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What do you look for in a math mentor?


lewelma
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My older son is a math lover and is working through the AoPS books independently. He has been doing some math research here and there, and I think he would be interested in doing more especially if he had someone guiding/mentoring him. I have never heard of a kid here who has ever had a math mentor. This is just not really a mathy country. So, if I start asking around, I am sure I will be asked what exactly I am looking for. And I don't really know.

 

For those of you with math mentors, what do they provide your child? How often do they meet/talk? How much do you pay? Where do you find one? etc

 

Thanks,

 

Ruth

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I do not have a math mentor for my students, because DH and I can do that myself, but if I were looking for one, my first requirement would be that the person is enthusiastic about math. I would want to see the joy and excitement, coupled with subject expertise, i.e. somebody who has studied more math than the student will cover. Since you are not looking for a tutor or teacher, it would not matter whether this person had actual teaching experience.

I would start by looking for local students who have been participating in math competitions/ math olympiad/ a problem solving club and find out who their mentor is. It could be a teacher, it could also be a college student, or a university instructor. I would then contact that person and find out whether my student could join the already existing group, or whether the mentor could meet with my student one on one, or whether the mentor can recommend somebody else. It could be that the teacher can get you in contact with an older high school student who would like to work with a gifted younger student.

If you can not find any information about local programs, I would next contact the closest university's math department and ask whether they are running any outreach programs, or whether any students or faculty would be interested. If there is no close university, contact ANY university and ask whether something like this would be possible as long-distance, via skype or similar.

 

How often you'd meet would depend on whether you find somebody local or have to travel or meet online, and what exactly your student wants to do with the mentor. I could imagine several scenarios: if the student has a research project, the mentor could provide guidance, check over proofs, suggest literature, discuss concepts. If the student is currently not working on a project of his own, he could get together with the mentor to discuss challenging competition problems, or he could ask the mentor to assist him in self-studying subjects which are off teh beaten path.

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Back home, our math and science mentors in middle school were university lecturers who were doing research in our area of interest. It was free and the lecturer gets a "free" research assistant to work with. While my school did the matching for us, it was easy to find out which lecturer specialise in what areas and match ourselves up.

 

Here I have read news of children managing to get university lecturers as mentors for their projects.

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thanks for all the ideas on where to look. Unfortunately, I cannot act as mentor because my field is statistics, and I have very little interest or knowledge in number theory and geometry, which is currently his passion.

 

My ds doesn't have a research project, just little ideas that he follows for a week or so. I would think that a mentor could direct him to some exciting questions and provide ideas of books to read etc. And be available to just talk about what is exciting and interesting to my son. Is this a realistic expectation?

 

We have some adult friends (not close ones) who are mathy guys. One is a physicist and the other a computer scientist. My son talks to them a few times a year about what he is thinking about, but it is always with other adults around listening in, which is just not good for long or honest discussions. I do not think that either of these people could act a a mentor, but I could be wrong. I have not asked.

 

Ruth in NZ

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Thanks for starting this, Ruth!

 

We were just introduced to a math mentor for DS. He's a friend of a friend, a computer scientist by trade who is not in academia, but rather, works in a top software company with a few patents to his name. The first chat was great as DS poured out his questions on imaginary numbers, some real-life physics phenomenon that he's musing over and so forth. Personality-wise, it was a great match. The chat went on for nearly 3 hours! The next chat isn't scheduled until after the holidays. But I'm wondering what should be done as well. This is what I'm mulling over. If anyone has suggestions, please do jump in.

 

1. I've asked DS to keep a notebook of questions that he has (I'm even scribing for him :p as he's dysgraphic and hates to write), but it's becoming very haphazard. We'll muddle on but it's not structured at all.*

 

2. I'm thinking of starting them on a textbook, say, AOPs Counting and Probability or Number Theory, both of which DS has seen and wants to do (but he wants to do everything!). This way, new bunny trails may arise which they can follow.

 

3. Puzzles. They could work on a series of puzzles together, or DS is assigned some in advance and then explain his thought process whether he got it or not. I know this math mentor is a hound for puzzles, so that could work out too.

 

I'm inclined towards #2 or #3, and will speak with the math mentor at the next opportunity. Ruth, would one of these be an ideal structure you and your son could consider too?

