Thursday, September 16, 2010

Should You Mentor High School Students?

I have mentored many high school students on projects (21 in the past, 6 right now). Is this a good use of ones time? I note my experiences and advice- if you have different experiences and advice, feel free to share.
  1. Unlike PhD students you don't have to worry about the job market, support money, or if they prove something original.
  2. I have not gotten papers out of it. Even very good students lack a certain maturity for paper writing. (There have been exceptions.)
  3. It is good of society. (The most important problem facing society today, that I can do something about, is that not enough high school students know Ramsey Theory.)
  4. By explaining material to them it has helped me sharpen my own understanding.
  5. Most of the students I have advised have been pretty good mathematically (they already know discrete math and induction and how to prove things). Some have been good at coding which also comes in handy. Most have come from Blair High School's Magnet Program. (They have a very strong physics department which specializes in Magnetism.)
  6. Having students do a project where they can code some stuff is good in that SOMETHING will come of it. Also, this may be something you wouldn't normally do so it may help you.
  7. The standards of what is original are different on this level. The project does not have to really be original in the sense we would mean it. If they work out something that you already know the answer to and write it up that's fine. It may be more accurate to call it a research experience.
  8. The mostly did projects that DID NOT require a lot of background. Even if they are very good, they are unlikely to have a lot of background. This is why many of them have worked in Ramsey Theory. You may be saying but bill, you like Ramsey Theory anyway. True- but one of the reasons I got interested in it was to help mentor high school students. Its a chicken-and-egg thing. (This metaphor may die soon as scientists now think the chicken came first.)
  9. The student of mine who has gone the furthest in Math is Jacob Lurie. who is now a full professor at Harvard (in Math). He didn't need much help; however, I did help him learn some recursion theory (we went through all of Soare's book) His project was on Recursive Surreal Numbers.
  10. Many of my students enter various contests. For every thousand dollars they win, I get a free lunch. (If Jacob wins the Fields Medal I'll get 15 free lunches!)
  11. Recruitment. Some of my mentorees have come to UMCP, though that is not really on my mind when I agree to be a mentor.
  12. Why have I mentored so many? I have never sought them out--- they find me since I have mentored people in the past. Also, if a HS student comes around and wants a mentor they are often pointed to me.
  13. Should you mentor high school students? It is unlikely to help you with your research program (there are exceptions). But if you do mentor high school student then (1) make sure its not a big time sink, and (2) use it to learn or relearn results you've forgotten (Recently I was forced to relearn the Erdos-Szekeres Theorem).
  14. So, what have they worked on. Including this years gang and their tentative projects here is the breakdown:
    1. 11 worked on Ramsey Theory (3 of these worked together).
    2. 3 worked on Duplicator-Spoiler Games (together).
    3. 3 worked on Empirical Algorithms (2 of these worked together).
    4. 3 worked on Crypto.
    5. 2 analyzed some Simple Games.
    6. 1 worked on Recursive Surreal Numbers.
    7. 1 worked on Graph Isomorphism.
    8. 1 worked on Monotone Circuits.
    9. 1 worked on the Prob Method.


  1. How do you schedule time with them ? a once/week meeting, ad hoc meetings as needed, mixture of both ?

  2. Good question!
    Over the summer we meet once-a-week
    or more as this is a time we are both free.
    That is when the bulk of the work gets done.
    During the year once every 2 weeks in the fall and then as needed. Somewhat ad-hoc.

    Might also depend on deadlines they have
    for both their school and for various contests.

  3. This is great!

    Fantastic post. I totally agree that not enough high-school students know Ramsey theory. :)

  4. As an undergrad I tutored, both formally and helping friends struggling with Calculus. I was always amazed at how much you can accomplish one on one or in small groups. You can identify conceptual difficulties and explain the relevant details in different ways until their eyebrows unfurrow. In a class setting you can't address everyone's individual difficulties, or even identify what they are reliably.

    Good for you contributing to knowledge on a per-person basis: it really is an important part of learning that our education system largely skips.

