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I act as a tutor sometimes for students who are self-studying undergraduate-level math. Most of the students have already earned an undergraduate degree in something and some of the students are PhDs from other STEM fields. How do I deal with students who seem to not really be doing the work but seem to be shifting that onto me like "No one ever showed me that?" or "Why do I need to do this anyway?" even though they have proclaimed to wanting to learn?

Here is an actual case study. A student claims to have a PhD in a STEM field and to be a published faculty member at an R1 institution, and to have taught there for 20 years. He wants to learn calculus, differential equations, linear algebra, probability, stochastic processes, and "the equivalent of a math degree" in order to aid him in a research idea he has. He does not want to enroll in school again for some reason. He claims to want to learn how to read and write proofs and make mathematical arguments. He is happy spending several years or so self-studying.

At the start the student said he knew some calculus - up to basic integration. After an assessment it turns out that he did not know any trigonometry, for example, how to solve equations involving logarithms, and that he could not differentiate $f(x) = \sqrt{x^2 + 1}$, for example. He considered writing $f(x) = \sqrt{x^2 + 1}$ as $f(x) = (x^2 + 1)^{1/2}$ as something "not obvious". I think he knew some ideas of math or even advanced math, but could not actually solve any problems or something.

So we spent weeks/months reviewing precalculus. The setup was that he reads sections from a textbook (he picked the book), I assign problems from that textbook, and then we review a selection of those problems. What would happen is that when reviewing the supposedly already attempted problems he would just say "I got stuck" or "no one showed me how to do that" and not have even attempted half of them. At first I was patient and emphasized the gain that could be realized by practicing reading (which he said he knew that fact), but after a while it seemed that he was not really reading closely at all or not reading and working on problems regularly and just started being disagreeable about the problems for some reason.

We finally moved into calculus using a well-known text. For some of the basic problems he did fine. But for some of the true/false style questions or prove-using-the-definition questions he would get stuck and ask "what do I need this for" and be argumentative. I reviewed how to do the questions anyway, but I feel like I am being bs'ed. I mean at the outset he said he wanted to learn to prove things, but I do not sense a genuine interest at all.

The money is good, but this feels wrong to me, like I have to accept some level of bs from him. My feeling is that your education is your responsibility; self-studying is not compulsory. Am I nuts? How do I handle such students professionally? Should I care? It is hard to believe that this was really even a faculty member somewhere.

EDIT After some consideration and after reading the comments here I have decided to drop the student. After some digging around online I see that the student has an MD, not a PhD, and the institution shows only a brief affiliation at a lab for several years in the early 2000s. At that time he was listed along with six others on a publication. He turned out to have a personal website too where he lists himself as a current assistant professor at the institution, but the institution only shows the old medical lab affiliation.

I have also resolved as per the answers to state upfront what I offer, where it might fit with the student's goals, and my expectations, mathematical and behavioral. I think a detailed mathematical plan at the outset is important as well as periodic check-ins.

