Advice for math tutoring

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mmx49
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Advice for math tutoring

Postby mmx49 » Fri May 16, 2008 7:54 pm UTC

I'm about to start a job at college as a math tutor, and I haven't really tutored anyone before. Y'all are pretty smart folk, so are there any tips I could keep in mind to help me be a decent tutor? Thanks!

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Re: Advice for math tutoring

Postby Robin S » Fri May 16, 2008 8:15 pm UTC

I don't have a huge amount of tutoring experience, and what I do have is one-on-one (though I've got a three-week placement at a high school in a month or so). I can say, though: don't try to go to fast, and ask every so often to see whether people have questions, because otherwise they might be too embarrassed to ask. These may sound obvious, but it's still important to keep them in mind.
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Re: Advice for math tutoring

Postby Yakk » Fri May 16, 2008 8:29 pm UTC

How is your empathy?

In general, teaching one-on-one is insanely easier than teaching one-on-many.

Have a clue what the person already knows, what they need to learn, and make sure you understand the subject material well.

What level of math are you tutoring?
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mmx49
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Re: Advice for math tutoring

Postby mmx49 » Fri May 16, 2008 9:19 pm UTC

I shouldn't be tutoring anything above Calc III, and as far as I know it'll be mostly injective (I'm so sorry...).

I think my empathy is all right, bad jokes aside. Thank you for asking; I've been worrying about the, er, educating side of teaching/tutoring, and actually almost forgot about that aspect.

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Re: Advice for math tutoring

Postby Yakk » Fri May 16, 2008 9:46 pm UTC

By Calc3, I assume you mean the first ~12 months worth of post-high-school calculus?

Are you confident that you understand that material backwards and forwards? Remember, in some institutions what different branches are taught is different (ie, science calc 123 can be different than engineering calc 123 or math calc 123. Arts students get calc ABC instead for obvious reasons...)

That can trip you up. :) But it might not apply.

Presuming you know the material backwards and forwards, the next problem is understanding that the people you will be helping won't. They will probably be missing prerequisite knowledge to understand what is going on.

They will possibly be perfectly willing to smile and nod as you blow through the examples, and still not get it.

I'm presuming we are talking about remedial tutoring -- it, tutoring for people who are having problems?

Will your calculus involve proofs, or is it more engineering number-hacking?

Insist that your subjects come to the session with their notes and their textbook. Often the problem will be "solve the problem using the tools the student has" instead of "figure out how to solve the problem".

Try to teach a rough pattern of approach. Simply saying "using technique X, the problem is easy", and watching them solve it using technique X, often won't help: the hard part to some is figuring out which technique to use.

Try to figure out how the person you are teaching learns. Some people learn abstractly, some people learn concretely. Some people best soak things up kinetically, others visually, others like to hear it. People who like to learn via smells are probably screwed if they are trying to learn calc 3.

Teaching via multiple methods sometimes helps. Giving both an abstract approach and a concrete approach, and noting how they connect, can help people bridge between them. Using visual, audio and kinetics to describe things can help someone get things that they might be having problems with.

The empathy thing is important -- you want to be able to pick up on when the person you are talking to gets confused, and know when to give and take your educational conversation. It will be really easy to blast someone with a wall of knowledge and don't give them a chance to soak it up.

Having a white/black board rocks. :)

Have you taken any educational psychology courses? Or been exposed to them? Dunno if they help, but it would make most of the above blather rather redundant. ;)
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

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Re: Advice for math tutoring

Postby kira » Sat May 17, 2008 1:35 am UTC

I think the best advice anyone could give about teaching math is to prepare in advance. If you have a way of knowing what part of the text they are covering each week (maybe a copy of the syllabus?), you'll be able to go through and at least glance at the content.

The point of this exercise is not to refamiliarize yourself with the problems. The majority of the problems you'll be approached with will probably seem trivial - that is the problem. It's extremely helpful to go back and think through the problems as if it were the first time you saw them. What steps are you supposed to do (that, of course, you skip because you know how to do them)? Try to write out at least one complete problem from start to finish showing all your work.
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Re: Advice for math tutoring

Postby btilly » Sat May 17, 2008 3:22 am UTC

Two points that I would like to emphasize since they cannot be emphasized enough.

The first is that people who think their problem is that they don't understand X are usually wrong. Their problem is that they have an incorrect notion of Y and Z that they will need to fix before they can understand X. Furthermore they think they already understand Y and Z and may resist backtracking. But you need to get them to understand the basics.

