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I'm a Math Teacher for highly talented students in High School.

It's hard for me to determine how fast can I move through topics and how deeply can I dive into different math subjects for enhancing their abilities, while also keeping their interest and fondness for mathematics high. I know that it's a quite ambiguous question but I'm asking about teaching methods and the psychology of teaching for high talents because I don't have much experience and I don't want to ruin their talents.

Can anybody provide some suggestions or rules for teaching Math to those talents? Or maybe some books about teaching?

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    $\begingroup$ Define GENIUS? Independent of the type of student, I believe your methods of teaching shall be the same and equal for all. All Geniuses went to school. :) $\endgroup$
    – MonK
    Commented Feb 9, 2015 at 10:01
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    $\begingroup$ If they really are genius and in high school chances are they already know more than you (or in a little while they will) and they need, and quick, college or university level. If they are, as more usually happens, "only" very talented then you can try some university themes with them. Anyway, this question belongs, more probably, to other section. $\endgroup$
    – Timbuc
    Commented Feb 9, 2015 at 10:01
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    $\begingroup$ It's probably a good idea to avoid the word "genius" — it promotes the stereotype that skill in mathematics is primarily a matter of some mysterious innate talent, which implicitly devalues effort, practice, and experience and discourages many students who don't instantly "get it". (There's also some evidence that such framing especially tends to discourage underrepresented groups.) $\endgroup$
    – Daniel Hast
    Commented Feb 9, 2015 at 20:24
  • $\begingroup$ I think no difference shall be made. One can push the best students, but a very important thing to teach is to bw humble. $\endgroup$
    – Diego Robayo
    Commented Feb 10, 2015 at 4:20
  • $\begingroup$ My advice (based on being a student in this sort of situation) is to just teach the standard stuff but accelerate it. If you want to enrich very slightly, do so. DON'T go off the deep end though. It is enough to cover the starred sections of the book or the harder HW problems (more than a normal class). If you don't have the ability to accelerate students because of course structure, don't sweat it. Many will do a year ahead in 8th grade. Some will do summer school (and you can encourage the strongest students). Also realize they have other classes too, so there is a limit on their time. $\endgroup$
    – guest
    Commented Dec 7, 2017 at 17:07

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The key with students like this is to allow them to dictate the pace of teaching, while providing interesting and challenging material. Now, that is very easy to say, but here are a couple of pointers:

  • Don't force them to go through the motions with topics they are already comfortable with. Allow them to test out of any unit, and find them extension material until their colleagues catch up.
  • Use their natural competitiveness by giving them the same problems in the same order, while keeping track (not necessarily publicly) of progress. A useful aid to this could be the tracking features in something like Schoology.com
  • You are going to need a lot of problems! Try any of the books on this list, especially the Mathematical Circles, the Stanford Problems, and if you are feeling insanely confident in their abilities, the IMO one: https://www.goodreads.com/list/user_vote/4298881

Good luck!

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This is triggered by @AmyB's and @DanielHast's remarks.

I think it would be useful in the OP's environment to understand and foster Carole Dweck's growth mindset theory. This theory is memorably described in Malcolm Gladwell's article, "The Talent Myth." There Dweck says,

"Students who hold a fixed view of their intelligence care so much about looking smart that they act dumb."

Recognizing when students have the fixed mindset, and nudging them toward the growth mindset, can dramatically change their ultimate achievements, at the same time as reducing their stress. The website Growth Mindset Maths offers a number of practical strategies. That website attributes this quote to Thomas Edison (but see Benjamin's comment):

"You must learn to fail intelligently. Failing is one of the greatest arts in the world. One fails forward towards success."

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    $\begingroup$ I wonder if One fails forward towards success is really due to Edison. There seem to be a few different attributions, including one to Charles F. Kettering. That's the one that came up first when I checked through google books... $\endgroup$
    – Benjamin Dickman
    Commented Jun 23, 2015 at 1:53
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A big part of the psychology of talented students is their attitude to errors that they make. Remember that no matter how bright the students are, they can still be overconfident and make mistakes. One of your jobs is to teach them to accept errors as part of the learning process and not an indication that they're not as smart as they thought It is important that you evaluate their work, and give them a chance to correct any mistakes. Don't be surprised if they insist they're right or are unable to handle being wrong. Make sure you model being wrong on occasion, so that they see everyone makes mistakes.

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