Are students discouraged from becoming the 'Renaissance man/woman'?

red_red_wine

During the Renaissance, students aspired to being polymaths, with a huge level of knowledge and competence in a variety of fields.

Now, obviously most of us don't have the raw talent or intelligence to be Da Vincis. That being said, it seems as if in our education system, one is encouraged to either excel in the scientific field or in the humanities.

If a student is very good at Maths, it is assumed and accepted that he/she will not be good at English/History etc. Indeed, there is a perception that it is almost impossible for one to be both scientifically and creatively inclined.

This encourages a certain sense of complacency, i.e. students are told that it doesn't matter if they do Ordinary Level Maths, becaus the fact that they are excellent at writing essays compensates for it. My current English teacher, an extremely intelligent woman, proclaims with what is almost pride that she is hopelessly numerically incompetent. In a sense, it seems to be a badge of honour.

My problem is that the fields are not as far removed as is assumed. Many of the same skills are necessary for both. English, at least for the Leaving Cert, requires a certain level of analytical skill, which is also applicable in Maths. I've noticed a certain amount of snobbery among the teachers of the humanities. Maths, Physics and the other sciences are seen by them to be completely devoid of creativity or beauty and regarded as purely practical subjects.

While the Leaving Cert demands a basic standard in all three core subjects, Irish, English and Maths, the message seems to be given that students cannot excel in all of those fields, but that they should choose one of them, because after all, one can't be both scientific and creative. Yet, the sciences often are quite creative and the humanities often scientific, or at least, logical.

nyarlothothep

I think the sciences can require a high level of creativity, the snobbery attitude in the humanities just seems like defensiveness in the face of a general sense of the reduced status of the arts in relation to the sciences insofar as intelligence and use value are concerned.

You are right that society is becoming more specialized, whether this is a good thing or not remains to be seen. In my opinion, being good at multiple things but not necessarily the very best at any one of them can be beneficial, in the respect that you can take what you've learned across disciplines and combine this knowledge to generate something new rather than simply being the most efficient cog in the system you can be, which I think is encouraged and possibly to society's own unwitting detriment. Its not simply good enough to maintain the societal machine imo, it needs to advance and doing that implies being unconventional which isn't rewarded until it yields great dividends.

I think it should really be left optional as to whether one wants to become a hardcore scientist/academic or to draw upon both, I would like to see a framework in universities which allows for this, I think in American universities you can study both humanities and the sciences until you major but I may be mistaken.

Permabear

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southsiderosie

I say this as someone who is not mathematically inclined: I find this distinction to be quite odd. Mathematics and philosophy have historically been inter-related. I also seem to remember reading somewhere that there is a positive correlation between mathematical skills and the ability to learn a foreign language; math skills are also linked to musical ability. The ability to do high level math requires a great deal of creativity.

To be honest, this is why I think a lot of the policy focus on emphasizing math and science at the expense of the humanities is problematic. I don't think these things need to be either/or. Personally, I think that at the university level there should be a real return to a classical liberal arts education where regardless of major, students need to take classes outside of their core subject - REAL classes, not "Physics for Poets". The basics would include philosophy, literature, history, math & science, political/social theory, and composition. The University of Chicago's core curriculum has stood them well over time, and few would argue that someone who majored in economics or psychology from U of C is somehow underqualified to work at a bank or an ad agency; they will be better read and have better composition and critical thinking skills that most marketing majors will. But I think this speaks to a much broader problem that a lot of countries are facing today: what should be the role of the university in modern society?

Permabear

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red_red_wine

red_red_wine wrote: »

This encourages a certain sense of complacency, i.e. students are told that it doesn't matter if they do Ordinary Level Maths, becaus the fact that they are excellent at writing essays compensates for it. My current English teacher, an extremely intelligent woman, proclaims with what is almost pride that she is hopelessly numerically incompetent. In a sense, it seems to be a badge of honour.

Oh yes, I've had this rant many times. You hear people proudly announcing they're useless at maths, but it's not as fashionable to declare you can barely write or read anything. Although considering correct spelling is now 'being a nazi', we may be headed that route.
But yes, it's such a pity and so wrong that people separate the two so much.
I think the emphasis is certainly leaning away from maths competency :mad:

It's interesting how many people combine maths & music though - there is hope yet

Eliot Rosewater

I'm a student of maths myself, but I love to branch out.

(Except at the moment. I'm studying for exams, so I'm infatuated by maths. I'm thinking about it morning, noon and night. I had this erotic dream the other night that involved maths. It was bizarre. Because there were two of us in the dream the imaginary components of our persons multiplied and became -1 (thus turning us from a skew-adjoint map to a self-adjoint map, in the spectral theory). It was quite strange.)

