcting one mistake at a time, or should I point out all of them?
I fear that a barrage of corrections will only confuse the students. On the other hand, correcting only something may not be enough for them to complete an exercise, and I may not guess what issue or which issues are worst ones.
Is there any literature on this, or any best practices?