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Need some advice on tutoring

  1. Jul 28, 2005 #1
    Hello, I am tutoring someone Calculus 2 and I am desperately needing help at the moment.

    Alright, I try to be clear to this person as much as possible.

    We're taking derivatives of natural logarithms and exponentials, and we're also integrating functions that will lead to a natural logarithm answer. So I began working problems with the person. I work the problem on my paper and he works the problem on his paper. The deal is, I am trying to show him how to work the problem.

    He looks at my paper while I solve the problem and also try to explain as I solve the problem. We do this for awhile, and so I decide to see if he can solve the next problem by himself. He couldn't even make a dent in the problem but only a dent in the paper with his pencil writing what he thinks is solving the problem. So I simply explain to him as clear as possible the first step. Well, then he has no clue how to do the first step. So I show him on paper how to do the first step like how I was showing on my paper earlier on solving a couple problems. The 1st step is done.

    Then I explain to him in words, the 2nd step. I throw a couple word hints out there for him to catch and use. Well, it doesn't work. He always writes things down wrong, and always says things backwards. For instance, I say "divide by x", he'll mumble to himself, "hmm,,,divide by y" and I'll correct what he says. But the thing is, he divides by x in the first place. However sometimes I'll catch him not doing what I am clearly stating to do, but he would do something different. In his mind he will alter what I told to him and do exaclty on the paper his "altered statement" of mine.

    There was one problem, I could of sworn we stayed more then enough time on. And it was all Algebra simplification after doing the calculus.

    It got to the point where I just gave up in trying to help him understand. So I whipped out my pen and paper and I would do the problem and explain every step of the problem while working the problem myself. He would simply follow along. He doesn't even look at my paper while working the problem, he actually does it with his eyes on his paper. Getting almost exactly what I put down, with almost no errors (Unlike he was doing earlier where there was an error in every thing he said, and put down on paper)

    I figured since the guy had a problem with listening to my clear statements for solving the problem, that he might be a visual learner. I go about showing him how I work various Calculus II problems on paper, and he goes about following what I did on paper. This goes on for awhile, and I became convinced he might have actually gathered a couple of essential tools for taking the integral and taking the derivative of various Mathematical Equations.

    So then I stop, and I say to him, "Okay, let's see if you can work this next problem by yourself without my intervention"

    So I kind of look off into the other direction, because I certainly don't want to intimidate him. I can hear his mumbling and I occasionally glance over at the paper and I can tell he is thinking really hard about this problem. He gets no where with the problem. In fact, I look on the paper and it looks as if he took a completely alien approach in which he magically divided by 5 which was completely irrelevant to solving the problem.

    When we are done doing the derivative or taking the integral of an equation, it's all algebraic simplification from then on. So I let him do the algebra simplifying by himself, since it is more important that he learn how to take the derivative and integral of particular functions. I can literally wait 2 hours, look at his paper and spot his first mistake at the beginning step of algebraic simplification. He started from that beginning step to the end of the last step of algebraic simplification with his whole paper full of nonsense simply due to his 1st mistake and the various multitude of illogical actions where he'll put a plus sign right in between two quantities that are supposed to be multipying to each other. Just the many examples of the various mistakes he would make.

    I ofcourse was almost shocked as to how this guy is in Calculus 2. It turns out he had a tutor in Calculus 1 that actually quit in tutoring him. I can almost imagine he had a tutor in Pre-Cal, Trigonometry, Algebra 2, and Algebra 1. Another thing is, I am not getting payed by him to tutor him. I am getting paid by the College. His Calculus 2 teacher whom was also his Calculus 1 teacher convinced me to tutor him. Interestingly, the guy gets a tutor to work with him all Semester, he fails the Final anyways. But because he had a tutor working with him all semester, he passes the class! That's my Theory behind this person!

    So, I feel bad for the person, and I am nice to him. I almost good friends with the person. We can talk about movies, music, and food.

    So let me ask you guys. Anyone have any suggestions as to what else I can do to maybe get some Calculus 2 knowledge in his head? Knock him out, cut his head open and stick a Calculus 2 book in? Then sew the head back together?

    I havn't looked up characteristics of Dyslexia, but I seriously think the guy has some amount of dyslexia.
  2. jcsd
  3. Jul 29, 2005 #2
    My way is simple, let him speak!!
    Force him!!
    You give him the problem and say: "Now try to solve it and tell me the theoretical reasons of everything you write on the paper."

    I think you must intimidate him, because there are some doubts which our mind would rather hide, instead of facing them.
    It can be noticed in some teachers, mainly women, when asked a question they look embarassed, try not to answer, and the reason is that your doubt is their own doubt, too! It's been so since they were student, but they avoided to face it, that's the difference between a good and a bad teacher.

    Then, if he is not interested in understanding the subject in depth, let him down.
    There's an italian saying: "Patti chiari, amicizia lunga" = "Clear pacts, long friendship"
    Last edited: Jul 29, 2005
  4. Jul 29, 2005 #3


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    It might be worth it to take the time and teach him algebra before continuing with calculus. It will take time, but it is a necessary tool to understand calculus, and he doesn't seem to be able to use it.
  5. Jul 29, 2005 #4


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    I like Maxos' idea: 'My way is simple, let him speak!!
    Force him!!
    You give him the problem and say: "Now try to solve it and tell me the theoretical reasons of everything you write on the paper."'