 

* Light bulb! I'll get him to start a blog!!

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For those of you with math mentors, what do they provide your child? How often do they meet/talk? How much do you pay? Where do you find one? etc

 

Thanks,

 

Ruth

 

A stream of consciousness reply for what our mentor provides my child...I want to explain why I chose this mentor so I hope you don't mind the ramble, Ruth.

 

We searched for a mentor when DS started showing obvious signs of resisting "easy" math and started putting all his thoughts into equations...just spontaneous equations for multiple things like how to find triangle numbers and what (x-2)(x+1) means in relation to the area of a rectangle etc (by drawing it on our whiteboard), all without planned prior parental instruction. For example, he figured out some of the stuff that's here as well as several Pascal triangle relationships on his own when he was between the ages of 7 and 8, through trial and error and using some of his own made-up notations. I now realize that I can be good at math but at that time, I had pretty low self esteem about my higher math abilities so I naturally freaked out and started searching for someone who wouldn't laugh at me when I told them what he likes to do in his free time. That was my very first criteria. I needed someone to trust me and believe me and support me. And if absolutely needed, someone who could be trusted to lead him through his math journey without my involvement if necessary so that I can focus on other subjects.

 

I asked around on gifted groups and was given two names to choose from. One was very highly regarded by parents of radically accelerated kids but for some reason I didn't feel comfortable when I spoke to him on the phone. He did not return my email promptly either (took about 2-3 weeks to even call me back...I understand if it takes 7-10 days but 2-3 weeks is a bit much). The other called me back in 2-3 days although when I first contacted him, it was during the busy holiday season. He patiently listened while I was trying to speak to him in a busy bookstore. Patiently waited while I told him I couldn't find my son while I was on that call lol (kiddo is a kid in a candy store in bookstores and needs to be watched closely or I can lose sight of him very fast...he was just turned 8 at the time). The mentor fixed a day and time to "meet" us and kiddo online. This mentor doesn't use face-to-face video by the way. You see an online whiteboard and you hear his voice and he hears yours but you don't see him and he doesn't see you.

 

During that first web meeting, he started asking kiddo about his math journey so far and gave him some problems. Kiddo stumbled over some fractions problems if I remember correctly but warming up quickly to this mentor, he started talking about his triangle number equation and his (x-2)(x+1) idea and how to draw that. When the mentor quickly showed him the FOIL method, kiddo caught it quickly and loved that another adult was taking him seriously and teaching him new stuff, never mind that he still wasn't entirely confident with fractions. My DH and I were not expecting much other than to find him a good mentor. We were told very confidently after this meeting that kiddo was ready to begin algebra. We were already homeschooling and were used to out of the box decisions so we went with it knowing that if things got too sticky we could cancel.

 

The first year (algebra 1) was quite structured and kiddo's first experience with textbook math. Kiddo baulked at showing his work but wanted very much to please this mentor so he started going the extra mile despite the mentor not requiring him to show everything. I was super nervous because this boy is not keen on writing anything and I was worried that kiddo's writing on the online whiteboard was huge and messy...you know little things that you wish your kid was better at lol. But he did hid best for this mentor and refused to quit although it was getting hard. It was a proud moment when he finished his algebra with a solid recommendation to move on to geometry.

 

The second year (I think geometry will take more than a year though) is going really really well. I asked the mentor to go slowly when they began but the mentor has this uncanny ability to read my son and predicted that in a month, he'll be writing proofs willingly and confidently. I was nervous again about that expectation but son rose up to the challenge. I also love that this man can assuage my fears and predict exactly where kiddo will be in 3-6 months. He says things like kiddo doesn't need a traditional one year of algebra 2 and I know that if absolutely necessary to accelerate some more, I can trust this opinion. I know that kiddo is going to work really hard for this man and for himself because he really loves this relationship they have and he loves that he is being trusted with hard problems.

