# Tutoring a recalcitrant/awkward/exasperating student---special needs?

As part of my duties at a GTA, I spend several hours per week in our department's drop-in tutoring center. The center is open to all students enrolled in 100- and 200-level math courses, with the majority coming from Calc 1 & 2. A typical load would be 20-50 students with a roving staff of 5-10 tutors (graduate students/adjuncts/junior-senior undergraduate math majors). As with any good tutoring, our stated policy is to provide help with learning material by explaining concepts, finding and explaining errors, etc; we are explicitly not a "what's the answer to problem #3" service (although difficulties with problem #3 are a great starting point).

I find the work generally enjoyable and have had nearly universally positive interactions with students. However, there is one student that I have come to dread seeing every week.

Said student is enrolled in Calc 1 and is extremely difficult to deal with, to the extent that my armchair diagnosis would place them somewhere on the autism spectrum. Interactions with them are by far the most frustrating I've ever had teaching mathematics, out of literally thousands of students I've tutored over the years. I have gotten so frustrated with helping them that I've had to "tap out" and go for a walk around the building after trying to help them. I'm not the only one either--I've seen every other tutor become similarly exasperated by this student.

## Sample Interaction

For an idea of a sample interaction with this student, consider the problem:

• If $$f(x) = x e^{2x}$$, what's $$f^{(30)}(x)$$?

My usual approach for walking a "completely stuck" student through a problem like this would go like:

1. Can you compute $$f'(x)$$ for me? (Possibly leading to a reminder discussion of the product and chain rules)
2. How about $$f''(x)$$ and $$f'''(x)$$?
3. Do you notice any patterns? Can you predict what $$f^{(4)}(x)$$ will be? Does your prediction hold when we compute said derivative?
4. Can you formulate the pattern you're noticing in mathematical notation?
5. Profit.

Usually the problem clicks around step 2 or 3 and they can take it from there. In comparison, here's how an interaction with this student goes:

Student: [raises hand]

Me [walk over]: How's it going? What are we working on?

Student [computer open to online homework problem, blank sheet of paper in front of them]: What's the answer to this problem?

Me: What have you tried so far? (Again, they have a blank sheet of work in front of them)

Student: I don't know how to compute the 30th derivative

Me: How would you compute the second derivative?

Student: Prime of the prime [we'll let that slide, bigger fish to fry]

Me: Right! Can you go ahead and find $$f'(x)$$ for me?

Student: I know how to do that. The problem wants the 30th derivative.

Me: True! I think we should try to compute the first couple derivatives and see if we can find any patterns

Student: [Lough sigh/uggh, audible across the entire room] Fine. [starts computing $$f'(x)$$, nowhere close]

Me: Hold up a sec--is that derivative correct?

Student: What do you mean.

Me: Well, there's an $$x$$ times $$e^{2x}$$ --

Student: So?!

Me: ...so we need to use the product rule, right?

Student: [crickets]

Me: When we want to take the derivative of a product, we use the product rule. [write $$\frac{d}{dx} f(x) \cdot g(x) = f'(x) g(x) + f(x) g'(x)$$]

Student: DUUHH. I know this. Why are you explaining stuff I already know; I need to know how to find the 30th derivative.

Me: Well, it doesn't look like you used product rule or chain rule to compute $$f'(x)$$ there. Can you try to fix what you have for $$f'(x)$$?

Student: How?

Me: [more detailed explanation of product/chain rules. Look up to see that they have opened a tab for facebook on their computer] Dude...do you want me to help you or -

Student: I know that stuff. I NEED TO KNOW HOW TO COMPUTE THE 30TH DERIVATIVE! [entire room looks up]

Me: [fighting to be calm] Please don't shout. I'm trying to explain how to find the 30th derivative to you. There isn't a magic "30th derivative formula"---we find it by computing the first few derivatives and finding some patterns. [I go ahead and write down $$f'(x)$$ and $$f''(x)$$]

Student: Why are you doing this? That's exactly what I have written.

