Seeking advice about teaching maths
November 26, 2014 8:56 PM Subscribe
I'm interested in teaching high school students mathematics through a tutoring agency. I have the required experience in mathematics, but very little in teaching. This doesn't seem to be a massive problem for many tutoring agencies, but I want to know: do you have any specific tips/advice about teaching mathematics? And more broadly, any advice about applying for and going to work for a tutoring agency?
I'm a big fan of maths, and very interested in teaching it. I don't simply like it because 'there's only one right answer' etc, I like it for a frajillion reasons: the beauty of elegant proofs, the fun of problem solving, and the fact that it underlies the functioning of the universe as we know it. Heck, I do maths in my spare time. I make lame maths jokes. I am ready to accept that I am a fully-fledged maths nerd.
I understand that enjoying maths is not the same as being capable to teach it. I have gone through much of the high school maths syllabus (I am in Australia) and understand how to teach it from first principles.
Anything you can give me that would help me more ably engagingly teach mathematics to potential future students would be much appreciated.
I'm a big fan of maths, and very interested in teaching it. I don't simply like it because 'there's only one right answer' etc, I like it for a frajillion reasons: the beauty of elegant proofs, the fun of problem solving, and the fact that it underlies the functioning of the universe as we know it. Heck, I do maths in my spare time. I make lame maths jokes. I am ready to accept that I am a fully-fledged maths nerd.
I understand that enjoying maths is not the same as being capable to teach it. I have gone through much of the high school maths syllabus (I am in Australia) and understand how to teach it from first principles.
Anything you can give me that would help me more ably engagingly teach mathematics to potential future students would be much appreciated.
Best answer: I've tutored junior high and high school mathematics (and science, and reading, and writing, and standardized tests, and once every subject for a student who could not attend school at the time), and, for me, a more pertinent question to start with would be what the expectations are for your agency.
Just to give my personal examples: for a few years, I worked (both junior high and high school students) with one agency which contracted with various schools to provide tutors for a special after-school program. The program existed as an attempt to supplement the education of children, mostly performing shockingly below their grade level, who were attending various low-performing schools in low-income neighborhoods. (In the U.S., this was a Title I program.) The students completed an evaluation examination when they joined our program, and after the prescribed number of weeks, completed an exit examination to compare their progress. Students who attended enough weeks were rewarded with a prize of their choice of one of several expensive, high-demand electronic items. Of course, most of them were attending only because they wanted the prize, so motivation was usually an issue.
In my experience, for the environments in which I worked, the tutoring in actual mathematics (etc.) skills ended up being somewhat secondary to all the other considerations--many if not most of these kids came from very difficult personal situations--drug addicted or absent parents, public assistance, and so on. One of the students I visited at home and turned her assignments in at school for her because a restraining order, involving violence against her, prevented her from going to campus. When trying to figure out how to tutor a thirteen-year-old in basic multiplication tables, in addition to finding out ways to make the information make sense and be memorable, one had to figure out ways past the issues that made it so that they hadn't gotten the concept in the first place. Sometimes tutoring, especially home visits, ended up turning into mild therapy / mentoring. (Of course, we received no actual training on teaching or any of the rest of this. Most of us were recent college grads trying to pick up some work, and having a college degree seemed to be the main thing they were looking for.) Sometimes, reporting to parents could be challenging.
There was a curriculum used by the tutoring company, so that provided materials for a starting point, but we were allowed to deviate from it and I usually did, to help personalize it to the student. We weren't supposed to actually work on their homework with them, but I usually started the lesson by asking what they were working on currently in class and tried to help bring them up to speed on that. Making up example problems with some relevance/interest is always a plus, and you can pick up on that by talking to them--in our program the kids had a snack time before we started when we could sit with them; presumably it wouldn't work that same way at the high school level, but you can still ask them a lot of questions and try to target their interests. Sometimes, if another tutor was absent, we would tutor two or more students at once, which is an interesting juggling act especially if they're in different places; but often if you're clever you can turn this to your advantage, and integrate their lessons together while making sure to alternate helping each individually.
In my program, we met with the students for only on the order of 1.5 hours twice a week for 10 weeks or so, so it was difficult to make much progress of the level that was sometimes ostensibly required. Eventually you got to a point where you learned not to take this too personally. Obviously, you should give it your very best effort, but the tutoring only supplements the classroom teaching the student is receiving elsewhere, from teachers who get to know the student much better and more continuously over a longer period of time. However, your job is still super important, because this one-on-one attention gives you a chance to interact with your student in a way which they usually don't get much opportunity for otherwise. So I guess my advice if your situation is anything similar would be to aim for continuous improvement from visit to visit, but always try to find a way to tie it back to the current topic being studied in the regular class. One of my students was frustratingly forgetful about how to multiply decimals, week after week in tutoring, but we were both super proud when she earned very good marks on her next class exam.