 

They meet once a week. It started with his mentor assigning problems from the textbook (Dolciani for Algebra and Jurgensen for Geometry). Now the mentor knows my son well and tells him to just choose what he'd like to do knowing full well that the boy will choose the hardest problems. Kiddo does his homework for about 5-7 hours a week. When they meet, they discuss the problems and examine each other's strategies. Sometimes his mentor will use a different strategy and kiddo will use his own and they will discuss each one, pros and cons etc. They each use a pen tablet (Wacom Bamboo) and the online whiteboard every week. They take many detours and sometimes need to review a bit of algebra that kiddo might have forgotten and it still works out great. Or his mentor may suddenly introduce a concept that kiddo has never seen before and they take those bunny trails for a few weeks. Something else that I really really like: whenever kiddo encounters those head-hurting problems, his mentor lets it stew for a few weeks, even months. Kiddo has really grown from this. He has learned to be patient and not get frustrated and come back with vigor to previously difficult problems. There are problems they still haven't solved from last March and I'm okay with that. This mentor may not be the best fit for a kid who thrives on speed math and extreme perfectionism and always getting things right. But for DS's plodding, really-need-to-think, yes-I-do-make-mistakes-and-it's-ok personality, he's perfect.

 

Sometimes, before they begin the online lesson, they will have a "jam session": kiddo on the piano on our end and his mentor on the piano on his end. Sometimes, the talk about dogs. Sometimes, they talk about kiddo's love for detective novels and tv series and British things. Usually just 3-5 minutes, then his mentor gets right into the lesson. The first year, it was a mentor-mentee relationship. This year, they behave like buddies but with obvious respect from kiddo towards mentor. I like this very much.

 

We enjoy a good rate but I think he charges a little more for new families. When we signed on, his private mentoring rate was more affordable than the rate charged by the other contact I was given. Let's just say we will be reluctant to pay more than USD50/hour.

 

There is one thing I was a little disapponted about in the beginning. I had wished that the mentor would be a little more flexible with choice of materials but he is quite fixed on the books he wants to use. I wanted very much for kiddo to have a number theory mentor using AOPS NT for e.g. because that was his passion for a long while but this mentor made it clear that he was not going to be that. Still, I liked him enough to carry on and am glad we stuck with him. He keeps his direction clear from the beginning so that you know that he's going to do A and B and maybe a little C but he won't add the D and E because he is on a tight schedule too or your kid is not ready or it's just not something he does. If he is not going to do something, he says it upfront. Very important for the parents to keep the line of communication clear at all times but I guess that's true for any mentor.

 

This got long but hope it helps Ruth and good luck!

 

ETA: I guess his mentor is more like a tutor in some respects so may not be what you're looking for...but their relationship is more mentor-mentee like than tutor-tutee (hmmm...is there such a word as tutee?)

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I think #1 or #3 would work, but my son likes to do AoPS independently.

 

What I really think he would enjoy is working through problems like what are on the Mathpath qualifying exam. Obviously, he cannot get help on this year's questions if he wants to attend, but perhaps I could find previous years exams and they could work through those. Not together, but perhaps the mentor could be available for questions and evaluation/discussion of the proofs he writes.

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Quark, Thanks so much for the ramble. Wonderful thoughts and ideas. I totally get the point about not being laughed at. I think that is my biggest concern. How do convince someone, who has probably never known a homeschooler (not many here really), and has never seen a program like AoPS, that my son is a serious student? Not just algebra done by 6th grade, but AoPS Introductory Algebra done independently by 6th grade including the challengers. They are just 2 very very different things.

 

I mentioned wanting a math mentor to a 17 year old who has had a writing mentor for the novel he has just finished, and he said "do you mean a math tutor? What in the world would you need a math mentor for?" He just could not make the leap from writing mentor to math mentor, it is just.not.done.here.

 

Well, I'm off to hunt down some of Regentrude's ideas for finding someone. And perhaps if I hand that person a copy of the mathpath exam, it might become clear.

 

Ruth in NZ

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Thanks for your thoughts, Quark! I want to keep rereading for inspiration. Yes I know how it is about not being laughed at, especially when I'm no mathematician too. AND i have a gap-py DS who needs to learn harder things before he learns easier things (completely upside down, I know). Love the hive!

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AND i have a gap-py DS who needs to learn harder things before he learns easier things (completely upside down, I know).

 

This is so my son. People thought I was nuts to put him into algebra before he had finished computation, but I figured if he was passionate about math, the rest would catch up. I compare it to proof reading a phone book -- you might go in with a good attitude, but you. just. can. not. do. it.