The second is that our culture has an incorrect belief that simple is the same as easy. They are not. Our brains are wired to work in particular ways, and piling simple notion on top of simple notion in a big stack like we do in math is not one of those ways. I like to point out that it is easy for us to recognize people but very hard for us to add a list of 10,000 numbers correctly. But the first task is very complex and the second one is simple. Math is a very simple but hard subject for people. So if you don't get something, it is probably simpler than you think. And when you realize that something you had trouble with was really simple, that's a sign that you're human, not stupid.

If you can encourage people to develop really solid foundations, and to have patience with their own difficulties, then you'll have gone a long way towards making them not really need you any more.
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Re: Advice for math tutoring

Postby mirashii » Sun May 18, 2008 4:37 am UTC

My only advice for tutoring, is that never in tutoring mathematics should you, the tutor, be holding the pencil and writing. A professor and head of the math department at a college I attended briefly was big on this, and I learned that it truly is great and worthwhile advice.

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Re: Advice for math tutoring

Postby MostlyHarmless » Sun May 18, 2008 6:12 am UTC

Always ask them if they understand what you just went over, but don't stop there. The problem is that a lot of people think they'll sound stupid if they still don't get it after your explanation. I tutor five high school students on a regular basis, and after a whole semester four of them still say they understand everything, even though I know they don't. I think the way to get around this is to ask them if they understand, and then when they say yes, tell them to do the next example for you. Other than that, the advice other people gave seems pretty good. I don't know about never holding a pencil, though. There are way too many times when I want to draw a picture or show a simpler example. What I do is make sure we both have a pencil and some paper. They solve the problems on their paper, and I scribble on mine to try and help explain.

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Re: Advice for math tutoring

Postby mmx49 » Sun May 18, 2008 8:29 pm UTC

Thank you all for your advice. Like I said, this is all quite new to me, and I just want to make sure I'm actually helping people. Thank you. :)

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Re: Advice for math tutoring

Postby Something Awesome » Sun May 18, 2008 11:09 pm UTC

Have your tutee explain his thought processes, step-by-step. That way, you get opportunities for both positive reinforcement of correct thinking and you can pinpoint more precisely what they don't understand.

Also, I believe these have been previously stated, but always be patient and let him do all/most of the work; it's his homework, after all. It's not always as easy as you expect, but he won't learn nearly as much if he's just watching you do his work.

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Re: Advice for math tutoring

Postby Fafnir43 » Sun May 18, 2008 11:29 pm UTC

One thing you might like to try, if the situation allows it: as a student, I've been in a few situations like the following:

Supervisor: *Extremely fast explanation*
Me: Erm... Sorry, could you explain that again?
Supervisor: Sure. *Infinitesimally slower explanation*
Me: OK... I guess... *clueless*

The problem here is that even if someone doesn't quite understand something the first time and actually asks, if they don't get it the second time they're almost certain not to ask - especially if you're in a one-on-two or one-on-three environment rather than a one-on-one. One possibility here might be to go exceptionally slowly - not quite at an insulting "and a minus times a minus is a plus, so..." level, but almost - and wait for your tutees to ask you to speed up. Obviously you'll need to let them know it's OK to do so at the start of the session, but it's much easier to ask someone to speed up if you're happy with the material than to ask them to slow down if you're not. I suspect the end result would be that you get slightly less covered than you otherwise would, but your students go away much happier with what they've learned.

Of course, I have no teaching experience, so feel free to take that with a wagonload of salt! :-)
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Re: Advice for math tutoring

Postby Herman » Sun May 18, 2008 11:43 pm UTC

As far as I know it'll be mostly injective (I'm so sorry...).


Ahhhh! Hurts... so... much...

Okay, some advice:

By far the quickest and easiest way for both the student and you to get through the session is for you to do each problem, and for them to copy what you did. DO NOT DO THIS!! Make it clear that you will not do this.

In my experience, more students seek help because their teacher is not effective than because they aren't good at the material. Often, if you clear up one or two ideas, they can happily go right through the homework.

If they use certain words or notations, use them too even if you don't like them. You're not writing a textbook, and being rigorous and correct about terminology isn't the highest priority.

Be on time.

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Re: Advice for math tutoring

Postby 3.14159265... » Sun May 18, 2008 11:44 pm UTC

* Do lots of questions.

* Help as little as possible, make them learn it by doing it. The best tutoring help is one where you didn't have to do anything.