I feel like I should mention my other experience with tutoring, which was through volunteering with a selective weekend program that helped extremely bright low-income students get into good colleges, through tutoring, mentoring, summer enrichment programs, scholarship applications, and cultural exposure. These students usually came from the exact same schools as the students I met through my tutoring job--I often met one when I was visiting for the other--but they were at the opposite end of the spectrum, and had their own set of challenges and delights. It was a very well-run program, with a large volunteer base. I double-volunteered, tutoring and mentoring, and for this group, and it was a great experience. In this context, I often searched for brain teasers, logic puzzles and math tricks to keep them interested, as well as teaching test-taking strategies and speaking from my own experiences, such as in applying to college or on the test in question.
I also privately tutored students (usually, these either want supplemental homework help or have some kind of online or book curriculum they are working through) but those experiences don't speak to the agency part of your question.
It's very late here and I need to wrap up for now, but I hope I didn't get too off-track with describing my personal experience. My point is that every agency is probably quite different, and you'll need to figure out what is expected for yours. If it's got as much going on beyond just math as mine did, that will affect the sorts of strategies you use to interact with your students and make yourself understood. A program trying to help failing students will be very different from one designed to further supplement high-achieving ones.
A few more tips regarding working for the agency: I don't know if you'll be expecting to do this for anything approaching full-time, but make sure you get a good idea of how many hours you can expect to work, with how many students, and what "success/good performance" means for that agency. (Is it better performance on an exit exam? Customer satisfaction? or what?) Find out if there is a curriculum you're expected to use (or even a method you'll be trained in) or if you work on the student's schoolwork with them. Ask about their cancellation policy. (Often we did not find out until the last minute whether the student was absent from school that day or simply didn't stay for the program; my agency's policy was that if we were able to be notified before traveling, we just stayed home and were not paid, but if we had already set out, we were paid, and usually put to work with a different student.) Find out the job classification you'll be under--as what is called in the U.S. an "independent contractor," I had different tax responsibilities than a full-time employee would. I wouldn't worry too much about the application process; obviously, this will vary from agency to agency, but if you're really interested in math yourself and care enough about teaching it well to ask this question, it'll probably show and I wouldn't think you'd have a hard time. You may be asked to complete a background check of some sort, if you will be working with children, but I can't speak to how that would work in your area.
Oh, something else: I tutored junior high school students when I was literally twice as old as most of them. However, I am petite and young-looking and both students and teachers/staff usually mistook me for another student. Sometimes this was helpful, but mostly it was a hindrance (the time a teacher yelled at me to get back to class, before seeing my staff badge, was awkward) and in a perfect world where I had sufficient funds, if I could do it over again, I might try to dress or otherwise present in ways to garner more respect (while still being approchable for students). Not sure if this is an issue for you.
posted by spelunkingplato at 1:25 AM on November 27, 2014
Just to give my personal examples: for a few years, I worked (both junior high and high school students) with one agency which contracted with various schools to provide tutors for a special after-school program. The program existed as an attempt to supplement the education of children, mostly performing shockingly below their grade level, who were attending various low-performing schools in low-income neighborhoods. (In the U.S., this was a Title I program.) The students completed an evaluation examination when they joined our program, and after the prescribed number of weeks, completed an exit examination to compare their progress. Students who attended enough weeks were rewarded with a prize of their choice of one of several expensive, high-demand electronic items. Of course, most of them were attending only because they wanted the prize, so motivation was usually an issue.
In my experience, for the environments in which I worked, the tutoring in actual mathematics (etc.) skills ended up being somewhat secondary to all the other considerations--many if not most of these kids came from very difficult personal situations--drug addicted or absent parents, public assistance, and so on. One of the students I visited at home and turned her assignments in at school for her because a restraining order, involving violence against her, prevented her from going to campus. When trying to figure out how to tutor a thirteen-year-old in basic multiplication tables, in addition to finding out ways to make the information make sense and be memorable, one had to figure out ways past the issues that made it so that they hadn't gotten the concept in the first place. Sometimes tutoring, especially home visits, ended up turning into mild therapy / mentoring. (Of course, we received no actual training on teaching or any of the rest of this. Most of us were recent college grads trying to pick up some work, and having a college degree seemed to be the main thing they were looking for.) Sometimes, reporting to parents could be challenging.