E2R0NS
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    For me, your last paragraph suggests an answer. Assuming you really need the money, then of course you need to keep working with that person, but to make it easier to not care, perhaps try to find someone desperately interested in thoroughly learning something in math (regardless of level, as long as within your background knowledge) even if that person can't afford much. Then the current person will help with your finances while the new person will help with your mental health. – Dave L Renfro Sep 05 '21 at 17:17
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    "Some level of bs from him" sounds like about 1,000%, if your post is accurate. Personally I would call him out to prove he has the qualifications, work history, and publications he claims. Since all the information is in the public domain (if it is true) that won't be difficult for him. If his real name is Walter Mitty, stop playing games and find a student who does want to learn something. – alephzero Sep 06 '21 at 01:59
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    @alephzero It did to me too, or else he was greatly exaggerating. In any case, I respected the ambition, but lying about how much math he already knew was ridiculous. What's the point? I am just tired of feeling like I have to do the work for him for little respect, I guess, or gratitude. – E2R0NS Sep 06 '21 at 02:23
  • @E2R0NS Has he lied about how much math he knew though? Nothing in your post really suggests that. I agree that his attitude is BS, but I totally buy that someone could get a PhD in a "STEM" field and know very little math. There's only one other major (besides mathematics itself) that I assume graduates will know any math, and that's physics. In any case, I'm sorry you have to deal with this situation! – Thierry Sep 06 '21 at 14:56
  • @Thierry I gave him a standard precalculus assessment of 25 problems and he could only complete 30% of it successfully. I gave him a calculus 1 level assessment and he could only do one problem. – E2R0NS Sep 06 '21 at 17:14
  • @Thierry I mean he can explain the idea of a limit but for infinite limits, say, does not know enough algebra to re-write rational functions in order to simplify them. He has gaps - no problem - but maybe not the real willingness I guess to do the grunt work; instead I think he just pays lip service to it. I mean he does some work, but seems to not be able to handle problems unless an explicit example of it has been shown. – E2R0NS Sep 06 '21 at 17:15
  • @Thierry I believe him that he has a PhD and probably works or worked for an institution based on some stories, but perhaps just as a lab worker or something less demanding. In that way I guess it's possible to get your name on some lab publications. – E2R0NS Sep 06 '21 at 17:17
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    To me, the whole idea of having a "PhD in STEM" is crazy without studying calculus, differential equations, linear algebra, probability. – Rusty Core Sep 06 '21 at 17:21
  • @Thierry It almost felt like the way he treated me sometimes was like he was a mean or belligerent drunk. I'm not saying that he was drunk; only that he had that attitude of a bar patron sometimes, I guess. Maybe he's tolerated by others due to his money or something, not sure. – E2R0NS Sep 06 '21 at 17:23
  • @Thierry He explicitly stated that he could do limits, derivatives, integrals, and had completed courses in calculus and probability from coursera or edx. But then he did not know the unit circle at all. He just seemed all over the place in his statements. – E2R0NS Sep 06 '21 at 17:24
  • @RustyCore The case study student's PhD is apparently in chemistry. I think he earned it at least 20 years ago if his timeline is accurate. – E2R0NS Sep 06 '21 at 17:28
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    @E2R0NS on behalf of chemists, I apologize. In either case, must be a limited field of chemistry that didn't require any maths. Some exotic case of organic chemistry? And even there you get in trouble with quantum chemistry rather quickly. I mean, even the basic thermodynamics or any other physical chemistry calculations requires being comfortable that level of maths and more. Physical measurements themselves are hopeless to understand properly without Fourier analysis knowledge. (for instance; electron microscopy) – Stian Sep 07 '21 at 08:55
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    @StianYttervik Organic chemistry is a huge field, and most of it doesn't require anything more than the four basic operations. Organic chemists usually would have learned basic calc in the past, but often by the time they are PhDs, that knowledge is long gone. You'll need some maths if you're digging into mechanisms and rate equations, but for most 'turning the crank' organic chemistry, all you calculate is how much material to add to your reaction. – Ingolifs Sep 08 '21 at 02:06
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    My god, you still "care"? I hope you have a good support system. This is the exact reason my mother stopped teaching special ed and never above 7th grade; after that the mold is cast, and for Spec ED the mold is broken in the first place; there's no reward. You got paid so that's that. At that age level the rewards will be few and far between and mostly their own accomplishment. – Mazura Sep 08 '21 at 09:50
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    If a STEM PhD can't teach themselves mathematics then they probably don't deserve the PhD either. It's literally a certificate that says "I can learn all by myself now". – J... Sep 08 '21 at 16:20
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    Weren't "No one ever showed me that?" or "Why do I need to do this anyway?" enough in themselves? The rest seems to be justification, which would suggest the miscreants might have a point… though I don't for one moment think that.

    Are there not well-recognised tests for use in "hard" subjects like maths?

     – Robbie Goodwin Sep 09 '21 at 19:57
  • @RobbieGoodwin They really were enough in themselves now that I gave processed this. As for well-recognized tests for assessment if that's what you mean, there are none to my knowledge. – E2R0NS Sep 09 '21 at 23:45
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    @E2R0NS Sorry if I'm rocking someone's boat and isn't "self-studying undergraduate-level math… students already earned (other) undergraduate degrees…" much the same as maths for non-mathematicians?

