How Would You Feel If High School Students Beat You in a Math Contest?

[andytoh]

This may sound like a strange question, but I am really curious how others would feel. Suppose you are a fourth year university student, or even a graduate student, specialized in math and got virtually all A+'s from solid studying and hard work. Then, somehow, you were able to write a high school math contest, and results reveal that though you did well, there were many high school students who actually beat you.

Would you then realize then that those A+'s that you got in those many university math courses were because you studied hard, but your higher-order and creative thinking never really improved (as much as university math knowledge, which were of no help in the high school math questions)? Would you feel that you were not as smart as you thought you were, even ashamed that high school students who never studied the some four years of sophisticated university math actually beat you and are more clever than you?

 

[andytoh]

By the way, this is not a far-fetched question by any means. Some high school students are just so gifted in creative math thinking that virtually any university math specialist would be beaten by these gifted high school students in math contests in their own grade. No matter how good your university grades are, I'm sure that there will be some high school students (perhaps many) from your country, perhaps even from your city, that would beat you.

 

[waht]

I actually have a couple copies of high school math contest tests which I blew. Looking at them years later I realized a lot of questions are from number theory and geometry. The questions have you rearrange digits, take mods, or find the last the digits of an incredibly large number. I'm not sure what the state of todays tests questions are, but I assume it's the same. Basic arithmetic, and geometry can be all understood by high schoolers. It's just being taken to the next level. But I wouldn't feel bad, if a high schooler aces those tests, and I didn't. When was the last time you bisected a line with a compass?

 

[Zenparticle]

It's a bit like chess for me- I love to play and have worked hard to understand the game-this was no easy task for me. For Years I've studied by tooth and nail, worked through books and lessons just have some 12 year old kid beat me not once, but again and again in what seemed effortless on his part. It is annoying, I will always have to work harder at it then the kid will, but some people are just gifted. The rest of us work hard to make up for no gift- There will always be someone smarter and better at things that is just the way life is.

 

[andytoh]

But I wouldn't feel bad, if a high schooler aces those tests, and I didn't. When was the last time you bisected a line with a compass?

What if you prepared for the high school math contests, refreshed your knowledge in all those high school topics, and the top high school students still demolished you due to their higher order thinking in those questions that you simply cannot prepare for (i.e. are more clever than you despite your years of univerisity training)?

 

[ice109]

umm who cares? do you do what you do so you can boast and be better than other people or because you enjoy doing it?

 

[waht]

It's no big deal. I would go down with hope, and knowing that there are more smart people out there. What this world needs.

 

[andytoh]

umm who cares? do you do what you do so you can boast and be better than other people or because you enjoy doing it?

I agree that you should not stop following your passion just because kids are better than you at it (I'm sure Zenparticle is still studying chess for his love of the game despite losing to 12 year olds), but would it make you feel bad in any way? Remember, that math is what you've specialized in for 4+ years in university/grad school.

 

[Zenparticle]

Well my point to the chess story was that there will always be someone better, it's expected! No need to beat yourself up or feel resentful or throw away 4+ years of grad work just because some one younger grasps ideas better- And of course I love chess and that is why I play- in a sense that kid who beat me only inspired me to try harder. PS I am not a guy.Just weird being called that.

 

[morphism]

Remember, that math is what you've specialized in for 4+ years in university/grad school.

Unless you specialized in olympiad-style math, why would you give a flying ****?

 

[wdoe999]

I hate to generalize, but I have found that good marks on math tests may not necessarily indicate a good overall intelligence, or the ability to use logic and critical thinking.

I have known a several people that know what was taught to them in math class, and can crunch math problems like a computer. Some of these people, however, know what was taught to them and that is all that they know. They don't know how math relates to the rest of the world, and how to approach problems from different angles using math as one tool.

My favourite example of this phenomenon was a physics exam that I wrote in University. We had a question where we were given some electromagnetic experimental results and were asked to use these results to calculate the mass of an electron. When the professor returned the exams to the students, he couldn't hide his disgust. A good portion of the class did the math correctly, but made the same mistake when interpreting the question. These people computed the mass of an electron to be greater than the mass of the Earth! This is an example of too much reliance on math skill, and no reliance on common sense.

So don't be discouraged. Just the fact that you raise the question indicates that you care about knowledge. It is good to be concerned about knowledge, as it is a motivator to keep learning.

BTW - Some of those people who thought an electron had more mass than the Earth are now designing buildings and bridges.

