Is problem solving an inborn skill?

[navneet9431]

I asked this because I find myself in situations which trouble me deeply.

I solve a deep interesting problem, I learn a new concept, its good but a single question which I'm not able to do, leaves me depressed, sometimes I can't just understand whether I CAN or CANNOT apply a concept to solve a problem , even though I may have practiced on it.

Seeing solutions to some problems I'm like "Hey I knew this concept, but why didn't I apply it, don't I have that much common sense to apply a concept which I have learned :-( ". So I just wanted to know, won't I ever get any more good, and seeing all the smaller kids doing these problems makes me kind of even more sad about myself, so I wanted to ask you guys, is it a inborn skill ? I just feel like it is so. Please help

 

[symbolipoint]

What kinds of problems to solve?
Nearly everyone has some problem solving ability inborn. Some have more, some have less; but experience, sometimes much of it, in some field, topic, idea/set of ideas helps in learning the territory. One should also not under-value study and effort.

 

[berkeman]

and seeing all the smaller kids doing these problems makes me kind of even more sad about myself

But your only 16 years old...

 

[verty]

You need to have real determination if you want to succeed at something difficult. You have to try every possibility and approach it from every angle until you find the one that works. Although sometimes you will find problems that you can't solve even though you do try that hard, but luckily those occasions are quite rare. But complexity exists, so there will always be complex cases that are hard to solve.

The thing about complexity is, you need to be ready for it. You need to know the theory and you need to have practice as well, so that when you are in the exam and you see that complex problem, you are ready for it. Then you just have to see how to apply the theory and in what way it relates to problems you've practiced. And look out for any tricks that could catch you out.

 

[QuantumQuest]

I asked this because I find myself in situations which trouble me deeply.

I solve a deep interesting problem, I learn a new concept, its good but a single question which I'm not able to do, leaves me depressed, sometimes I can't just understand whether I CAN or CANNOT apply a concept to solve a problem , even though I may have practiced on it.

Seeing solutions to some problems I'm like "Hey I knew this concept, but why didn't I apply it, don't I have that much common sense to apply a concept which I have learned :-( ". So I just wanted to know, won't I ever get any more good, and seeing all the smaller kids doing these problems makes me kind of even more sad about myself, so I wanted to ask you guys, is it a inborn skill ? I just feel like it is so. Please help

Aptitude as an inborn skill may be one important factor but it is quite a bit overrated in my opinion. There is a multitude of other important factors like family, conditions (...) when someone grows up and then come the efforts he / she puts and if they are spent wholeheartedly. Additionally, there is the experience gained along the way. So, for one thing, I think that it's early to be discouraged by the notion of "inborn skill" - I don't say there isn't such thing but you may already possesses it and you just need practice for instance; time will tell, and for a second thing - I don't know what sort of problems you're talking about, but whatever it is, there is always a methodical way to follow and learn.

 

[Nik_2213]

IMHO, different people solve different problems different ways. One approach will not fit all. Some people are better with a linear logic, some may stubbornly grind a problem down until it yields, others may 'twirl' the puzzle in their 'mind's eye', find an accessible perspective. YMMV. It does help to be widely read, so you have a bigger 'toolkit' of prior solutions and possible analogies.

My wonderful wife was a very intelligent, hyper-analytical person. I was a ravenous reader, had a knack for finding useful analogies and devising 'sideways' solutions. Happens we both loved Physical Geography, so our wits had more in common than we first thought. We made a good team...

 

[Matterwave]

Everybody can get good at basketball (barring some debilitating disabilities) but unfortunately not everyone can be Lebron James. What makes a Lebron James...how much of it is innate talent and how much is hard work is hard to say. One should not give up something one likes because they feel a lack of "innate ability" imo. Perseverance and determination are important.

 

[navneet9431]

Thank You everyone for boosting my belief in "Hardwork" back again!
One more thing I would like to know is.
How does I.Q. affect the problem solving capabilities of a person?Is it influenced by the genetics or can it be improved with practice?
I have seen some students with GREAT I.Q. in my classroom.They are able to grab the concepts very fast and apply them in difficult questions.

