1. Tell the teachers that advanced students who are in lower classes should be treated with as much respect as a teacher could have for a student. I've had too many teachers who disliked me because I was better adapted at mathematics, shall we say.

2. Most likely the students will be bored with what the class contains (if they're stuck in a lower class and not a challenging one). Have the teacher encourage the advancement, by either giving challenging assignments, or simply making the class more interesting.

Tell them, do not make us feel quity when we have to skip few days of classes for ARML, or other math competitions.

Tell them, American culture does not highly value talent in math, but the modern world cannot live without math. One of their duty is to prompt and reconize highly talented math students, they should be treated as super stars and role models, at least should not to be ridiculed, as it happened in some place.

It may seem hard to believe when you're in middle or high school, but American culture does *highly* value math skills. Perhaps more so than nearly any other culture. It's just that it does so with high salaries and more satisfying careers, which aren't as visible to middle and high school students. Yeah, it's not cool in most places to be good at math when you're 12. But it's very cool when you're 22.

(1) How would you handle teaching a class where some of the students find the material very easy/have learned the material before and are bored, or wasting their time, and the other students are struggling?

(2) What do you do when some of the students are being singled out and made uncomfortable because of something? I've been picked on because I was smart, but also because the male/female ratio in the math club was skewed and I was the only girl in a room full of testosterone But I could also see it happening because one smart student was significantly younger than the other people in their class, or (imagine your own scenario here).

where in NC ?

Osud:

(1) Fight with the administration to split that class. As for what I'd do in the classroom, if it were an honors class, I'd teach to the top group. The other kids have a place to go -- a lower class. If it were not honors, I'd teach to the lower group, and fight with the system to create an honors class or move the other kids to an existing honors class.

(2) I think this is a much larger issue than just gifted education (which is what I'll be speaking about), and I don't think there is a sweeping answer to it.

Mystic: Greensboro, I think (I'll know for sure when I get there )

I think high-performing students benefit a lot from being exposed to exploratory learning. For instance, the teacher can have bonus problems on homeworks that are worth a tiny amount of extra credit: enough to provide some incentive for everyone to give it a try, and challenging enough to attract the students who normally breeze through.

Barring the amount of time it would take to implement the above, an easier thing to do might just be to drop hints during class about certain concepts that are being taught. Rather than merely presenting material to be accepted as truth, the teacher can mention that the theorems/formulas can be proven/derived if one has the interest to look into the necessary assumptions and background knowledge.

Engaging the high-performing students in the material that everyone else is learning is probably better for class dynamics than just giving them an AoPS book and letting them work on their own, I imagine.

Suggest that the teacher ask students to teach each other
(maybe have students pick different sections to study/learn/know before the class, and have them teach it to each other)

haoye - I'm not so sure about this. It really depends on the classroom and the gap between the top students and the rest. At a typical high school, an AoPS-like student is so far above the rest of the room that it may be impossible to engage them in a conversation without completely abandoning the rest of the room. For that student, handing them a book and cutting them loose seems like the only just thing to do for that student. If the average student is still very strong (like at a magnet school), then trying to keep the top kids integrated in the classroom might work.

I was singled out in middle school for being somewhat of a math fiend. At the time (sixth grade, if I recall correctly) my middle school was located across the street from a local high school known for its rough students and gang-related violence, among other things), and I (along with two other students) was encouraged to enroll in a high school geometry class, rather than sit through another less intellectually stimulating year of pre-algebra.

The other students and I agreed to this proposal, hoping for a change in circumstances to better help us get ahead in math. (Well, at the time, I'm not sure that was the motivation.. I'm fairly sure I remember wanting to go to the high school because enrolling there would grant me some semblance of respect amongst my age-conscious peer group.)

In any case, we all arrived in the big halls of the scary school as a trio of diminutive sixth graders on the first day. As any high school freshman can attest to, this is perhaps the scariest moment of the next four years, due to the uncertainty and sense of constant change that you are forced to adapt to. In retrospect, it was probably too much for us to handle, both emotionally and physically.

Our situation was made decidedly worse when we learned what class we had ACTUALLY been enrolled in: remedial geometry for seniors.

Well, we were shocked. Having expected to go into a class with bright freshman, we were not ready for such a massive age gap, and neither were the seniors. Our conversations in that class were really awkward for a time, because the social differences between 11 year olds and 18 year olds is immense. I felt alienated, away from my comfort zone, and I recall my friends felt similarly.

A small kernel of good erupted when we realized that our geometry teacher was passionate about math, and dedicated to kindling those same flames of passion in the students. It was quite clear at the time that the seniors in that class were not there of their own volition; rather, they were forced to undergo yet another nine months of being beaten over the head with formulae that they thought they would never need.

Our teacher, however, tried his best to foster an imaginative and exploratory spirit towards geometry. We worked in groups (the CPM method, if I remember right) which harbored an interesting dynamic. I distinctly remember taking a group test with some of the seniors, and I remember that their attitude toward me was basically that I was going to do the work and they could relax and not bother to study. This appalled me at the time, but even then I realized that I really couldn't do anything about it without confronting the administration, which isn't really an option as an 11 year old.

The teacher noticed that I was having some difficulties adapting to what was shaping up to be a bad decision, and he intervened (to my benefit!)

He had recently heard of this contest known as the AMC10, which was designed to challenge math students, and so on...

Well, I had never heard of it, but I jumped at the opportunity to finally be recognized for a talent which most people would mockingly scoff at. The AMC10 that year was a real eye-opener for me. I had gone in, expecting that it would be roughly the same difficulty as any average school test. I was completely stumped by the time I had hit problem 15. Never in my life had I been so out-witted by a math test, and this experience served to demonstrate all of the math that was still out there for me to learn.

