I used to teach competitive math problems. An observation: These math challenges resemble real-world problems much more than routine textbook stuff.
You need to apply knowledge from disparate areas, combine them creatively, prod it and often fail several times before you get it right.
It's a good way to prepare one's kids (or oneself) to solve hard problems in real life.
I’d also argue such problems ought to be part of the curriculum for “normal” kids too. They might just more time and hints along the way than gifted kids. Once they get the taste of solving interesting problems from a young age, they might enjoy math more as well.
Note how many kids are attracted to games—-some of which are objectively more challenging than routine school math problems.
I used to do that too. First as a competitor, then for my national organization, and now I'm back at my former high school as a coach.
There's a very large variety of difficulty levels in math competitions. You go from almost trivial to olympiad level (= almost impossible even for most professional mathematicians).
That level also steadily increases as time goes on. Problems from the same competitions are already vastly more difficult than ten years ago, when I used to compete. Might be that I'm growing white hair, but it's almost unbelievable what the very top kids can do. They're very, very, very good.
> I’d also argue such problems ought to be part of the curriculum for “normal” kids too.
I wish there was a way to do it. I agree that the educational value is simply off the charts, but even low-level competitions are way too hard if you won't train, and most kids understandably won't.
> I wish there was a way to do it. I agree that the educational value is simply off the charts, but even low-level competitions are way too hard if you won't train, and most kids understandably won't.
It does require a different approach for most kids. An effective approach would involve some or all of the following components:
- interactivity
- visual imagery
- gamification
- social problem solving
- customized problem set
Technology will probably need to play a major role since teachers cannot do all of these for a large group of students.
Have you got resources to recommend? That's exactly the kind of thing I want for my kids, but apart from a blob of questions from my old math teacher, I don't have any.
There are also online gifted programs, incl at John Hopkins' Center for Talented Youth. The center is quite well-known in the gifted education community, with many famous alumni.
(not parent, but I used to do that thing as well and you might find this helpful)
It depends on their age and skill level. It goes without saying that younger kids need more guidance if they aren't extremely motivated.
This is worth looking into: https://artofproblemsolving.com, it's kind of the go-to website for the competitive math community. There are a lot of free high-quality resources on the wiki, and they sell courses and books.
And obviously, competition problems! For example, this is the AMC: https://amc-reg.maa.org/default.aspx; competition websites usually have an archive of past editions freely available. Studying past problems is the meat and potatoes of actual competition training. Make sure they are age appropriate, because the difficulty level ramps up VERY fast.
Aside from the Art of Problem Solving books mentioned by others, you may find https://web.evanchen.cc/faq-contest.html worth reading. I learnt a lot about math (contests (strategy, experience), undergraduate material, etc.) and more by deep-diving into Evan's site.
Seeing by myself how the Korean kids hack out gold medals in international math/physics olympiads by drilling the hell out in cram schools (and then most of them going to medical school with these credentials anyway), I really don’t have a good impression for these contests. Often the problems seem incredibly contrived and its connection to the real world (or at least higher-level academia) seems dubious. These contests might seem to test creativity in a superficial glance, but these cram schools have a database of past/potential problems in their “problem bank” and once high schoolers grind away thousands of these questions for a long period of time they can solve these like robots. (Obviously you still need to be smart enough to do this, but I really don’t believe it is a good nurturer of creativity.) I’ve seen lots of friends passionate and skilled in math and science but either fail to do well in these contests, or
don’t give a single fuck about it due to the problems I’ve described.
You need to apply knowledge from disparate areas, combine them creatively, prod it and often fail several times before you get it right.
It's a good way to prepare one's kids (or oneself) to solve hard problems in real life.
I’d also argue such problems ought to be part of the curriculum for “normal” kids too. They might just more time and hints along the way than gifted kids. Once they get the taste of solving interesting problems from a young age, they might enjoy math more as well.
Note how many kids are attracted to games—-some of which are objectively more challenging than routine school math problems.