 

[symbolipoint]

Thank You everyone for boosting my belief in "Hardwork" back again!
One more thing I would like to know is.
How does I.Q. affect the problem solving capabilities of a person?Is it influenced by the genetics or can it be improved with practice?
I have seen some students with GREAT I.Q. in my classroom.They are able to grab the concepts very fast and apply them in difficult questions.

Forget about I.Q.!

Intelligence Quotient does not do your learning for you.

 

[Rive]

influenced by the genetics or can it be improved with practice?

Most likely has some genetics in it, but early childhood also has a great part, and then at the end it still can be improved by practice.

It is easy to find references what makes you feel dispirited. Especially in a competitive environment.
To always look for such references can become a bad habit and if you are unlucky you can slowly sink into depression and lose motivation.

If you are 16 then it's just the right time to start learning about how to manage your own self.

 

[pinball1970]

How does I.Q. affect the problem solving capabilities of a person?Is it influenced by the genetics or can it be improved with practice?
.

A high IQ is an advantage IMO, BUT (a its big BUT) focused, regular, consistent, practice & study can produce excellent results and you don't need to be a genius.

Those really smart guys in your class who get the concepts quickly? Talk to them, study with them and hassle your teacher if there is part he went through that you did not understand.

What subject is it by the way?

 

[navneet9431]

Thanks!
I have started to gain my motivation back.
It's Physics and Maths

A high IQ is an advantage IMO, BUT (a its big BUT) focused, regular, consistent, practice & study can produce excellent results and you don't need to be a genius.

Those really smart guys in your class who get the concepts quickly? Talk to them, study with them and hassle your teacher if there is part he went through that you did not understand.

What subject is it by the way?

 

[navneet9431]

Thank you so much for guidance!

Most likely has some genetics in it, but early childhood also has a great part, and then at the end it still can be improved by practice.

It is easy to find references what makes you feel dispirited. Especially in a competitive environment.
To always look for such references can become a bad habit and if you are unlucky you can slowly sink into depression and lose motivation.

If you are 16 then it's just the right time to start learning about how to manage your own self.

 

[navneet9431]

Studying with them is a good idea!
Isn't it?

 

[HAYAO]

Short answer: Yes.

Long answer: Well you see, people are born with different brain with each of them particularly good at one or several type of problem solving while not being so good in other. Put experience in that and it will complicate even more. Some people have significant learning curve while other may grasp the problem solving ability much faster. However, some people may have higher or lower upper limit in problem solving. Moreover, some people may have experienced "proper" training while other may have experienced training of much less quality. Some people may simply be uninterested in certain type of problem solving. There are so many parameters here that it is simply not easy to judge whether you are fundamentally good at problem solving or not. Just because you are bad in one particular type of problem solving does not make you bad in other type of problem solving neither. So yes, problem solving is an inborn skill, but it is not easy to judge whether one has it. You shouldn't be able to judge yourself...at least not yet if you are 16 years old.*I have completed an optional teachers course during my undergraduate program (which was tough to do in my applied chemistry course with high dropout rate), and I consider myself a legitimate speaker in this.

 

[berkeman]

How does I.Q. affect the problem solving capabilities of a person?

Being smart helps, but you don't have to be brilliant IQ-wise to be an excellent problem solver and scientist/engineer, IMO.

When I was about 10 years old, my father gave me a small paperback book on "Tricks for Problem Solving" or something like that (I wish I could remember the name and author -- it was a gem). It took me less than a week to read through it and start using some of the tricks. I've used what I learned in that book many times over the years, and have learned other tricks for problem solving along the way that I've incorporated into my thinking process.

Some of the tricks involved things like turning a problem around, or turning it upside-down, or thinking about the problem from the perspective of someone with a different background. Other tricks were to imagine part of the problem getting bigger or smaller or heavier, etc., and envisioning how that would change the problem.

Over the years I've learned other tricks that are great to include in your "mental toolbox" for problem solving. Things like always carrying units along in your equations and making sure they match at every step. Doing that often catches equation manipulation errors, and is also a good sanity check that you are approaching the problem the right way.