 

[mathwonk]

it means someone is better than you. live with it, celebrate it. did you think you were god?

 

[Hurkyl]

I was one of those high school kids: one of the best in Michigan. If it makes you feel any better, there have been a few times where I was quite worried that my skill was limited to a sharp memory, rapidity of thought, and a talent for spotting 'cheap tricks'.

 

[ice109]

lamenting a low iq is like lamenting not having superpowers and given the choice i would take superpowers of over iq anyday. that's how little importance it is, that even if i was able to indulge this kind of irrational desire i wouldn't.

 

[LukeD]

lamenting a low iq is like lamenting not having superpowers and given the choice i would take superpowers of over iq anyday. that's how little importance it is, that even if i was able to indulge this kind of irrational desire i wouldn't.

Ha, I'd definitely take super powers over math ability. Of course, given the choice between love and happiness and pretty much anything else, I'd also choose love and happiness. (unless maybe it was love and happiness and then death 5 minutes later, definitely would not pick that one)

But it's definitely true that being really good at something isn't going to make you feel satisfied with yourself unless that's really all you need (and for most people, it's not). So if it bothers you that much, just try to find something else that you enjoy. And if it makes you feel any better, just remember that some of those people who are really amazing at math (approximately the same percentage as the rest of the population) are going to be really miserable despite how much they've "got it made".

 

[matt grime]

So someone's smarter than you at questions that are specifically designed to have 'tricks' to answer them. So what. Take the math Olympiad. Excellence in that is little indicator of actually being good at research mathematics.

 

[andytoh]

I always thought that math contest winners are the best candidates for becoming successful researchers (whether they choose to follow that path is a totally different thing).

 

[Count Iblis]

...even ashamed that high school students who never studied the some four years of sophisticated university math actually beat you and are more clever than you?

Indeed, and you shouldn't be ashamed of being ashamed, because competition is something natural, people will try to beat others at games, maths, sports etc. and certainly won't like to be beaten by people who are a priori less qualified. If we psychologically weren't like this we would probably still be living amongst Gorillas and Chimps in the Congo

 

[nrqed]

This may sound like a strange question, but I am really curious how others would feel. Suppose you are a fourth year university student, or even a graduate student, specialized in math and got virtually all A+'s from solid studying and hard work. Then, somehow, you were able to write a high school math contest, and results reveal that though you did well, there were many high school students who actually beat you.

Would you then realize then that those A+'s that you got in those many university math courses were because you studied hard, but your higher-order and creative thinking never really improved (as much as university math knowledge, which were of no help in the high school math questions)? Would you feel that you were not as smart as you thought you were, even ashamed that high school students who never studied the some four years of sophisticated university math actually beat you and are more clever than you?

It's actually an excellent question.

It depends on the *why* you do maths. if it's in the spirit of competing with others, then it's a real bummer to suddenly come to face with someone much better at doing some types of problems. And this is why doing something for the joy of being better than others is a very dangerous thing to do. There is always someone better. And even if you would be recognize as the world top person in something (whether it's chess, bodybuilding, rock climbing), it won't last long, usually.


However, if you do something because you *love it*. because you enjoy it so much that you love spending your free time thinking about it. Because it feels fun to think about it. If, going on a vacation on a beautiful beach for a week once a year you still feel like thinking and working on your passion, then it's the best indicator for happiness in that endeavour as well as a good precursor for success.

It's important to have a certain level of intelligence but
being passionate about something is as important if not even more important. Sometimes ideas come not because one is brilliant but because one is constantly thinking about the problem to be solved. And that happens when one is passionate about something.

 

[matt grime]

I always thought that math contest winners are the best candidates for becoming successful researchers (whether they choose to follow that path is a totally different thing).

Maths contest winners are the best at doing maths contests. That isn't what research is about. Until you have more statistics about it, you should stop presuming things that may not be true at all.

Some great mathematicians were great Olympians. Not all Olympians (I think I heard less than 50% of the UK contestants) go on to research, and not all would have succeeded if they'd tried.

Olympiad problems are specifically chosen to be solvable in a short period of time, if you're sufficiently clever. People who do well at that aren't necessarily those who will survive when months of work is called for on problems that might not even have answers as stated.