* Make them realize the subject is interesting, by showing them why you are interested in it.
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Re: Advice for math tutoring

Postby Fafnir43 » Mon May 19, 2008 12:54 am UTC

3.14159265... wrote:* Make them realize the subject is interesting, by showing them why you are interested in it.


Seconded. And don't be afraid to stray a little from the syllabus to do it - maybe go through the Basel Problem [imath]\left(\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}\right)[/imath] when the course reaches infinite series, for example.
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Re: Advice for math tutoring

Postby btilly » Mon May 19, 2008 1:29 am UTC

Fafnir43 wrote:...One possibility here might be to go exceptionally slowly - not quite at an insulting "and a minus times a minus is a plus, so..." level, but almost - and wait for your tutees to ask you to speed up...

Don't knock going that slowly!

Seriously while teaching a university level calculus course I once had to take 10 minutes to explain to an honestly confused student why a negative times a negative was a positive. I was shocked. But the lesson is that you can't predict where the missing hole in someone's knowledge is.
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Re: Advice for math tutoring

Postby ConMan » Mon May 19, 2008 4:11 am UTC

Teach understanding, not memorisation (but don't go overboard). If the subject in hand is X, and X is based on the more advanced concept of X', which in turn is based on X'', go a little into X' to show how X actually works, and if questioned on X' explain that X'' exists, but is probably a bit too complicated to explain right now.

In other words, don't go down the high school mathematics path of saying "we do things this way, and if this way doesn't work, you can't do it" only to come back the following year and say "now we're going to do some of the things we told you that you can't do".

For a more concrete example, say you're tutoring in quadratic equations. The textbook says you can't take the square root of a negative number, but I'd suggest you say that you can, but then you get into complex numbers which behave in a whole bunch of kooky ways, and so you'll be sticking with the real numbers (where you really can't take the square root of a negative number) for now. Definitely don't go into quaternions, or fields and vectors, or anything like that. If the student is bright, though, feel free to let them investigate on their own ("Suppose you took the square root of -1, and called it i. How does i behave?").

As one of the recurring themes in the "Why do people dislike math?" thread points out, it's just plain annoying to keep getting told that what you learnt last year was actually wrong (even though it's actually right, but only in a given context, something high school teachers never really go into in detail).
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Re: Advice for math tutoring

Postby BeetlesBane » Mon May 19, 2008 6:29 am UTC

You might want to go through some of the homework help threads in the fora here. Pay special attention to those that are more elementary, since you'll have greater understanding of the different approaches the posters use.

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Re: Advice for math tutoring

Postby Nimz » Mon May 19, 2008 10:54 am UTC

When I first started with a tutoring job (I had already been helping other students, but not for pay), I had to take a tutor training course. One of central themes in the course was a 12 step tutoring cycle. At the beginning of the cycle is small talk "Hello" type stuff. The point: don't underestimate the value of a simple greeting. Then there's the problem ID steps. The point: you gotta know what you need to address, and like others have already said, it isn't necessarily what the student thinks it is. Then there are the explanation steps. The point: you're showing how to address the problem, and possibly problem-solving skills in general. Next is the student's turn - to explain the process in their own words, and to work out a problem on their own. The point: the student is actively involved, and you can provide positive reinforcement or back up to an earlier part of the cycle. Finally, the goodbye. The point: much like the greeting, saying a parting word helps to let the students know that you are a person.

Now, alot of that got paraphrased and combined, as it's been about 7-8 years since I looked at that stuff. That cycle was adopted for that course with a particular style of tutoring in mind: college tutoring in 1-hour or 1/2-hour appointments. There was a clear-cut amount of time to be spent with each student, a specific subject to be covered (there was a wide range of subjects besides just maths that I tutored, but I was able to know in advance what subject I would tutor when), and it was possible to plan accordingly. Currently I do more walk-in style tutoring, and at a highschool level. There may be 10 students that each need help with something different, and only 3 hours to help them all in. Many of the same things apply, but alot more stuff is on the fly. This style of tutoring also allows me to leave a student to work alone for a while while I'm helping other students. There are pros and cons to both styles, and the style you'll adopt will most likely be the one already being used where you're tutoring.