There was a curriculum used by the tutoring company, so that provided materials for a starting point, but we were allowed to deviate from it and I usually did, to help personalize it to the student. We weren't supposed to actually work on their homework with them, but I usually started the lesson by asking what they were working on currently in class and tried to help bring them up to speed on that. Making up example problems with some relevance/interest is always a plus, and you can pick up on that by talking to them--in our program the kids had a snack time before we started when we could sit with them; presumably it wouldn't work that same way at the high school level, but you can still ask them a lot of questions and try to target their interests. Sometimes, if another tutor was absent, we would tutor two or more students at once, which is an interesting juggling act especially if they're in different places; but often if you're clever you can turn this to your advantage, and integrate their lessons together while making sure to alternate helping each individually.
In my program, we met with the students for only on the order of 1.5 hours twice a week for 10 weeks or so, so it was difficult to make much progress of the level that was sometimes ostensibly required. Eventually you got to a point where you learned not to take this too personally. Obviously, you should give it your very best effort, but the tutoring only supplements the classroom teaching the student is receiving elsewhere, from teachers who get to know the student much better and more continuously over a longer period of time. However, your job is still super important, because this one-on-one attention gives you a chance to interact with your student in a way which they usually don't get much opportunity for otherwise. So I guess my advice if your situation is anything similar would be to aim for continuous improvement from visit to visit, but always try to find a way to tie it back to the current topic being studied in the regular class. One of my students was frustratingly forgetful about how to multiply decimals, week after week in tutoring, but we were both super proud when she earned very good marks on her next class exam.
I feel like I should mention my other experience with tutoring, which was through volunteering with a selective weekend program that helped extremely bright low-income students get into good colleges, through tutoring, mentoring, summer enrichment programs, scholarship applications, and cultural exposure. These students usually came from the exact same schools as the students I met through my tutoring job--I often met one when I was visiting for the other--but they were at the opposite end of the spectrum, and had their own set of challenges and delights. It was a very well-run program, with a large volunteer base. I double-volunteered, tutoring and mentoring, and for this group, and it was a great experience. In this context, I often searched for brain teasers, logic puzzles and math tricks to keep them interested, as well as teaching test-taking strategies and speaking from my own experiences, such as in applying to college or on the test in question.
I also privately tutored students (usually, these either want supplemental homework help or have some kind of online or book curriculum they are working through) but those experiences don't speak to the agency part of your question.
It's very late here and I need to wrap up for now, but I hope I didn't get too off-track with describing my personal experience. My point is that every agency is probably quite different, and you'll need to figure out what is expected for yours. If it's got as much going on beyond just math as mine did, that will affect the sorts of strategies you use to interact with your students and make yourself understood. A program trying to help failing students will be very different from one designed to further supplement high-achieving ones.
A few more tips regarding working for the agency: I don't know if you'll be expecting to do this for anything approaching full-time, but make sure you get a good idea of how many hours you can expect to work, with how many students, and what "success/good performance" means for that agency. (Is it better performance on an exit exam? Customer satisfaction? or what?) Find out if there is a curriculum you're expected to use (or even a method you'll be trained in) or if you work on the student's schoolwork with them. Ask about their cancellation policy. (Often we did not find out until the last minute whether the student was absent from school that day or simply didn't stay for the program; my agency's policy was that if we were able to be notified before traveling, we just stayed home and were not paid, but if we had already set out, we were paid, and usually put to work with a different student.) Find out the job classification you'll be under--as what is called in the U.S. an "independent contractor," I had different tax responsibilities than a full-time employee would. I wouldn't worry too much about the application process; obviously, this will vary from agency to agency, but if you're really interested in math yourself and care enough about teaching it well to ask this question, it'll probably show and I wouldn't think you'd have a hard time. You may be asked to complete a background check of some sort, if you will be working with children, but I can't speak to how that would work in your area.
Oh, something else: I tutored junior high school students when I was literally twice as old as most of them. However, I am petite and young-looking and both students and teachers/staff usually mistook me for another student. Sometimes this was helpful, but mostly it was a hindrance (the time a teacher yelled at me to get back to class, before seeing my staff badge, was awkward) and in a perfect world where I had sufficient funds, if I could do it over again, I might try to dress or otherwise present in ways to garner more respect (while still being approchable for students). Not sure if this is an issue for you.
posted by spelunkingplato at 1:25 AM on November 27, 2014
Best answer: I'm currently tutoring math kids from 3rd grade to Algebra I (the algebra is at a school and sometimes they toss me geometry and algebra II kids, but not enough to really feel comfortable doing it).
