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I work in a University Tutor Lab that covers content up to Calculus II. However, when a student in a Calculus III or Differential Equations class comes in, some other tutors and I will still tutor these students if they ask for it.

Moreover, some students in an Introduction to Proofs class and a intro level abstract algebra course have come in for help as well. But some tutors are more unwilling to help these students based on a cut-off point they believe in when it comes to tutoring mathematics.

This is a conversation that often comes up often amongst the tutors. Some believe there should be a cut-off right after Calculus II, while others feel it comes after Differential Equations. Even some believe there really isn't a cut-off point at all. (We only help these students in our free time, but are not required to do so.)

If there is such a cut-off when it comes to tutoring and helping students out with mathematics, where is it or should it be?

I am not discussing the lab's policy, but as educators should we have a cutoff point where we expect students to learn and do mathematics on their own? Or should they be able to seek tutoring at any level?

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    $\begingroup$ This sounds like a policy of your University Tutor Lab, which needs to be addressed with whoever is responsible for the policy (budget constraints? Math Department request? Tradition?). Asking users on a math education site where students should be cut off from tutoring misses the point, unless you plan to write an appeal after exploring the origins of the policy at your specific university. $\endgroup$ – Namaste Apr 4 at 22:29
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    $\begingroup$ @Namaste Shouldn't a question about whether students should be able to expect tutoring at higher levels of mathematics not be in closely related to Math Education? As educators, should we not consider a cutoff or time when we should expect our students to work independently and learn material on their own rather than be tutored or as some may put it "handheld?" $\endgroup$ – Hotdog Apr 4 at 22:38
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    $\begingroup$ Please don't assume that labels like Calculus I, Calculus III, etc. mean something standardized that everyone understands. Does Calculus II mean second semester? Second quarter? Second year? Second year calculus could mean all kinds of different things. $\endgroup$ – Ben Crowell Apr 5 at 3:55
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    $\begingroup$ What do you mean by 'tutoring'? Students should get support, but whether it's appropriate depends on what that support looks like. A high school student heading for engineering can reasonably be shown all the steps to follow, whereas a math major should be expected to do more thinking themselves, with help to work out what to do, not full instructions on what to do. $\endgroup$ – Jessica B Apr 5 at 6:03
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    $\begingroup$ @Hotdog You say "Wouldn't the expected counter-argument to a '"least counterexample" induction' be that if there wasn't a cutoff we should allow graduate students such as PhD students to receive tutoring up until dissertation? ;)" Isn't that kind of the job of a Ph.D. advisor? Also, I work with a lot of postdocs who get "tutoring" from their faculty advisors. I mean, what is tutoring, other than having a conversation with someone who knows more than you about a topic? $\endgroup$ – Xander Henderson Apr 5 at 13:18
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At University of Jyväskylä there is Ratkomo twice a week for some hours. It means at least one faculty member and typically some PhD students wander a corridor with tables and chairs and help everyone with whatever questions they ask. From my limited experience with Ratkomo, must of the students were from mathematics courses intended for the first two years, but some were asking for help with more advanced material.

I doubt there is any level in mathematics where discussing the problem with someone else stops being useful - this is one reason why there is cooperation among research mathematicians, for example.

In particular, since the students could ask about any and all courses, it was by no means certain that the person helping them was familiar with the material, or even if they were, there were no guarantees that they could just spit out a solution. Hence, especially for students asking about more advanced topics, it often became a process of figuring out the solution together. Engaging in this process with a peer or a more mature mathematician certainly remains useful far into one's career.

I believe there is no cut-off as such, but at some point explaining one's problems becomes sufficiently difficult that anyone who understands them and provides helpful insight is likely to become a co-author.

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    $\begingroup$ I agree that discussing problems with colleagues, classmates, or peers is extremely helpful. In my experience, if one discusses a homework problem with a fellow classmate, then that problem should be turned in bearing both students names just as a paper should bear the name of the co-authors who worked on it. But if I receive help/tutoring on a problem from an outside resource, then shouldn't the turned in homework bear their name as well? In my experience, most professors would not want to see the name of a paid tutor on a turned in assignment. $\endgroup$ – Hotdog Apr 5 at 13:42
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    $\begingroup$ @Hotdog That depends on the institutional culture and expectations. I would assume students to work together, and in fact, wish that they do so, but maybe the culture is different at your institute. $\endgroup$ – Tommi Brander Apr 5 at 14:49
  • $\begingroup$ Hotdog Your response in your comment does not necessitate university funding for official "tutoring". How are you defining tutoring? You seem to be lumping everything from university defined job-descriptions of funded and paid "tutors", to peer-initiated study groups, to merely being allowed to consult with one's prof/advisor. This question also applies to you, @Tommi. In the US, "tutoring" centers at universities involve far more guidance and assistance than does "working with someone else" [a peer/professor] to arrive at a solution. $\endgroup$ – Namaste Apr 5 at 16:45
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This is completely up to you to whoever is in charge of this center. There is no apparent reason that tutoring should stop after Calculus II, III, IV or V or something else.