    Then how could there not be a requirement "… to join the course, first pass this test"?

    I make no suggestion about content except that students demonstrate prior knowledge, capability or both separately from even multiple degrees in other subjects.

    The details above sounded like senior high-school, not the equivalent of a maths degree, which challenges the student's conception of maths…

     – Robbie Goodwin Sep 10 '21 at 20:52
  • @RobbieGoodwin I completely agree now. – E2R0NS Sep 10 '21 at 21:36

6 Answers6

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It sounds like your students are not getting what they wanted from your tutelage; since they are not getting a formal credential from their work with you, their likeliest motivation is that they think additional math knowledge will aid them in their research projects or careers. As you said, the case-study student's objective is to learn the equivalent of a math degree to "aid him in a research idea he has", but he questions the relevance of the material. It sounds like he is slowly realizing that most of the material in a 4-year math degree will not actually be helpful in efficiently advancing his research project. Might you suggest that he does not need a math degree himself but rather a collaborator with math background who can more easily help him separate the wheat from the chaff on his particular research idea?

Here are a few different choices for dealing with your students going forward:

  1. Be up front with the fact that you are offering to tutor a standard course of a given subject and that much of the material will not be directly relevant to their research project / career advancement and only provide unquantifiable 2nd-order benefits such as "general problem-solving skills". This approach is bad for business but cuts to the chase and deters students who will give you a lot of grief later. The students who are still interested might be more likely to actually do the work.
  2. Offer to create a custom curriculum for each student depending on their specific goals. Though highly labor-intensive, this approach would be less like tutoring them and more like collaborating with the students on their own projects (and thus possibly more rewarding than walking everyone through the same trite problem sets?). It could also be difficult to execute well without lots of experience and could frustrate the students if the topic sequencing is not optimal.
  3. Keep doing everything the same way but work on dissociating your personal response from the work you're being asked to do. This is the best option if you are trying to maximize your revenue and ROI from your tutoring activities.
Steve
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  • Great suggestions. I thought I had tried Option 1 with the case study student. I was very clear that I was only a math person and that we would follow the text. Option 2 sounds ideal to me in some sense, but the amount of work would be insane. Option 3 sounds deadoning, but may be necessary. – E2R0NS Sep 06 '21 at 02:18
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    For #2 I would still use a well-structured course, "flying" through the topics he knows and staying longer on the topics where he has gaps. This would be more personalized than a standard college course, and you will cover all the bases. – Rusty Core Sep 06 '21 at 17:34
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    Him working with a collaborator is probably the most practical suggestion in his case. Or to choose a tutor who has experience in his desired research areas. – E2R0NS Sep 07 '21 at 00:58
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I think the real issue here is that you thought you were essentially doing undergraduate tutoring, and you weren't. You were doing adult education, and that is not the same thing.

When someone is in their 40's and has not worked - daily - with math since college...they no longer know any math. They have probably even lost much of their high school math, as you discovered when your student could no longer do basic trigonometry.

If you talk to other people who do adult education for returning students in their 40's, you will discover that they have the same experience(s) you do - odd incongruities between the student's status in life and their knowledge level; often inexplicable gaps in what seems to you to be obvious knowledge or necessary sequences of knowledge; seemingly random patterns of retained and lost knowledge. And, most importantly, "grumpiness" on the part of the student, who is at least as confused as you are by the amount of skill they have lost in this area.

Unless you are prepared to rebuild the student's fundamentals before proceeding and unless you are prepared to tolerate a little curmudgeonliness, you shouldn't take on students of this type.