Anyway ... branching out! I don't buy this notion that "you're good at maths or at English". In fact, I hate that notion! I think all the branches of intellectual activity - maths, economics, physics, philosophy, literature, history, political theory, etc - are complementary, and a base knowledge of all leads to the most fulfilling kind of education and thus life. It's hard to describe what a fulfilling education is, of course - for me it's being able to understand a lot of the world around you (taking a broad definition of world). All these branches give you new perspectives on different parts of the human experience.

That's my opinion, and with the major caveat that I haven't actually attained a base knowledge of most if not all of those fields ... yet.

Eliot Rosewater

Specially about maths (I have to defend my corner ). A good maths education gives you critical thinking skills. I challenge any University debater to take a pure pure maths module and actually fully understand it - then they can talk to me about critical thinking.

As an example,

One of the key concepts in maths is the axiomatic method, by which one starts from a certain small number of assumptions and deduces everything else from that. When engrossed in a pure maths subject I find I'm constantly thinking of the root of everything. This theorem is true, but why? Why are the things that make it true true? What are the key switches, the key facts of the theorem, that turn it to absolute truth? How can we trace the pillars of this theorem back to the core assumptions of the system?

I find myself constantly applying this method when reading peoples' views on politics and other issues. When I'm confronted with a view, say "the government should make Irish compulsory", my first instinct is to head for the root, to determine exactly which assumptions that person's moral system is operating under so that the statement "the government should make Irish compulsory" could be produced. If you're analysing a person's broad views you start to find contradictions, as when you head to the root you find exclusive assumptions. And so on.

The point is that there's more to maths than boring formula and methods. If you devote some time to the really pure conceptual stuff you develop sharp critical thinking skills. And it's not a one way relationship, either. Philosophy can enlighten maths. I took a course in Linear Algebra last year, and I remarked to a friend how many of the proofs bore resemblance to the kind of discussion found in Plato's Republic. (Make statement, accept objection, account for objection, accept next objection etc etc until objections are exhausted.)

My primary fear about current maths education in Ireland is that it spends so much time on the formula stuff (solve this quadratic; find centre of this circle; find probability of this coin toss) at the expense of the conceptual and philosophical stuff, where the real rewards lie for applying maths outside the subject, in my opinion.

EDIT: I'm sorry if this post is too long and self-indulgent! :pac:

southsiderosie

Permabear wrote: »

This post had been deleted.

Well I think part of the problem is that so many universities have set up multiple schools - business, education, and communications being the main culprits - that pull undergraduates away from a core curriculum, and starve the liberal arts of resources and students. On most campuses, especially at large state schools, it is widely viewed that the School of Communications and the Ed School are the two softest. And from what I have seen, both in terms of student performance and employer complaints, most undergraduate business school curricula are sorely lacking in terms of critical thinking and writing components. Most of these 'specialty' programs are unnecessary at the undergraduate level; I had a job offer from Goldman Sachs with a history degree, and most of the best private colleges and universities in the US only offer undergraduates a traditional liberal arts education, yet their students have no problems getting jobs in banking, journalism, or education. And frankly, if a traditional undergraduate English course is too difficult for somebody (as opposed to an undergraduate Education degree), then they have no business becoming an English teacher.

Looking at this from the other direction, most people would also be surprised to note that MIT has departments in areas outside of math, science, and engineering including urban planning, anthropology, political science, and literature. And they have truly amazing faculty in these areas, people who would not try to tackle any great problem in their field without taking account of what was going on in other areas - cognitive science, environmental engineering, materials science, etc. So I'm always slightly amused when I see policymakers pushing for specialization at the undergraduate (and even secondary level) as a way of generating competitive advantage because arguably the world's foremost technical university takes a much more holistic approach to learning.

southsiderosie

Eliot Rosewater wrote: »

One of the key concepts in maths is the axiomatic method, by which one starts from a certain small number of assumptions and deduces everything else from that. When engrossed in a pure maths subject I find I'm constantly thinking of the root of everything. This theorem is true, but why? Why are the things that make it true true? What are the key switches, the key facts of the theorem, that turn it to absolute truth? How can we trace the pillars of this theorem back to the core assumptions of the system?

I find myself constantly applying this method when reading peoples' views on politics and other issues. When I'm confronted with a view, say "the government should make Irish compulsory", my first instinct is to head for the root, to determine exactly which assumptions that person's moral system is operating under so that the statement "the government should make Irish compulsory" could be produced. If you're analysing a person's broad views you start to find contradictions, as when you head to the root you find exclusive assumptions. And so on.

Which is exactly why traditionally math and philosophy have been so closely related. I took a logic class as an undergraduate as part of my humanities requirement, and was surprised that so much of the work consisted of essentially writing proofs.