Me: Well...notice how I have $$1 \cdot e^{2x} + x\cdot e^{2x}\cdot 2$$ and you have just [point at their work] $$e^x$$?

Student: So what?

...[15 more minutes of Abbott & Costello]

...I give up and just give them the answer to escape from this nightmare. Other students are waiting for help.

I have noticed that this student wears a medical bracelet, and there's a few other behaviors as well---things like no sense of personal space, bad personal hygiene, a pronounced facial tic, not looking at me when I'm talking (or looking at anything I'm writing down), etc.

So my question is, in my best Edward James Olmos meets Eric Cartman,

## How do I reach [this] kid?

Myself and the other tutors have come to dread any interaction with this student, and have reached the point that we more or less just give up after a minute and write down the answer in order to placate them for the next 20-30min so we can provide actual help to other students. I honestly struggle to understand how they've made it to the point in math of studying calculus, and sincerely wonder if they've just learned this behavior of being obstinate until they're given the answer. This approach is demonstrably wrong as:

• They aren't learning anything, but are getting credit for it.
• They clearly need help with basic calculus concepts, but absolutely refuse to be provided such help.
• Just giving this student the answer belittles the work of all their other classmates
• Our attempts to earnestly help this student seem to wastes everybody's time, including the other students waiting for help.
• I don't really have an answer to the actual question. However, you should probably talk to whoever runs your math lab. The student's behavior sounds quite disruptive to the other students and more rude to you than you should be expected to take. – Adam Mar 15 '17 at 0:10
• However, as a partial, qualified, "I'm not really qualified" answer: If the student really is far along the autism spectrum, you might try to minimize the number of social cues needed to understand what you are saying. (Go for blunt as possible without actually being rude.) Also, give him a firm and explicit limit on the number of minutes you spend with him. i.e. "I have 2 min to talk to you, then I must move to another student." Set a timer and leave as soon as it goes off. – Adam Mar 15 '17 at 1:27
• What does "You're allowed to 86 students if they're disruptive" mean? – Joel Reyes Noche Mar 15 '17 at 1:47
• Sorry, American English vernacular, meaning to "eject / refuse service." en.wikipedia.org/wiki/86_(term) – erfink Mar 15 '17 at 1:53
• You're lucky to have only 1 or few people like that. I feel like everything you write in your conversation, besides the shouting part, is my routine experience in the tutoring center with a similar set up. – user2139 Mar 15 '17 at 5:39

How do I reach [this] kid?

Let me be blunt: You probably don't. This is a person who is so intransigent that you effectively need to black-tag them. A hard lesson is that you can't save everyone. At this point the priority is to make some kind of defense so you aren't overly stressed, psychologically damaged, or burnt out.

A couple personal reactions to the example interaction: I would not let any minor points slide by. Part of the job is to communicate clearly when someone does not have the adequate basics. When they said "prime of the prime" I would totally stop and ask them for the correct name. When they couldn't find the first derivative correctly, I would absolutely go no further until they had corrected that. When they said, "I know this", I would say clearly, "Let's be honest: you do not know this, because your first derivative calculation was incorrect." (Actually, I pretty much said exactly that each of the last two days.) Points like these are perfect exit spots; "I'll let you work on that and I'll come back".

You should also have the capability of refusing service if someone is rude. For me, if I'm answering a question someone has asked, and they look down at a phone-tablet-Facebook -- then I'm out, game over, the end. (Usually accompanied with an "If you're not interested in my answer, then I'm moving on to someone else..." exit).

I like the idea above of setting an explicit time limit for the interaction and possibly setting a watch or timer to enforce it (hence my "related" link in the comments above). You may need to do that uniformly with other students while the student is in the room so you're not accused of bias (unfortunately). Indeed, other students deserve your time at least as much as this one. E.g., in class I try to limit my interactions to one or two problem-resolutions per person at most (so that I can get to everyone).