Another helpful trick for remembering a word or phrase that you are having trouble recalling is to run through the alphabet mentally quickly and sound out the beginning of the mystery word with each letter of the alphabet. Often that helps my brain to make the association to get back to the word I'm looking for. I figured out that trick on the fly in an undergraduate computer science class where the exam question had to do with how multitasking is handled in some computer architectures -- it asked for the term for the multitasking technique, and I knew that I had read the word but could not recall it. So I started running quickly through the alphabet, sounding out the beginning of the word I was looking for in my head, "ah...", "beh...", etc., until I got to "i...", "ill...", "in...", "interleaving!". Hah! that was cool.

So maybe check out a few books on Problem Solving Tricks at your local library to see if any of them help to give you some useful tools for your mental toolbox. They will help you no matter what subject you are studying or working with, IMO. Here is a list from Amazon to show you some of the books that are available:

https://www.amazon.com/s/ref=nb_sb_noss_2?url=search-alias=stripbooks&field-keywords=problem+solving

 

[StatGuy2000]

In this thread (as in a number of other threads on PF), people talk about IQ as if it is a validated and effective measurement of the degree of "intelligence" among humans, when in fact that is far from the consensus among cognitive scientists, psychologists, and many other researchers who have studied the human mind.

I have already posted the criticisms (including links to critics of IQ) elsewhere, so I will just my link on PF on this topic here, on post #41.

https://www.physicsforums.com/threa...d-maths-researches.957126/page-3#post-6069726

 

[QuantumQuest]

How does I.Q. affect the problem solving capabilities of a person?Is it influenced by the genetics or can it be improved with practice?

While IQ is surely of great importance for problem solving capabilities and what this further implies for the life/career of a person, is there any widely acceptable, reliable way to measure it? On the other hand, can you imagine a world renowned scientist for instance, who is said to have a very high IQ, doing any of his / her great discoveries just by living in a vacuum since he / she was a kid, without the proper education, efforts and gained expertise? I wouldn't. Or along the way, can the attribution of high IQ in achieving the desired success be measured and compared to the attribution of proper education, mentoring / guiding, and most importantly, of putting the required efforts? I don't think that it's that simple. So, what you have to do is put the proper efforts in the direction you're interested in.

I have seen some students with GREAT I.Q. in my classroom.They are able to grab the concepts very fast and apply them in difficult questions.

Is this the sole result of their high IQ or maybe also - or in some cases even only, good guidance combined with hard work? Did you try your best in a problem for which you have the relevant / appropriate background - which again implies efforts put, and failed to solve it? Again, as I said above for aptitude as an inborn skill a.k.a. talent, try not to get caught in the trap of overrating things because - at least according to my experience, the net result will be to "gain" unnecessary disappointment.

 

[pinball1970]

In this thread (as in a number of other threads on PF), people talk about IQ as if it is a validated and effective measurement of the degree of "intelligence" among humans, when in fact that is far from the consensus among cognitive scientists, psychologists, and many other researchers who have studied the human mind.

I have already posted the criticisms (including links to critics of IQ) elsewhere, so I will just my link on PF on this topic here, on post #41.

https://www.physicsforums.com/threa...d-maths-researches.957126/page-3#post-6069726

Myself and a few posters have mentioned IQ/ability but we have also mentioned hard work, good mentoring etc.
The other thread OP specifically mentioned University level mathematics not just “advanced” maths.
I don’t think anyone thinks high IQ is a free pass to success.

 

[Nik_2213]

I must agree on the 'IQ + Hard Work' thing. Hard work is essential.
I've seen too many 'really clever' students breeze through their early years then 'come to grief' due lack of a 'work ethic'.
Being 'quick on the uptake' helps a lot, but you must still work hard all year.

And, per my earlier comments, please read widely, both to give you handy background material aka 'General Technical Knowledge', and a broad perspective on problems. Such may defeat 'Out of Context' situations that stump most others...