  5. Nice post.

    My experience is mainly with students preparing for IOI and IMO. You can expect more from them. Interestingly, many IMO Gold medalist become very good mathematicians and theorist, familiar names among them are Babai, Matyasevic, Lovasz, Suslin, Håstad, Shor, Razborov, Gowers, Perelman, Tao, ... .

  6. Thanks Bill !
    Do you find that most progress happens during meetings or in between meetings for the most part ? (where progress can be defined any way you see fit.

  7. I think it is hard to underestimate the impact these types of experiences can have on the students themselves. I went to Montgomery Blair HS, and also did research with a UMCP professor (Prof. Samir Khuller) when I was at Blair. The experience was one of the major ways I started being interested in theoretical computer science. Now as a grad student at MIT doing TCS, I can really appreciate all that Samir did for me.

    I think one difficulty in such endeavors is finding high school students who are really interested in research. One thing Bill didn't mention is that the reason so many of his high school students come from Blair is that there is a gifted and talented program there (which unfortunately is undergoing some budget problems, see ). There are various similar programs around the country, and they can be a good resource for finding enthusiastic students.

  8. some corrections to above post:

    1) I see Bill actually did mention Blair's magnet program (sorry Bill!). ("magnet" here really means "gifted and talented", so even the computer science teachers emphasize "Magnetism")

    2) "hard to underestimate" -> "easy to underestimate"

  9. Suresh- During the meeting they LEARN lots of stuff. get motivated, and are
    GIVEN things TO DO AT HOME. From that point on its a mixed bag- some do LOTS at home, some not-so-much. But the MEETING
    are very productive in any case.

    Important to have well defined agendas
    for the meetings. TODAY WE WILL GO OVER

  10. Last comment was from me- I must have
    pushed the wrong button which is why
    it looks like its from Anonymous.


  11. In Albany (upstate New York), we start with middle school students and go up to High School level ( to help Students) appreciate Math. Students did not do any projects with us - but we encouraged students to publish solutions in various journals. is our blog spot.

  12. USA needs to get high students involved unless brain superpower India is going to crush it. India has 10 million engineer graduates a year, many top geniuses, like Deolalikar, a new TCS God in making. So humble, so honest, such genius like Deolalikar is rarely born, he should win the Darwin.

  13. protip: If you want to leave an anonymous comment on a not particularly busy thread, it helps to wait more than a minute after leaving a signed comment. :)

  14. Since I am a second winner of IOI, I am peerless.


  15. They should be taught not to forget about integrals and polynomials, in the whole life. But, that is absolutely not enough.

    Cosmic Farmer

  16. The most incapable tutors are gathering in high schools...

  17. but not the same degree of incapability

  18. Yaahh, due to their ability, they are trying to make their next classes better.

  19. hs students dont need to do all the assignments, but some small easy ones are interesting.

  20. Gasarch alluded to the idea that his students were advanced, but did not go into detail. I think some people got the wrong idea about this group's level. Many of his students are IOI, IPhO and IMO gold medalists. Most of Blair's best students of mathematics work with him.

  21. This comment has been removed by the author.

  22. Excellent post. I would love it if you could elaborate on point 3. What are the benefits to society of high school students (or anyone) knowing Ramsey Theory? Since reading your post a few days ago I have been trying to understand enough about it to answer this question. Curious to know what you meant, and if it's anything like the conclusion I've reached so far as a thoughtful layperson (okay, I did a CS degree nearly 20 years ago, but found Theory to be the most challenging bit, and my memory's not great).

    (reposted as I forgot to check the Email follow-up box the first time...what was I saying about my memory?)

  23. Thanks for comment!

    I didnt quite mean Ramsey Theory
    in particular; however, if high school studeents had that kind of math maturity that would be good
    for society - better jobs for
    the student, more intelligent and logical political debates, etc.

    For a great book on math literacy and
    society see

  24. This is great, i need some help with getting my concepts clear on Automata and Complexity. Is there a way to get some help on this?

  25. (Not sure why you are asking this
    on this old post, but I will answer it anyway.)

    To learn more complexity and automata theory- these terms are somewhat ambigous, but if you
    go to my website and click on
    my Education thing about teaching
    CMSC 452 in Spring 2011 and goto
    the syllabus you will see some very good texts you can use, and what my syllabus is.