A study came out recently in the US which found that people who major in philosophy do better on the LSAT (the entry exam for law school) than any other major. Granted there is some selection bias here, but philosophy is enjoying a bit of an upswing on many campuses right now in part because of its focus on rigorous, careful analysis - something that is sorely, sorely lacking today! This is what makes me so crazy about all of the focus on standardized testing prep for primary and secondary students in the US: the kids who do the best on standardized tests are the ones who have high levels of reading comprehension skills and can think critically. You don't learn this by taking lots of practice tests; you learn it by reading a lot, and then having to write about or discuss what you have read. It's really, really frustrating to see, and to be honest, the thought of having to send my (potential future) kids to the average US public school is terrifying (and that's before you get into all the curriculum nonsense with evolution, etc)

red_red_wine

Have you read "The Two Cultures," an influential 1959 lecture by C. P. Snow? As a scientist and novelist, Snow lamented the fact that the humanities and sciences had divided into two separate spheres with very little communication between the two.

Actually I had never heard of it, but I had a look at its Wikipedia page and it seems very interesting, when I get a chance, I'm definitely going to read it properly. Indeed, I think I might give a copy to said English teacher, given that we spend much of our time arguing about this matter

I think the sciences can require a high level of creativity, the snobbery attitude in the humanities just seems like defensiveness in the face of a general sense of the reduced status of the arts in relation to the sciences insofar as intelligence and use value are concerned.

I agree with this and I can see why those working in the art fields would be defensive; the value of their subjects is completely underestimated. Indeed, as far as the Leaving Cert is concerned, the English exam seems to demand just as a high a standard, if not higher, of critical thinking skill as the Maths exam. (Of course, with the structure of the English paper, it's more susceptible to manipulation and rote-learning by the exam-savvy student.) There is almost hysteria on the part of the government and business bodies etc. when it comes to encouraging Honours Maths, when there is also a significant number of students that are struggling with English.

Personally, I think that at the university level there should be a real return to a classical liberal arts education where regardless of major, students need to take classes outside of their core subject - REAL classes, not "Physics for Poets".

This would, in my opinion, be the ideal situation. Even if it were the case where on top of your primary degree, you could take one or two modules a week in any subject of your choice, however unrelated to the base degree it may be. (Maybe there is some facility for this, I'm not sure.) I plan to study Maths next year, but I regret that, at least in the next four years, I more than likely won't take any formal classes in the other subjects that I'm passionate about - Irish, English, French...

It's interesting how many people combine maths & music though - there is hope yet

I've noticed this as well, not necessarily combining music with maths, but with a wide variety of subjects. The most intelligent people I know are all extremely musical.

red_red_wine

Eliot Rosewater wrote: »

My primary fear about current maths education in Ireland is that it spends so much time on the formula stuff (solve this quadratic; find centre of this circle; find probability of this coin toss) at the expense of the conceptual and philosophical stuff, where the real rewards lie for applying maths outside the subject, in my opinion.

I think a very simple, but effective way to change the attitude towards Maths would be to compel every student to read at least one popular science book. The first popular science book I read (Fermat's Last Theorem) transformed my view of the subject.

While the majority of the technical stuff was beyond my realm of understanding, it introduces the aesthetic, even romantic, element of the subject which is entirely ignored by the secondary school syllabus. It's obviously necessary to cover the technical stuff in school, but if there were even a suggestion that Maths is possibly an art as well as a science, it could begin to change the attitude that it's all about mindless calculation.

We would most likely have no hope of understanding the actual maths that mathematicians work on, but even to introduce the notion that it's an incredibly creative field; that some mathematicians spend their entire lives working on a particular problem - it could help people see the parallels between the subject and the humanities.

red_red_wine

red_red_wine wrote: »

I agree with this and I can see why those working in the art fields would be defensive; the value of their subjects is completely underestimated. Indeed, as far as the Leaving Cert is concerned, the English exam seems to demand just as a high a standard, if not higher, of critical thinking skill as the Maths exam.

I've got to disagree slightly, I think the underestimation of other subjects is across the board. I'm in Trinity myself, and the campus is quite literally science on one half and arts on the other. With the exception of one person, everyone I know thinks their course is the most important/relevant/difficult. Not that they go around saying it, but you can tell.

Also about the English thing, personally I think LC English is a bit of a joke. I knew plenty of hard working, intelligent people who didn't do great, whereas I was completely disinterested with doing any work, didn't even attend school 2 days of the week, and did well. It's basically a "how well can you waffle" exam. Thankfully I can waffle to no end. I actually feel a bit guilty about it, because I really didn't deserve to pass, let alone get an A2.

Byron85

Eliot Rosewater wrote: »

Specially about maths (I have to defend my corner ). A good maths education gives you critical thinking skills. I challenge any University debater to take a pure pure maths module and actually fully understand it - then they can talk to me about critical thinking.