 

[nuuskur]

I don't like the idea of being predisposed to being able to solve, say, math problems. I don't like the idea of 'being a genius'. I don't think I have some inborn ability to do these things. As an example, I can sing - that's something I've always felt was natural, but alone this ability wouldn't make me an opera tenor. Likewise, now that I have some understanding of predicate calculus, it alone won't just magically make me able to tackle some open problems in complexity theory or what have you. One must work hard, there is (almost surely) no cheap alternative.

I very much encourage you to not compare yourself with others. It is important how you have 'grown' with respect to yourself. Instead of despairing for how you couldn't solve the problem and those other kids could, study a solution of said problem and try to understand it. There are usually several solutions. For instance, I explain to myself (sounds very schizophrenic :D ) the details of some proof of a theorem or a solution of a problem I found interesting.

Spoiler: offtopic-ish

To elaborate on the singing part. I used to sing as a tenor in a local men's choir and there was another young baritone singer who wasn't very good at keeping clean tone, staying in tune, in rhythm and some other things that I find elementary. He went to study classical music and train as a baritone. I recently met him again and over the years these elementary things have become second nature to him. So what good is my supposed predisposition again..?

 

[pinball1970]

I don't like the idea of being predisposed to being able to solve, say, math problems. I don't like the idea of 'being a genius'. I don't think I have some inborn ability to do these things. As an example, I can sing - that's something I've always felt was natural, but alone this ability wouldn't make me an opera tenor. Likewise, now that I have some understanding of predicate calculus, it alone won't just magically make me able to tackle some open problems in complexity theory or what have you. One must work hard, there is (almost surely) no cheap alternative.

I very much encourage you to not compare yourself with others. It is important how you have 'grown' with respect to yourself.

Spoiler: offtopic-ish

To elaborate on the singing part. I used to sing as a tenor in a local men's choir and there was another young baritone singer who wasn't very good at keeping clean tone, staying in tune, in rhythm and some other things that I find elementary. He went to study classical music and train as a baritone. I recently met him again and over the years these elementary things have become second nature to him. So what good is my supposed predisposition again..?

I don’t like the idea of being 5 feet 10 and left handed but that is the way my genes have built my brain and body.
The singing reference is a good analogy, your friend went from mediocre to good through training, some things you can improve or improve a lot, other things you cannot improve significantly.

Can your friend hit a top A? (the A above the A above middle C) Why not?

 

[nuuskur]

The singing reference is a good analogy, your friend went from mediocre to good through training, some things you can improve or improve a lot, other things you cannot improve significantly.

Can your friend hit a top A? (the A above the A above middle C) Why not?

Yes he can :) He said himself that he had trouble even with D4, E4. He's received fantastic training. He doesn't sacrifice tone quality the higher he goes. Although, having to sing A4 is rare, he can also reach C5, though not with ideal tone. The point is, I am thoroughly impressed every way imaginable how much he has 'evolved', let's say. It shows that hard work trumps talent any day of the week. What's more, he has been seriously training for some handful of years and keeps improving. There is so much potential.

Formally
$$\neg \forall x(T(x) \Rightarrow S(x)).$$
Details are left to the reader :)

Of course, some things we have no control over. I have blonde hair, I'm 5'8'' and have flat feet. Not ideal, but that's what I have to work with. Also, let's not go overboard with extremal examples such as somebody who is paralised being able to move freely 'if they received enough training'. An intellectual activity can be taken up by almost everyone. Some natural talent to be able to solve the Rubik's cube won't make the champions solve it in a matter of seconds. A lot of training is involved. I'll make the concession that natural talents could be considered as a minor head start. That's it.

 

[pinball1970]

Yes he can :) He said himself that he had trouble even with D4, E4. He's received fantastic training. He doesn't sacrifice tone quality the higher he goes. Although, having to sing A4 is rare, he can also reach C5, though not with ideal tone. The point is, I am thoroughly impressed every way imaginable how much he has 'evolved', let's say. It shows that hard work trumps talent any day of the week.

Of course, some things we have no control over. I have blonde hair, I'm 5'8'' and have flat feet. Not ideal, but that's what I have to work with. Also, let's not go overboard with extremal examples such as somebody who is paralised being able to move freely 'if they received enough training'. An intellectual activity can be taken up by almost everyone. Some natural talent to be able to solve the Rubik's cube won't make the champions solve it in a matter of seconds. A lot of training is involved.