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This is so my son. People thought I was nuts to put him into algebra before he had finished computation, but I figured if he was passionate about math, the rest would catch up. I compare it to proof reading a phone book -- you might go in with a good attitude, but you. just. can. not. do. it.

 

That's why my mother put me directly into pre-algebra after I quit school in 2nd grade. It worked fine for me. I did the comprehensive arithmetic review/gentle intro to algebra over the next year and a half and then started algebra.

 

I was SO bored trying to do grade-level stuff.

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Mukmuk, always a pleasure and Ruth, glad it was helpful lol. I was wondering if I should shorten that post! :)

I love regentrude's ideas and just to add...sometimes it's just that extra thing that the person brings to the whole conversation. I've found 3 mentors for my son so far for various subjects and have been very lucky in all my choices. It's like a 6th sense thing. I'm not the smart person in my family but I can be very sensitive to a person's tone of voice or body language (2 of these mentors are IRL) and there's always something that stands out that will tell you if they could be the ONE. All three had a certain something that I can't put into words. His math mentor doesn't sound very friendly when you first speak to him...his tone of voice is rather serious...but he cared. I could sense that. The way he patiently waited, the way he spoke to my son when they first "met". The chemistry mentor my son briefly had was in contrast, a very jolly guy and always cracking jokes...just the reverse of the math mentor...but never for one minute did he ever talk down to my son. He spoke to him like an equal. Threw hard things at him and was prepared either way...to up the level if son could take it or go down a level to guide him through to understanding. I think it is this element of care that will stand out when you find the right person.

 

Wishing you the very, very best. It makes a huge diff in the child's life to have a grown up (other than family) care for them like this on a regular basis. Very, very affirming. I know I'm not educated enough to guide my son through the higher levels but I do hope I can continue to be fortunate in facilitating for him, i.e. finding him good mentors and guides and materials. Fingers crossed for you too.

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Quark, Thanks so much for the ramble. Wonderful thoughts and ideas. I totally get the point about not being laughed at. I think that is my biggest concern. How do convince someone, who has probably never known a homeschooler (not many here really), and has never seen a program like AoPS, that my son is a serious student? Not just algebra done by 6th grade, but AoPS Introductory Algebra done independently by 6th grade including the challengers. They are just 2 very very different things.

 

I mentioned wanting a math mentor to a 17 year old who has had a writing mentor for the novel he has just finished, and he said "do you mean a math tutor? What in the world would you need a math mentor for?" He just could not make the leap from writing mentor to math mentor, it is just.not.done.here.

 

 

Ruth, I think you know that you will have found a prospective math mentor when the person gets what you want and is willing to believe in your son's abilities without you having to explain or justify. The person you are looking for will be aware that young mathematically gifted students exist and need support. I think if you have to explain and justify, the person is not the right person to work with your son.

Most likely, you will be looking at somebody who was in a similar position as a youth and who remembers what that was like.

 

You mentioned adult family friends who talk to your son about math - why don't you ask them?

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More ideas - you might look for the math coach of local high school math club teams, as that information might be available on the school's website (I'd start with the faculty member in charge of the club). That person or someone else they know who has been involved in math competitions might have the type of enthusiasm you're looking for. At least they might put you on the trail. I don't suppose there's a Math Circles group out there?

 

Maybe Rusczyk knows someone in NZ - you never know - can't hurt to ask. Or how about an on-line mentor? I'm quite sure he'd know a college student or other person who would be interested in that. Just thinking out loud... I don't see a sub-forum for NZ at AoPS, but it might be worth poking around in those forums or asking there. Maybe poke around here: http://www.nzamt.org.nz/

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the first thing i did was go online to a university math dept in new zealand and look at the faculty list there.

 

http://www.math.cant....nz/php/people/

 

 

based on what i see there, i would give gunter steinke a call, e.g., and ask for help.

 

remember, math professionals are often just enormously pleased to find young people who are also in love with math, and welcome the chance to help them. of course some, especially people starting out, or socially awkward, are more focused on themselves. i go partly just by their faces and description of interests, and then talk to them of course. there are some very outgoing looking people on that website, e.g. liz ackerley, jennifer brown,.... and there is also a long list of emeritus faculty who are presumably less busy at the moment. i do not see anyone specifically in number theory there. so i would try another uni as well.