    It might help the student if you also require that HE verbalize what YOU are doing as you show him how to solve an example. To start with, don't just write the problem out with him watching, but verbalize yourself exactly what you are doing and have him parrot it back. For the next example encourage him to verbalize himself while watching you.

    And, of course, insist on him doing a lot of exercises himself!
  6. Jul 29, 2005 #5

    Tsk,tsk, never ever, divide by a variable :smile:
  7. Jul 29, 2005 #6


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    I agree. I tutor people at a local community college and many of them do not want to do the work required to solve the problem. I usually just put it in their lap and let them run with it (i.e. let them think about the problem as best they can). That way I can see where they might get hung up on a problem
  8. Jul 29, 2005 #7


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    I have a form of dyslexia and I certainly have a different 'style' to approching problems in comparison to most my peers, but actual mathematical process is not often afected by dyslexia, rather reading the problem correctly and being able to put the answer down without any 'silly mistakes' (things you know are mistakes when you reread them).

    I'm by no means a professional tutor but I do help a lot of fellow students and in some cases probably help them pass the course. I would agree with the above statements of getting him to vocalise what he is doing. I often get people to attempt problems no matter how much they say they have no idea, when their problem solving skills are not enough just too eventually find the solution I show them how to solve it using their ideas as much as possible. Then I get them to solve a similar problem talking to me about how they are doing it and again if they get stuck I show them again. I then repeat this step over and over again until they either have it perfectly (in which case I’ll repeat it again next time we meet up) or doing anymore looks like it wouldn’t help. Then I move on to the next topic.

    But I suppose I have the advantage that being on a degree course and being at a good University they already must have some natural talent for doing maths.
  9. Jul 30, 2005 #8
    Thank you guys for the advice and suggestions. Today I tutored him for 3 hours, and well this time I think we made some progress.

    We worked alot of Integrals and derivatives of Hyperbolic functions. As well as integrals of rational functions that lead to a trigonometric function or hyperbolic trig function as the solution.

    Today I finally found out what to do in allowing him to atleast work out the integrals and derivatives by himself. In the Textbook, there are integral formulas and derivative formulas for all cases of a particular Hyperbolic functions or Trigonmetric functions. Well, today I showed him that if you go by those formulas directly, there is absolutely no way you can get the integral wrong. Just go directly by the particular formulas and you'll be just fine.

    I also told him that, "it will be inevitable that you will make some mistakes when following the formula". However he will have a better chance of getting the solution if he does. Today it wasn't as difficult as the other days. It turns out he can follow the formulas quite well.

    You see, being me I don't memorise these formulas. I am able to derive the formulas myself with no reference. Nor do I ever really need to derive the formulas. However this guy is not willing to learn that way, in which I never intended to teach him that way anyways. The other way is to memorise how to take the integrals and go about them. This guy simply is not in the position to memorising anything that goes on. Luckily the teacher will let him use a huge cheat sheet that he will beable to put all those formulas on the sheet. So far, this is his best chance to passing. I let him go about taking integrals and derivatives of hyperbolic functions and the sorts, while following the formulas put in the textbook. I did not have to intervene very little as much as I did the other days.

    Here our some examples of the formulas im talking about.

    [tex] \int a^u du = \left(\frac{1}{ln(a)} \right)a^u + C [/tex]

    [tex] D_x [log_a |u|] = D_x \left[\left(\frac{ln|u|}{ln(a)} \right)\right] = \frac{1}{uln(a)}* D_x [/tex]

    [tex] D_x [sin^-^1 u] = \frac{1}{\sqrt{1-u^2}}*D_x [/tex]

    [tex] \int\frac{1}{\sqrt{a^2 - u^2}}du = sin^-^1\left(\frac{u}{a}\right) + C [/tex]

    [tex] D_x [sinh(u)] = cosh(u)*D_x [/tex]

    [tex] D_x [sinh^-^1(u)] = \frac{1}{\sqrt{u^2 + 1}}*D_x [/tex]

    [tex] \int\frac{1}{\sqrt{a^2 + u^2}}du = sinh^-^1\left(\frac{u}{a}\right) + C [/tex]

    The only thing he needs to beable to figure out is what his "u" is going to equal to interms of x, so that he can then take the derivative of u and solve for dx. That way he can plug into the original integral that is interms of x and dx, with what dx equals in terms of du, and replace what he substituted for u, with u into the original integral so that he can simply abide by the integral formulas above. Though he often picks the wrong thing for what u equals to. I told him to look at the integral formulas to see where his "u" is located at, and take a look at the integral problem he is working with and see where that "u" should be according to the integral formulas above.

    A big disadvantage here is that he is taking this class now during a Summer Semester. That means they have to cover alot within one month. His Calculus 2 class is 4 hours long, therefore they cover alot in just one day. So we got a bit behind when it came to tutoring him. Since I can only tutor the guy one hour a day for four days. The College is not willing to go further for they simply do not want to pay me much. He has to pay me if he wants to be tutored more after the 4 hours is up. Everything is beginning to look alot brighter now however.
    Last edited: Jul 30, 2005
  10. Jul 30, 2005 #9
    good for you, buddy.
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