Top A?? I was kind of hoping you would not say that!
Ok so if he can hit a top A with good tone then the guy has and always did have innate ability.
I disagree that hard work trumps talent and that is not what I was getting at, I am saying innate intellectual ability gives you a leg up.
What about if you have talent and work hard too? How will you compare to someone who is not a clever and works hard?
I also disagree that anyone can partake in an intellectual activity if that activity is mathematics to University level.
You say some things we have no control over, what about your neurons in your brain do you have control over them? Their efficiency, number, synapses, neuro-transmitters?
Is the structure and efficiency of your brain less physical than your height?

 

[Rive]

lot of training

I think it does matter how much effort is needed to accomplish a goal. And it is not necessarily effective // advisable // affordable // available // etc.
The price tag for a dream is an important thing.

 

[nuuskur]

I think it does matter how much effort is needed to accomplish a goal. And it is not necessarily effective // advisable // affordable // available // etc.
The price tag for a dream is an important thing.

Agreed. This is why I don't pursue further training in classical singing. My area is mathematics. I focus my efforts to study of semigroups and automata (for now)

 

[pinball1970]

I think it does matter how much effort is needed to accomplish a goal. And it is not necessarily effective // advisable // affordable // available // etc.
The price tag for a dream is an important thing.

Yes you can spend twice the amount of time on a subject to learn it gain qualifications and pursue this further sacrificing other things in your life.
One poster said this can lead to stress, anxiety, depression, break down and even suicide.

 

[navneet9431]

"How will you compare to someone who is not a clever and works hard?
...
You say some things we have no control over, what about your neurons in your brain do you have control over them? Their efficiency, number, synapses, neuro-transmitters?
Is the structure and efficiency of your brain less physical than your height?"

So does that literally mean i can't become smart like my those classmates who grab and solve questions quick!

 

[Rive]

So does that literally mean i can't become smart like my those classmates who grab and solve questions quick!

No. That means you have to understand both your weak and strong points and you have to decide if you try to work hard to compensate for your weaknesses in order to fit in somewhere or work hard to try to make and advantage out of your strengths.

At your age you are just too green to jump any conclusions. Work hard and stretch yourself. Not to compete, but to measure and understand.

 

[navneet9431]

Thanks ![emoji4]

No. That means you have to understand both your weak and strong points and you have to decide if you try to work hard to compensate for your weaknesses in order to fit in somewhere or work hard to try to make and advantage out of your strengths.

At your age you are just too green to jump any conclusions. Work hard and stretch yourself. Not to compete, but to measure and understand.

 

[pinball1970]

"How will you compare to someone who is not a clever and works hard?
...
You say some things we have no control over, what about your neurons in your brain do you have control over them? Their efficiency, number, synapses, neuro-transmitters?
Is the structure and efficiency of your brain less physical than your height?"

So does that literally mean i can't become smart like my those classmates who grab and solve questions quick!

No! There was another thread on something similar. Work hard you will get results

 

[EngWiPy]

In my opinion, problem solving skills = domain knowledge + experience + intelligence

 

[pinball1970]

Yes its interesting.

Over two different threads we have been rehashing an age old argument, Nature verses Nurture. Which is it?

It is of course both in terms of learning concepts, acquiring and applying knowledge and we have been arguing mainly over what has the greater impact.

Where one puts the weighting is difficult because to understand that, one would have to have all the facts relating to how the brain stores then applies learned concepts.

 

[Rive]

Over two different threads we have been rehashing an age old argument, Nature verses Nurture. Which is it?

For me the most disturbing part about internet quarrels is that the participants often has some kind of urge to reach a final conclusion without even checking if it is possible or not.

 

[symbolipoint]

For me the most disturbing part about internet quarrels is that the participants often has some kind of urge to reach a final conclusion without even checking if it is possible or not.

The better word is "debate" instead of argue; but both words will work. Currently, this topic here is not hostile so it is not (yet) a hostile argument discussion.