One of the cardinal sins of tutoring is doing the student's homework. That can make the explanation steps difficult, but if you can come up with similar problems, you can work those out instead. Often, instructors won't assign every single problem in the book, so if you know that every other odd problem is assigned, say, then you can show how it works with a similar even problem. Another cardinal sin is to allow the students to come to you before they have even tried the problems. That's part of the reason why there's reluctance to help people on the homework help threads that display no attempts made to solve the problem. It is also infinitely easier to spot a problem (if there is one aside from laziness) if you see how they have been trying to do the exercises.

As for the idea of never holding the writing instrument, that also has its pros and cons. It might be better addressed by considering seating arrangements. If you can sit so that it's easy for the student to write but difficult for you to write, it becomes easier to avoid writing excessively but still possible to write if necessary.

One other thing that is important to recognise is when to make the student take a break. I have tutored students that were on the edge of an emotional breakdown, partially due to frustration at not being able to get it, but also partially due to outside stresses. While it is possible to be a sympathetic ear and let the student get some of the emotional baggage off their chest, that isn't your job. Know what resources are available to the students, like counselling. Some places have services for certain groups of students, like first-generation college students, where those students can receive extra help. Some students won't even be aware that they might qualify to use some services. While not directly related to what you're tutoring, more benefit can be gained from a tutoring session when the student is of a sounder mind.
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Re: Advice for math tutoring

Postby Shinju » Mon May 19, 2008 1:23 pm UTC

Really important piece of advice, which hasn't really been stated with enough importance here.

Find out which school they go to and phone them up and ask for a copy of the syllabus. They'll almost be certainly happy to photocopy it for you. Knowing what speed the course is going and whats coming next can really help you prepare.

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Re: Advice for math tutoring

Postby greenblob » Mon May 19, 2008 4:35 pm UTC

http://www.maa.org/devlin/LockhartsLament.pdf

...actually, I'm not sure whether this would be such a great idea.

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Re: Advice for math tutoring

Postby maninblack » Mon May 19, 2008 6:22 pm UTC

Something Awesome wrote:Have your tutee explain his thought processes, step-by-step. That way, you get opportunities for both positive reinforcement of correct thinking and you can pinpoint more precisely what they don't understand.

Also, I believe these have been previously stated, but always be patient and let him do all/most of the work; it's his homework, after all. It's not always as easy as you expect, but he won't learn nearly as much if he's just watching you do his work.



Yeah, I was a math teacher for a short time, and have found that working one on one with students is as much about correcting bad information, assumptions, and habits as it is about learning new techniques. Hearing the student/tutee explain the problem/solution in a manner that is not correct will show these bad habits much more quickly than most other methods of work. Also whenever possible have the students use black boards. This will allow them to see their work they way the see the profs work in class...I know it sounds funny but it helps some students to see their work up there on the wall.
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Re: Advice for math tutoring

Postby moocow » Mon May 19, 2008 7:16 pm UTC

I possibly should have seen this thread at the beginning of this semester. I tutored a group of +/- 20 students in an elementary maths course. I worked my butt off to get them to understand, to explain as clearly as possible and help them to be able to do the problems rather than do the work for them. It was one of the most tiring but fulfilling things I'd done. And a short while ago I found one of them cheating in a quiz.

I don't know if I could have been more gutted. I mean, I am there only for them, I am a resource for them to use to their advantage. And then, instead of asking for my help, he cheats. It's up to the university to say what will be done with this cheater, but I hope he feels a consequence to that particular action.

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Re: Advice for math tutoring

Postby Something Awesome » Tue May 20, 2008 4:52 pm UTC

maninblack wrote:
Something Awesome wrote:Have your tutee explain his thought processes, step-by-step. That way, you get opportunities for both positive reinforcement of correct thinking and you can pinpoint more precisely what they don't understand.

Also, I believe these have been previously stated, but always be patient and let him do all/most of the work; it's his homework, after all. It's not always as easy as you expect, but he won't learn nearly as much if he's just watching you do his work.



Yeah, I was a math teacher for a short time, and have found that working one on one with students is as much about correcting bad information, assumptions, and habits as it is about learning new techniques. Hearing the student/tutee explain the problem/solution in a manner that is not correct will show these bad habits much more quickly than most other methods of work. Also whenever possible have the students use black boards. This will allow them to see their work they way the see the profs work in class...I know it sounds funny but it helps some students to see their work up there on the wall.


Oooh, I may have to try that when classes start up again in the fall! I've already found using a white board myself (especially with multiple different colors!) can be extremely helpful for students, whether one-on-one or more. Following tedious algebra is easier when the variables are color-coded. It never occurred to me to have them use it, though. I guess I'll see how it works!


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