 

at victoria wellington i had more trouble browsing the web site for peoples individual interests, but dr. byoung du kim is a number theorist there.

 

you might try the head:

 

http://www.victoria....aff/megan-clark

 

 

be bold. you represent someone schools are interested in, or should be, a bright interested student.

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I fully agree with wapiti and mathwonk. The worst that can happen is that they will ignore you or send a note to say they are not interested. I have written to profs and was well-ignored by most and received one short but polite letter from another declining involvement lol. But that doesn't mean I won't try again if I really need someone. I don't know if you have online classifieds there for tutors/ teachers? I found the chemistry mentor by carefully shortlisting ads on craiglist. And definitely ask with local gifted groups if you have any too.

 

ETA: Strongly agree with regentrude too. You shouldn't have to explain in any long detail other than the preliminary call or email to say what the situation is and what exactly you are looking for. If AoPS is not well-known there, email the mentor the difficult problem that your son solved. Mention specifically if he used some unique method and that you are wondering if the mentor would be interested to explore this further with your son. For example, some young kids can solve abstract stuff visually in one glance but cannot explain the steps because they don't have that knowledge/skill yet. But their ability is still impressive and the parent may need to mention this so the mentor's expectations are appropriate for the first meeting.

 

Your son may be doing something else very impressive--and his AoPS experience is definitely impressive to those of us who know the books--that is not usually expected at his age so mention anything that looks different to you that might attract this person's interest to engage, however briefly. I've found that including one or two quick examples to be very effective if I need to "draw" the person in but the kid should do the actual math-related talking/ showing and preferably, they should work on a new problem together so that it's obvious that it's not all pre-rehearsed with a parent. If the prof/ mentor doesn't get it after 15 miniutes or so with the kid, you'll know it's not going to work. In fact, you will sometimes know it in the very first few minutes of their conversation. Trust your gut!

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Ruth, the New Zealand math olympiad website mentions regular evening math sessions for high school students & lists contact info for three different locations around your country. It might be worth a visit to the nearest site to find people who enjoy working with young math talent & also to find math talented peers (even if he chooses not to enter competitions).

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Thanks everyone for all of your ideas.

 

Here are my current thoughts about what a mentor would provide.

1) Teach ds how to write mathematical proofs

2) introduce ds to different mathematical fields

3) suggest books to "co-read" and then discuss at meetings

4) answer questions about difficult challengers or research projects

5) suggest research projects

 

Does this sound appropriate? What else would you suggest?

 

Ruth in NZ

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Ruth, I also suggest signing up for Euclid Lab next summer (June-August) if possible (hat tip to mathwonk for mentioning it here some time back). There are some challenges posted that your son might enjoy thinking about for now. It was a great experience for my son this past summer and taught him how to "write" math...still intro level of course but enough to really stretch him and teach him what math writing entails at high school+ level. The fee is a suggestion--they had generous grants this year and we paid only what we could afford (PM me for details if you like). Hopefully they will continue to have generous grants next year.

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Coming in late but based on our experience I have three suggestions:

 

1. Don't ask for a commitment up front. Find someone who seems like they might have good ideas about math and ask if they could meet to give some direction to a student with mathematical talent. They may offer to mentor or they may have a suggestion of someone who could mentor. Or, maybe they just suggest a book he might like to read, but you've lost nothing.

 

2. If you are looking for an unpaid mentor like a professor (as opposed to a math tutor) I would not give a list of what you want the student to learn nor would I ask them to follow a particular path The feedback we've gotten from mentors is what makes it fun, is not having to accomplish a particular set of learning objectives. I see the main point of mentoring connecting the student with someone who can keep that spark alive and help them discover new directions to explore. If at this point has more particular learning objectives I'd think more of a paid tutor - possibly a graduate student.