However, what is important is that all of you follow the same policy (and it would be the best to announce this policy publicily). (If you have one a cut-off point, you could fix one hour per week where you answer questions beyond your cut-off point.) If there is no coherent policy, students are likely to complain.

When discussing which policy to use, keep in mind the following questions: - In which courses students struggle most? - Do you have enough time for low-level courses and their questions if you allow questions to, say, abstract algebra? - For which courses are the tutors qualified?

What I don't quite understand: why is "Introduction to proofs" only after some other courses in your university? Do people not do proofs the first few semesters?

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  • $\begingroup$ For clarification, a student cannot take Introduction to Proofs until they have taken and passed an undergraduate Linear Algebra course which some students take concurrently with Calculus II or the semester after. I listed it after simply because it is a different type of math class than the calculus sequence that most students look for help for. $\endgroup$ – Hotdog Apr 4 at 21:54
  • $\begingroup$ So Linear Algebra is without proofs? What do you do in those courses? $\endgroup$ – guets Apr 4 at 21:58
  • $\begingroup$ As guets suggests, there is likely, in an ideal world, no cut off point at which tutoring must absolutely stop. But tutors at universities are often paid by supplemental instruction fees allocated to give the "biggest punch" for the dollar (of such funding), a utilitarian decision of sorts. That's not to say that you shouldn't tutor other students, but probably not on the time or dime of the tutoring center, but rather on your own time. $\endgroup$ – Namaste Apr 4 at 22:35
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    $\begingroup$ @guets The majority of students in the undergraduate linear algebra course are computer science and applied math majors. This is usually the first time some students see matrices or vectors, and covers row operations, solving systems, determinants, vector/null/solution spaces, eigenvalues and eigenvectors, nullity and rank, and various other topics. Based on the makeup of the class, most professors tone down the proofs in the course to sketches rather than rigorous proofs, since students haven't taken the proofs course or probably never will. Granted some professors do more proofs than others $\endgroup$ – Hotdog Apr 4 at 23:20
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    $\begingroup$ @Hotdog: I am not quite sure what you mean by tutoring. In my view, a tutor is someone to ask questions about the material, who you can ask about the material, who goes with you over the material, so someone who helps you learn (like office hours would do). Even on the P.h.D. level, students can (and should) ask questions to their collegues/professors. What does your tutoring center do exactly that you say it makes the students not independent? $\endgroup$ – guets Apr 5 at 6:27
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There's no cutoff point after which people, students or not, should be expected to learn and do mathematics exclusively on their own. I'm a mathematics professor, and I have no qualms about "receiving tutoring" - that is, asking other mathematicians about when I'm struggling to learn something new.

Your center might, of course, have a cutoff for any of a number of practical reasons, but there's no pedagogical reason that there's something wrong with helping students after a certain point.

The flip side is that there's no level at which students should be working entirely with tutors: students at all levels should also be working to understand material independently. Students in Intro to Proofs shouldn't be "handheld", but students in Calculus I shouldn't be either.

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  • $\begingroup$ So you are defining "being tutored" as "not being expected to learn and do mathematics exclusively on" one's own? That's hardly a standard definition of "being tutored" or tutoring, now is it, in any standard use of "tutoring" centers? $\endgroup$ – Namaste Apr 7 at 3:31
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    $\begingroup$ @Namaste: No, I am not defining tutoring that way, and that is not a reasonable interpretation of the words I wrote. $\endgroup$ – Henry Towsner Apr 7 at 15:27
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As others have said, for a broad definition of tutoring, there really isn't a point at which anyone at any level should be completely alone. However, in the more narrow sense of a university tutoring lab, there is some point at which this is just not the right venue.

At some point, students need to get used to talking to professors directly, and not just about grades. (Also, their peers.)

If they are taking upper level courses, they are likely majors or minors in math or a related field. They are going to need letters of recommendation and to develop personal relationships. They aren't going to get that in the relatively anonymous tutoring lab.

Of course, you also have the practical question of whether or not they can get good answers for advanced questions from the staff of the lab. I remember being one of the only people both willing and able to answer these questions when I was in grad school. A fair number of the tutors answering the factoring questions were only a class or two beyond that material themselves.

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