 

[Gib Z]

This thread makes me feel much better, because I was sort of thinking the same thing as andytoh. There are different ways of being "good" at mathematics, like andy said. Theres hard work and study to gain the knowledge and method/techniques, and there's being simply really clever and finding the "cheap tricks". I was quite worried that I wasn't learning the odd techniques in the Olympiad style questions, which may perhaps come in useful, and I got * a tiny bit* better in it, but so far I have found it hasn't helped in any other mathematics than the competitions, which I don't study mathematics for.

The only thing that makes me slightly sad in when teachers and other students say that I'm not actually good at mathematics (or else I would do exceptionally well in Olympiad Competitions, though I do moderately well, just no where near as well as the other type), It's just that I study a lot. On bad days, I become depressed over this, On good days I tell them to **** themselves.

 

[Count Iblis]

B.t.w., I saw a documentary about British math olympiads just a week ago or so on BBC tv. They were following their performance, training, selection process for the international math olympiad etc. What was striking is that some atypically large fraction of the olympiads had Asperger's syndrome (a mild form of autism).

So, perhaps they are using parts of their brains that are normally reserved to recognize and interpret things like facial expressions etc. to "see" the solution to math problems.

 

[disregardthat]

This thread makes me feel much better, because I was sort of thinking the same thing as andytoh. There are different ways of being "good" at mathematics, like andy said. Theres hard work and study to gain the knowledge and method/techniques, and there's being simply really clever and finding the "cheap tricks". I was quite worried that I wasn't learning the odd techniques in the Olympiad style questions, which may perhaps come in useful, and I got * a tiny bit* better in it, but so far I have found it hasn't helped in any other mathematics than the competitions, which I don't study mathematics for.

The only thing that makes me slightly sad in when teachers and other students say that I'm not actually good at mathematics (or else I would do exceptionally well in Olympiad Competitions, though I do moderately well, just no where near as well as the other type), It's just that I study a lot. On bad days, I become depressed over this, On good days I tell them to **** themselves.

Excellent post. It is weird how mathematics is treated so much different than other hobbies. Take football for example. If you play football and are pretty good, you play on a good team that have an good win\lose statistics, you are not getting remarks because you are not one of the "best". You don't play on the national team, or on games that is shown on television. Does that makes no "No better than anyone else"? You can certainly be good in a field, just because you don't excell in the field. And what I've seen of you you are very good in mathematics, and that you get such remarks is absurd.

 

[Feldoh]

Unless you specialized in olympiad-style math, why would you give a flying ****?

To add, the kid that beats you probably did, throughout high-school I mean. Of lot of the stuff on those tests like the AIME, USAMO, etc. Are not taught in a regular high school curriculum. Those kids study for Olympiad-style math a lot.

 

[eastside00_99]

The words of one of the greatest mathematicians of the 20th centuary:

"In our acquisition of knowledge of the Universe (whether mathematical or otherwise) that which renovates the quest is nothing more nor less than complete innocence. It is in this state of complete innocence that we receive everything from the moment of our birth. Although so often the object of our contempt and of our private fears, it is always in us. It alone can unite humility with boldness so as to allow us to penetrate to the heart of things, or allow things to enter us and taken possession of us.
This unique power is in no way a privilege given to "exceptional talents" - persons of incredible brain power (for example), who are better able to manipulate, with dexterity and ease, an enormous mass of data, ideas and specialized skills. Such gifts are undeniably valuable, and certainly worthy of envy from those who (like myself) were not so "endowed at birth, far beyond the ordinary". Yet it is not these gifts, nor the most determined ambition combined with irresistible will-power, that enables one to surmount the "invisible yet formidable boundaries" that encircle our universe. Only innocence can surmount them, which mere knowledge doesn't even take into account, in those moments when we find ourselves able to listen to things, totally and intensely absorbed in child's play."

-Alexander Grothendieck

 

[yasiru89]

I wouldn't trade my interest nor skill(regardless how little of the latter I actually possess) for super powers. Nor would I throw away four years of my life to go off and do something else just because the next guy beat me to something. People who magically crack problems and apparently annoy most, often fit the high memory and IQ profile. They are genuinely talented and this needn't bother other people. Some of them never really pursue mathematics further and sometimes cannot or will not venture beyond problem solving, the standard IMO basis. There aren't many Fields medalists who scored gold at the IMO(though any self-respecting mathematician would reject a Fields medal if presented one)and by your tone this might well make you feel better.
I, on the other hand lay claim to mathematics not for the intuitive choice that one should persevere at what one is good at, but rather one should persevere at what one holds interest in. It is a pleasure excursion for me and I simply cannot care less of another that may choose to run while I walk.