You're going to need resources. There are some good free apps out there for the younger kids, but I haven't found anything amazing for the older ones. Some places I've found with work so you're not spending all of your time generating work for them: released state exams (don't just choose your state, either!), kutasoftware.com has some free worksheets, and of course the textbook. Keep blank copies and answer keys for anything you work with in a separate folder so you never have to re-dig for something you might need.
I find a lot of students need visual aids or spending the time to talk through why a problem works. I'm not a huge testing fan, but their word problems are sometimes so long they create a clear story we can re-enact and link back to how equations are built. Once they 'live through it' they feel more comfortable considering it in more abstract terms.
posted by lownote at 6:13 AM on November 27, 2014
You're going to need resources. There are some good free apps out there for the younger kids, but I haven't found anything amazing for the older ones. Some places I've found with work so you're not spending all of your time generating work for them: released state exams (don't just choose your state, either!), kutasoftware.com has some free worksheets, and of course the textbook. Keep blank copies and answer keys for anything you work with in a separate folder so you never have to re-dig for something you might need.
I find a lot of students need visual aids or spending the time to talk through why a problem works. I'm not a huge testing fan, but their word problems are sometimes so long they create a clear story we can re-enact and link back to how equations are built. Once they 'live through it' they feel more comfortable considering it in more abstract terms.
posted by lownote at 6:13 AM on November 27, 2014
Best answer: I did a few weeks at a big tutoring center with kids (and a few years tutoring at university, more on that later).
My place was literally a tutoring center. Students came in to the center, and there were usually 10-15 students (ages 5 to 16) with 3 tutors. Because this kind of bulk tutoring was one of the cheaper options in a very affluent area, the kids were mostly middle of the road type kids. Reasons for being there were usually things like, "Johnny only gets C+s on math tests" and "Jane's parents both stay at the office late so they enroll her in lots of after school activities, and they thought math tutoring would be better for her than 5 days a week of soccer". Not to harsh on the parents, it wasn't really a hugely bad option, but most of the kids were bored with being there and it showed.
This wasn't helped by the curriculum, which was strict and involved full time worksheets done in a specific order (to keep that many kids occupied with that few tutors). We were allowed to go slightly off curriculum, but not much, not even with kids who were obviously picking it up way faster than the worksheets. Most of the tutors jobs ended up being more about keeping the kids on task with the worksheets than actual teaching. The kids were pretty well behaved, but they were definitely still kids and there was a lot of asking Susy to sit down, please, or listening for two minutes to Carl talk about the band he's interested in and then telling him that's nice but not related to what we're doing now.
You can tell I didn't really like this kind of place, a lot of it was the format but also pretty much all tutoring with kids is going to be mandatory (parent or school imposed) for the kid, so I completely understand the lack of enthusiasm. Also, I don't see anything in your question about if you like kids or not, or if you have a lot of experience with kids, and that's a big thing. Even if you're super lucky and your students want to be there, they're still not the ones paying you (your actual customer) so you usually have to do the best you can to keep doing lessons even when they have normal distractions and things going on. (See what spelunkingplato said about what "success" is for your agency.)
The math was usually arithmetic, algebra, and geometry (geometry was hard because I'd forgotten almost all of it).
In contrast, I tutored at a university for about 3 years. We usually had about the same student-tutor ratio, sometimes even more students, but it was entirely student-driven so way less "work" and way more time to spend actually teaching individual students. Students would just walk in and ask whatever questions they had, and we would do our best to help, when they felt like they were done, they would leave. The only problem here was that the pay was poor (not many hours and also a very low hourly rate)...but this was probably the ideal of teaching math, lots of students were interested in random tangents about how x applies to y or some theoretical discussion of how a is like b.
I also did private tutoring for university students. I didn't really need the money at that point so I only took a few students, but a lot of my friends did this more than that. This was OK, since students were paying out of their own pocket they were very, very motivated. It can be exhausting, though, since they're trying to cram as much learning as possible into one or two hour sessions. This was the best pay out of everything, but it depends on your ability to get and keep students. The schedule is a bit erratic, since they like to reschedule (as much as you'll let them), or add extra hours near a test (and then fewer hours after the test). Sometimes you'll get lazy students who just want you to do the work for them, so the more selective you can be the happier you'll be (but the less money you'll have). Working for an agency you probably have to read between the lines to find out if you really have an recourse if you don't want to work with a specific student.