 

3. If finances are not an issue and he works well from distance there may also be some online options as well.

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Thanks for all the advice! I have followed up on Kathy's suggestion and done some digging on the math olympiad in NZ. First of all, you don't have to compete, you can just do the problems, and go to the camp if you get in (there is a qualifying exam that my son would do very well at even as a 7th grader). So, that is good from the point of view of my son, who is currently not interested in competing. Second, apparently there are only 150 applications for the Math Olympiad camp every year and they take 24 students, so my ds has very good odds. Nothing like a small country that does not focus on math education! They have mentors, fortnightly evening classes, and monthly problem sets even if you don't get into the camp. It is a win win situation, I think.

 

I went onto wikipedia and printed a summary of all the math fields and showed my son. I told him that High school math focused in only a few fields (algebra, geometry, trig, calculus), and that the olympiad material broadened the scope of his education (combinatorics, number theory, game theory etc). He very much liked the idea of keeping track of which of the fields he had experience in and even listing the books he has read in each field. He is very keen on taking a second class in math called "olympiad math."

 

So now there is one major hurdle. The site states that only students "studying in 2013 at a recognised secondary school in NZ" can go to the camp. They state that this is because any camp attendees must be qualified to go to the international math olympiad. I did some research and found that there was a homeschooler representing the USA last year, so perhaps this obstacle has been overcome. But sounds like I will be the one to push the boundaries here in NZ. Not sure when to bring it up with the committee. The form clearly requires not only a name of the school, principal, and head of the math department, but also your signature that ds is "is studying in a recognised secondary school in NZ." sigh. There is an alternative school that I could approach about allowing my son to use their name, but it is really kind of a pain in the neck, plus it is not a sure thing.

 

I am open to suggestions.

 

Ruth in NZ

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Is there a homeschooling advocacy organisation that might be able to give you some help or advice? Here we have the Home Education Association which provides PL insurance to members but also carries out advocacy with government legislation etc. In a situation like this they would be able to contact the Olympiad on your behalf to clarify the process.

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Thanks for all the advice! I have followed up on Kathy's suggestion and done some digging on the math olympiad in NZ. First of all, you don't have to compete, you can just do the problems, and go to the camp if you get in (there is a qualifying exam that my son would do very well at even as a 7th grader). So, that is good from the point of view of my son, who is currently not interested in competing.

 

that's terrific!

 

Second, apparently there are only 150 applications for the Math Olympiad camp every year and they take 24 students, so my ds has very good odds. Nothing like a small country that does not focus on math education! They have mentors, fortnightly evening classes, and monthly problem sets even if you don't get into the camp. It is a win win situation, I think.

 

even better; I like those odds!

 

I went onto wikipedia and printed a summary of all the math fields and showed my son. I told him that High school math focused in only a few fields (algebra, geometry, trig, calculus), and that the olympiad material broadened the scope of his education (combinatorics, number theory, game theory etc). He very much liked the idea of keeping track of which of the fields he had experience in and even listing the books he has read in each field. He is very keen on taking a second class in math called "olympiad math."

 

So now there is one major hurdle. The site states that only students "studying in 2013 at a recognised secondary school in NZ" can go to the camp. They state that this is because any camp attendees must be qualified to go to the international math olympiad. I did some research and found that there was a homeschooler representing the USA last year, so perhaps this obstacle has been overcome. But sounds like I will be the one to push the boundaries here in NZ. Not sure when to bring it up with the committee. The form clearly requires not only a name of the school, principal, and head of the math department, but also your signature that ds is "is studying in a recognised secondary school in NZ." sigh. There is an alternative school that I could approach about allowing my son to use their name, but it is really kind of a pain in the neck, plus it is not a sure thing.

 

hmmm...In the USA, the only non-mathematical requirements for representing our country at the International Math Olympiad are that the student be a citizen or permanent resident, & that he/she be under the age of 20 and not yet matriculated at a college or university. I know that homeschoolers have long been eligible here. My son was selected for the summer training camp (MOSP) several years ago, & homeschooling was not a problem at all. In fact, many homeschoolers have attended the US camp & have even been selected for the US team over the years.

 

 

I would think that the IMO eligibility rules would be universal. Maybe the New Zealand committee has that particular requirement because they're making sure that the participants are still in high school & not college. It's worth inquiring at least; most math people are quite reasonable about these things. You could always refer them to the long-standing acceptance of homeschoolers in the US. Good luck!! :001_smile:

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