tbrookside
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    This really isn't accurate. It's why I gave the assessments in the first place despite his claims. Time on fundamentals was not the issue. He had never heard of a unit circle, but claimed to know this material, for example. My guess is that he did not do trig in high school or that it was before the unit circle approach became the norm, nor go beyond trig; he may have just skirted by. It may be that he only thought he knew what he claimed, or had heard the words before, and it really was not exaggeration or outright malevolent deception/lying. – E2R0NS Sep 06 '21 at 23:23
  • As I said he told me had just completed a course in calculus from Coursera or EdX, but if so, did not gain much or do enough work for it. I gave him the assessments in order to figure out a good starting point. – E2R0NS Sep 06 '21 at 23:24
  • The main issue for me is the behavior of the student towards me, I guess. I don't care at what level we start at, but it just felt dishonest in some way for me. Tolerating crap from students just seems wrong regardless, the more I dwell on it. I guess he just did not respect me (the feeling is mutual now). I think I should have thought about my boundaries and expectations more before engaging or just trying to make it right. – E2R0NS Sep 06 '21 at 23:29
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    I don't think anyone should have to tolerate any "curmudgeonliness" from any kind of student, I guess. You'd think that "adults" would understand that more than anyone. – E2R0NS Sep 06 '21 at 23:31
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    I know my polynomial calculus, and that root is something I could have broken down, but actual trig ... bletch. – Joshua Sep 07 '21 at 20:26
  • @Joshua Yeah, this is a common outcome of business calculus level courses where they go through some parts of the subject without trig. The trig might be more useful for the trades or engineering in the beginning I guess is the reasoning. – E2R0NS Sep 07 '21 at 22:41
  • @E2R0NS: I had the engineering calculus and I learned the stuff. There was never any point. Integral tables are a thing. Incidentally, I only used my calculus for optimizing video game strategies. But learning polynomial and exponential calculus sharpens the mind. – Joshua Sep 07 '21 at 22:46
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    This is the best answer. I work mostly with older students as well, and a lot of them are highly motivated, because it's a path they've chosen themselves. They're also highly frustrated, for all the reasons noted. The best thing to do is to be reassuring, and remember that "when am I going to use this?" is code for "I'm feeling overwhelmed and would really like to move on." Help keep their heads up, and try to find problems they can solve. Once you've built their confidence some, you'll find it much easier to get down to the math. – A. Thomas Yerger Sep 08 '21 at 21:26
  • This is the best answer, and your comments, @E2RONS, sort of exemplify that in converse. You're not hearing what you want to hear, and so you're coming across somewhat curmudgeonly! I'm all in my 40s, and had excellent high school/college math - 5 on the AP Calc AB exam, took two years of college-level beyond that. But I doubt I remember almost any trig beyond, maybe, the basic derivative, and I am not even sure I remember that. I just don't use it - and very few people do, outside of math professors or teachers. You forget things as you get older, and it gets harder to learn! – Joe Sep 08 '21 at 21:33
  • @Joe I completely understand that. But I believe this student was not telling the truth about his mathematical background in the first place, either in high school or college, or about his recent courses in calculus by coursera or edx. I mean he may have watched a video, but .... In either case, I can't agree now that it's ever okay for me to absorb negative comments or outright disrespect from students, adult or otherwise, or act as if what he is saying is true when it's demonstrably false. – E2R0NS Sep 09 '21 at 17:03
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    @AlfredYerger I totally agree. But tone and attitude is everything. I also do not accept responsibility for having to answer "when am I going to use this". I mean I do not know, nor does anyone including yourself. But if that's the attitude towards learning, then uh move along. As I think more about this and about all of the thought that goes into gaining the knowledge, organizing the material, thinking about the student as an individual, then the more I think this is wrong in general. If there is no faith or trust, then there is little point. So I guess I'm answering my own question now :) – E2R0NS Sep 09 '21 at 17:10
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    In a mentoring/tutoring/teaching environment, you are the leader, and your student(s) are following. A rhetorical tool you have as the leader of the conversation is refocusing the dialogue. You're allowed to answer "when am I going to use this?" with a question of your own, such as "what's stressing you about this/where are you confused?" or even by just saying you understand that "when am I going to use this" is code for "I'm annoyed with this." You don't have to treat the question as literal - you are allowed to address the underlying meaning and refocus the conversation. – A. Thomas Yerger Sep 09 '21 at 19:06
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Organic chemists are well known for "only needing to count to 4". Sure, they have some math in their studies, but it's really not used for natural products synthetic chemists.

I disagree with the commenter who said to confront the fellow, demanding proof of his professorship. If you really care, look it up yourself. But it's inappropriate to make the lesson an interrogation of him.