That year, the school winner was announced. I believe they won with a score of 96, or 98, or something. That winner didn't make the AIME, I believe, but when I found him in the halls the next day, BOY did I make sure I started talking to him. He was a junior at the high school, and he had been in a similar position to me. He gave me some helpful tips on how to remain passionate about math without alienating yourself from the general public.

I guess my long winded story is finally coming to a conclusion, and possibly a point:

I would like teachers of gifted students to recognize that merely teaching difficult material to a small group of students is not ensuring their academic success. It's hard to say for sure what, if anything, will ensure this success, but I can guarantee that another important aspect of academic success is a solid social framework. Teachers should certainly try to foster a sense of harmony between the students, rather than singling students out. Rather than verbally being singled out, perhaps take the students aside afterward and point out interesting opportunities (such as contests or scholarships, etc.) It's important not to fracture a middle schooler's social confidence, because as many developmental psychologists will agree, a negative experience during those formative years in middle school can be correlated with a negative outlook on life.

I had a very difficult middle school experience, but I had gained valuable social skills by interacting with high schoolers for three years. Once I actually entered high school, dealing with kids my age became much easier. It helps that I've found a peer group that will respect me for wanting to be interested in math, but I know that not everyone is lucky enough to have supportive friends and caring teachers.

Richard, I wonder what your perspective on the social aspect of gifted education is?

EDIT: God, that was nearly a thousand words. I guess I had a lot to say.

I think the social issues are critical, which is a significant part of why I started AoPS in the first place. To me, it's the probably the biggest value of math contests/math clubs/math camps/etc. I have very few close friends, but nearly all of them are people I met through math contests in high school. (And none of them went to my high school.) Building a good culture for the top students is one of the things I stress most in talking to parent and teacher groups.

Mr Rusczyk, it would be a very enriching experience if you could come to my school to give that talk but that seems impossible.

From personal experience, in a class of gifted students, many of them are still not be very interested to learn more maths than what is required. It would be nice if it were as you write ‘For that student, handing them a book and cutting them loose seems like the only just thing to do for that student.’ However, it would not be nice to ask that student to move to a corner of the classroom for every maths lesson and to be virtually ignored by the teacher and be kept out of the lessons for the entire school year.

Ultimately actions do speak louder than words, even if the teacher did not mean it that way. I feel that it hurts the student’s feelings and self-esteem.

Thank you.

mathbear -- interesting. Would you prefer to just go along with the class in what they're doing at their pace? Or would you prefer to be allowed to go to your own room and work? Or would you like your current situation, but with a little teacher time now and again? (I realize that your ideal would be to be in a class that is going at the correct pace for you, but that's simply never possible for the top 1-2 students in any class.)

Personally, I'd like the relaxed math class instead of an actual work one. It's one class that you won't have to stress about in high school and it's one that you can spend however you want. The unfortunate downside is that you won't learn anything.

Welcome to the Piedmont region of NC. If you come to Greensboro, the Academy at Lincoln seems to have attracted good math students to middle school recently. There must be something good going on there - but to be honest, I've not talked with their teachers despite living just 1/2 hour away.

Many teachers might benefit their top students by helping them connect with other bright people in the community who are able to provide an appropriate challenge - perhaps, math profs, kids with similar interests in other grade levels, or parents who might volunteer to coach math teams and the like. Many teachers don't have the ability to challenge top students and often don't handle them well. This is a big reason that there are not more math teams.

There seem to be some misguided efforts to get these teachers to do something for top students that is just beyond their capabilities. It would be much better for all concerned if that teacher could be honest about the situation and help the kid connect with good challenging resources. Getting this message to teachers without bruising egos might be an interesting challenge - guess you'll need all the tact you can muster when you have these discussions. You'll probably find that many teachers will be relieved to find ways to challenge these students without trying to get really smart really fast.

That's something I will be including in my talk -- teachers have to accept that their role changes when dealing with the very top students. "Teaching math" is no longer near the top of the list. Most of the very top students are largely self-taught, since they can teach themselves faster than anyone can teach them. So, our role as teachers becomes that of a guide -- provide access to resources and opportunities, and point out that there's more out there than what's in the textbook. I do think there are plenty of teachers who understand this, but I think there are many out there who don't understand how important it is not to simply think, "Jane is getting 100s, so she's doing fine." The student who gets 100s all the time is just as much a problem as the one who is getting 40s. It's just hard to convince people that this is the case. (And not just the teachers, but the students, too.)

If this reply is too late, hope the talks went well. That's a lot of talking!

If not, I don't have a lot to add to the good advice you've gotten and to what you've already thought about yourself about teaching gifted math students -- somehow find ways to get bright students together, give students challenging problems to work on, offer the AMC tests early in the students' math careers, and encourage interested students who do well on one level to pursue the next level.

One thing my son's mathcounts coach does is to work problems herself, and when she gets stuck she asks her brighter students for help. They learn that even the teacher works problems, even the teacher gets problems wrong, and that's okay. They also learn to explain respectfully!

I've recently read Li-Ping Ma's book comparing elementary math education in China and the U.S. One difference she notes is that while the American teachers assume that they know the math (in this book, basic arithmetic -- subtraction, long division, dividing by fractions) and focus on the best method of teaching it, the Chinese teachers work on their own practical understanding of the math. They work on the problems in their textbooks and talk to their colleagues about them. Not surprisingly, the teachers in China are able to articulate better understanding of the arithmetic and are better equipped to explain it to students and to help students correct errors in their understanding. I'd encourage all the teachers to keep thinking through the problems they're teaching students to solve.

If you get a chance, forget The Omnivore's Dilemma and enjoy some real NC barbeque -- it's not sweetened with corn syrup or anything else.

Blue Morpho (expat Carolinian)