On that note, be prepared for the student to complain to some higher authority. Possibly get a shared plan with the other assistants to confirm your experiences if possible. Best of all, see if you can get one faculty member to engage the student and make recommendations to you after.

I have also had (in a decade+ of teaching) maybe one single interaction where a student became completely outraged by my responding to a question by asking a follow-up question (so as to gauge where their understanding started and ended). "You're the teacher, you're supposed to answer questions, not ask them!!" and stormed out of the room. If someone doesn't even get the concept of how teaching should work as a give-and-take, then that's outside the scope of your responsibilities (or maybe anybody's) to fix. Even Socrates himself couldn't deal with that.

• Thank you for your bluntly honest answer. Since posting, my thinking has been shifting towards these lines. Amazing how much soul searching one problem student will make you do (maybe I'm a terrible instructor after all and the socratic method is BS and ...). I really appreciate the pragmatic suggestions, re timer etc – erfink Mar 16 '17 at 1:48
• And yeah..."prime of the prime" and "taking the prime" grates me to no end, almost as much as "minusing two things." Let it slide in interactions with this student, having been down that road before... – erfink Mar 16 '17 at 1:51
• Over time I've evolved more to following my instincts... if something like that really bothers you ("prime of the prime") that's likely a signal that some correction needs to happen. I trust my gut on that more and more. – Daniel R. Collins Mar 16 '17 at 2:22
• Opened a separate question on this point, matheducators.stackexchange.com/questions/12125/… – erfink Mar 16 '17 at 3:00
• "the concept of how teaching should work as a give-and-take" I really like your characterization. I understand it as it is impossible to teach a person to think if that person does not try to think on their own. This is how teaching is different from other types of service: it requires effort from the client. – beroal Apr 11 '17 at 8:30

This is a student who doesn't understand social cues. He only knows that if he is rude you keep trying. If acts disruptive, he will get the answer without working for it. As long as you reward him for being difficult by giving him the answer, he'll have no motivation to change behavior. You are essentially letting him walk all over you because you want to help and don't know how.

I suggest that before you can reach him, you have to teach him to behave. Make a plan with the other tutors. Sit him down with at least two tutors and tell him before you can help him, there are new rules for him to follow because he has been rude and disruptive. Explain what is acceptable behavior, e.g. no Facebook while talking to you, no shouting, etc. Tell him the consequences of not following the behavior - eg the tutor will walk away and help another student if he looks at Facebook, he will be asked to leave if he shouts. Make sure he understands that he can come back when he behaves. If you and the other tutors stick to this plan he will start to behave differently and then you can try to reach him.

• I don't disagree with the underlying advice, which would be appropriate for any disruptive student no matter the reason, but I don't think it's appropriate to compare an (allegedly) autistic adult to a toddler. – Henry Towsner Mar 15 '17 at 14:44
• I certainly didn't mean to offend. I will take out the last sentence so as not to offend anyone. I only put it in because the behavior reminds me of my granddaughter when she was a toddler and didn't get her way. – Amy B Mar 15 '17 at 15:33
• @HenryTowsner edited post and wrote the above comment in response to your comment. Forgot to alert you with your name. – Amy B Mar 16 '17 at 9:30

There are both intellectual and interpersonal issues here. It seems that, in an effort to be professional, you have ignored the interpersonal issues and have tried to focus only on the intellectual ones in the things you say to this student. This has not worked.

Don't try to diagnose the student. He could have autism, he could have ADD, he could have some other invisible disability, or he could just be a person with an unpleasant personality. Instead, just discuss his behavior with him explicitly, using language that you won't feel bad about afterward if you find out he did have a disability.

"Fred, I've been using social cues to let you know that there is a problem with your behavior, but it seems like you haven't understood those cues, so I'm going to be more explicit now."

Go on and tell him what the behaviors are and how he needs to change them. No shouting, no facebook, etc.