Summary: Tutoring can be fun, but it's more about people skills than math or teaching--you'll learn how to teach and you can brush up on your math when you need to.
posted by anaelith at 6:53 AM on November 28, 2014
My place was literally a tutoring center. Students came in to the center, and there were usually 10-15 students (ages 5 to 16) with 3 tutors. Because this kind of bulk tutoring was one of the cheaper options in a very affluent area, the kids were mostly middle of the road type kids. Reasons for being there were usually things like, "Johnny only gets C+s on math tests" and "Jane's parents both stay at the office late so they enroll her in lots of after school activities, and they thought math tutoring would be better for her than 5 days a week of soccer". Not to harsh on the parents, it wasn't really a hugely bad option, but most of the kids were bored with being there and it showed.
This wasn't helped by the curriculum, which was strict and involved full time worksheets done in a specific order (to keep that many kids occupied with that few tutors). We were allowed to go slightly off curriculum, but not much, not even with kids who were obviously picking it up way faster than the worksheets. Most of the tutors jobs ended up being more about keeping the kids on task with the worksheets than actual teaching. The kids were pretty well behaved, but they were definitely still kids and there was a lot of asking Susy to sit down, please, or listening for two minutes to Carl talk about the band he's interested in and then telling him that's nice but not related to what we're doing now.
You can tell I didn't really like this kind of place, a lot of it was the format but also pretty much all tutoring with kids is going to be mandatory (parent or school imposed) for the kid, so I completely understand the lack of enthusiasm. Also, I don't see anything in your question about if you like kids or not, or if you have a lot of experience with kids, and that's a big thing. Even if you're super lucky and your students want to be there, they're still not the ones paying you (your actual customer) so you usually have to do the best you can to keep doing lessons even when they have normal distractions and things going on. (See what spelunkingplato said about what "success" is for your agency.)
The math was usually arithmetic, algebra, and geometry (geometry was hard because I'd forgotten almost all of it).
In contrast, I tutored at a university for about 3 years. We usually had about the same student-tutor ratio, sometimes even more students, but it was entirely student-driven so way less "work" and way more time to spend actually teaching individual students. Students would just walk in and ask whatever questions they had, and we would do our best to help, when they felt like they were done, they would leave. The only problem here was that the pay was poor (not many hours and also a very low hourly rate)...but this was probably the ideal of teaching math, lots of students were interested in random tangents about how x applies to y or some theoretical discussion of how a is like b.
I also did private tutoring for university students. I didn't really need the money at that point so I only took a few students, but a lot of my friends did this more than that. This was OK, since students were paying out of their own pocket they were very, very motivated. It can be exhausting, though, since they're trying to cram as much learning as possible into one or two hour sessions. This was the best pay out of everything, but it depends on your ability to get and keep students. The schedule is a bit erratic, since they like to reschedule (as much as you'll let them), or add extra hours near a test (and then fewer hours after the test). Sometimes you'll get lazy students who just want you to do the work for them, so the more selective you can be the happier you'll be (but the less money you'll have). Working for an agency you probably have to read between the lines to find out if you really have an recourse if you don't want to work with a specific student.
Summary: Tutoring can be fun, but it's more about people skills than math or teaching--you'll learn how to teach and you can brush up on your math when you need to.
posted by anaelith at 6:53 AM on November 28, 2014
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The most helpful thing I've found in general, is encouraging students to allow themselves to be wrong. As a TA, I'd deliberately follow dead-end lines of thought in integrals and proofs, in order to show the students that going down to a dead end is less time consuming than looking at a few possible lines of reasoning and worrying whether one will lead to a dead end (also, absolutely nothing is gained by the worrying, whereas pursuing a dead end at least rules out that line of reasoning).
If at least a few of the students have enough confidence to be wrong (preferably in front of their peers, hopefully emboldened at least a little by your being deliberately wrong), and the format of the class permits it, then the other generally helpful thing I've found is try and get the student to answer questions *before* they're given a theory, technique or formula that they can just plug'n'chug their way through. There's something that really deepens the understanding these things if they're learned through guided discovery, rather than through being told how to do it and practicing. In these circumstances, try to solicit many different approaches to solving the problem, so you can compare them, and troubleshoot some of them.
None of this works terribly quickly at getting specific concepts into students heads (which sadly, is often a goal of many techniques of teaching math--often at the expense of proper understanding), so if there's a lot of pressure to be able to do a thing in time to pass a test on it in class, you might find the students less than appreciative of the additional understanding you're making available. On the other hand, it does equip students to do a lot more subsequent learning on their own. (You can probably adapt these techniques to more efficiently use class time through the careful and judicious use of homework).
posted by kiwano at 10:06 PM on November 26, 2014 [2 favorites]