I think this person is pretty much a rare case. That said, if you are doing individualized tutoring, you should realize that it's not just the material gaps of your students that will vary, but also motivation, personality, etc. For one thing, he's truly an "adult learner". There will be some differences in how you handle him versus how you handle what is essentially a delayed adolescent (undergrad, not working full time). That doesn't mean you don't want to move him along. But just have a little feel for how people can be different. And still try to bring him along. The "not compromising" gave me an impression you expect everyone to be the same, respond to the same sort of plan.

I wouldn't think of it as "compromising", but just try to help the trainee, given his tendencies. It's not that strange to have a client in physical training, music, etc. who pays for help but does not always practice rigorously.

Rather than getting into an argument (the direct approach) see if you can gently tease/encourage the fellow to do more. Like..."sure, I agree it's boring to do drill problems...and after all you wouldn't want to master things."

Try to come up with some plan that gets the fellow interests and that is not 100% boring drill. Maybe some chemical applications or the like. Or have some aspect of the lesson that is more gamified. Like a 5 minute quiz at beginning. Donno, exactly. Try some different things.

I doubt proofs are a good use of time. He has more basic skill deficits. And it's not well connected to his needs in chemistry (maybe being able to read mathy articles in J. Phys. Chem.)

P.s. I would also encourage you to encourage the student to buy Frank Ayres First Year College Math. It's at about the right level (precalc, with a VERY gentle "intro to calc"). Having something shorter and friendlier versus a bunch of logorrheic doorstops may be helpful for him to refer to. Also, there is a strong emphasis on drill.

https://www.amazon.com/dp/B0007DPVM2

guest troll is also a chemist
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  • Good ideas. By compromise I meant not tolerating repeated rudeness. I get that people are not always disciplined to do the work. That's no big deal. His research interests are a combination of chemistry and something else. Maybe physics or something with probability like making a prediction? Couldn't follow his brief explanation at the time. It was something where he needed a strong math background. – E2R0NS Sep 07 '21 at 00:46
  • Right, it's hard to say if he would benefit from proofs or not. I picked those few problems from the text since he said he wanted to learn that stuff and all the logical notation down the line, but I'm not sure why exactly. I figured that if he eventually wanted to read work in stochastic processes he would need to be able to learn to read math pretty well. Proving that a function is continuous by way of other theorems or by way of the limit definition is fairly standard in Calc 1, so I thought such problems relevant in light of the goals. – E2R0NS Sep 07 '21 at 00:50
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It may be that his style of learning differs from yours. I have an MA in math, and when my son was in high school helped tutor him in math and physics. I always like the "aha moment" in proofs, where the purpose of previous obscure statements becomes plain. My son hates that - when I delivered the punch line he would get upset and say "where did that come from? How did he know to do that?"

He ended up going to college as a film major, changing to physics, and is now completing his PhD in quantum physics. He aced every math course he took in college and grad school (including differential equations, which I hated). He sees math as a tool, and my aesthetic approach didn't appeal to him at all. A more pragmatic approach, where he learned math as necessary to support concrete physics problems he was studying, made all the difference.

rwy
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I enjoy teaching math, I get paid for dealing with the b.s.. If it turns out that there is more b.s. to deal with that I initially expected, my price goes up.

I don't explicitly tell the client that that's the reason why the price is now higher, but I set my price to the b.s. level. So either the client pays me enough to put up with it all, or decides that they don't want to pay my price, and they are free to find some other tutor.

(Oh, and if it's not obvious, my price and willingness to take a particular job vary with my fiscal needs and current work load - Just like everywhere.)

JonathanZ
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You could consider using a less "pure maths" textbook in your tutoring. Instead you could use a maths-heavy textbook more related to their field of study and making them work through the proofs in detail. For example, if your student has a chemistry background you could use a book on thermodynamics and work through the proofs of thermodynamics and equations of state.

Where they get stuck on those proofs you can then turn back to your pure maths books to provide the necessary theorems or techniques.

tranquillity
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    I chose to go with the text the student already had purchased. It was Stewart's Calculus. Hardly a pure math book :) – E2R0NS Sep 07 '21 at 07:13