As an example,

One of the key concepts in maths is the axiomatic method, by which one starts from a certain small number of assumptions and deduces everything else from that. When engrossed in a pure maths subject I find I'm constantly thinking of the root of everything. This theorem is true, but why? Why are the things that make it true true? What are the key switches, the key facts of the theorem, that turn it to absolute truth? How can we trace the pillars of this theorem back to the core assumptions of the system?

I find myself constantly applying this method when reading peoples' views on politics and other issues. When I'm confronted with a view, say "the government should make Irish compulsory", my first instinct is to head for the root, to determine exactly which assumptions that person's moral system is operating under so that the statement "the government should make Irish compulsory" could be produced. If you're analysing a person's broad views you start to find contradictions, as when you head to the root you find exclusive assumptions. And so on.

The point is that there's more to maths than boring formula and methods. If you devote some time to the really pure conceptual stuff you develop sharp critical thinking skills. And it's not a one way relationship, either. Philosophy can enlighten maths. I took a course in Linear Algebra last year, and I remarked to a friend how many of the proofs bore resemblance to the kind of discussion found in Plato's Republic. (Make statement, accept objection, account for objection, accept next objection etc etc until objections are exhausted.)

My primary fear about current maths education in Ireland is that it spends so much time on the formula stuff (solve this quadratic; find centre of this circle; find probability of this coin toss) at the expense of the conceptual and philosophical stuff, where the real rewards lie for applying maths outside the subject, in my opinion.

EDIT: I'm sorry if this post is too long and self-indulgent! :pac:

That's effectively the basis for offender profiling of serial killers, one of my interests oddly enough.

As for the education system, I told you before that i'm effectively mathematically illiterate. I struggled with it my entire scholastic life and it never clicked with me so to speak. Most of the things I consider myself good at, are things that i've taught myself, be it music, photography, I.T skills etc. Granted those are hands on skills, there are other areas where I would like to think I excel at, such as history and psychology as well as having other areas of interest in which I am not an expert, such as physics, but would still have a greater than average knowledge of the field.

Due to this, I would consider myself a polymath along with yourself and other acquaintances of mine.

Does the education system encourage this though? At second level, not in the least. At third level, at least in the social sciences, which is my own field of undergraduate studies, I feel it does encourage it but not to the extent it should. For example, some of my lecturers are economists, with quite a few of them being polyglots and this is only in the sociology department. I know this is only a small, anecdotal piece of evidence but at second level, how many teachers are competent enough to teach outside their own particular area?

Somewhat related, but there's a great documentary about the public school system in the U.S called Waiting for Superman. It was a huge eye-opener for me.

red_red_wine

Byron85 wrote: »

at second level, how many teachers are competent enough to teach outside their own particular area?
.

Whatever about teaching outside their own particular area, what is more worrying is the amount of teachers who display utter ignorance and worse, indifference towards their own subject; whose method of teaching doesn't extend beyond reading out of the book.

Going with the anecdotes, my younger sister is in 2nd year. A month or two ago, they started the French Revolution and the name Marie Antoinette was mentioned for the first time. One girl raised her hand and said something along the lines of 'Oh, isn't she the one who said "Let them eat cake?'' ' The teacher had genuinely never heard of that phrase (yes, yes I know that it has been supposedly mis-attributed, but even so, it is a very famous quotation) and was convinced that the girl had made it up.

Now this is quite obviously an extreme example, but it is doubtful that this teacher will ever instill a passion in her students for the subject or motivate them to acquire a more extensive knowledge of History (unless she does it perversely by encouraging them to not be quite as ill-informed as she is :P )

Byron85

red_red_wine wrote: »

Whatever about teaching outside their own particular area, what is more worrying is the amount of teachers who display utter ignorance and worse, indifference towards their own subject; whose method of teaching doesn't extend beyond reading out of the book.

Going with the anecdotes, my younger sister is in 2nd year. A month or two ago, they started the French Revolution and the name Marie Antoinette was mentioned for the first time. One girl raised her hand and said something along the lines of 'Oh, isn't she the one who said "Let them eat cake?'' ' The teacher had genuinely never heard of that phrase (yes, yes I know that it has been supposedly mis-attributed, but even so, it is a very famous quotation) and was convinced that the girl had made it up.

Now this is quite obviously an extreme example, but it is doubtful that this teacher will ever instill a passion in her students for the subject or motivate them to acquire a more extensive knowledge of History (unless she does it perversely by encouraging them to not be quite as ill-informed as she is :P )

The state of our teachers and the institution can be summed up by my mindset that some of that people I know who are teachers or are training to be teachers, are too good for the profession. These are people who are far too intelligent to be in the profession in its current format.

red_red_wine

red_red_wine wrote: »

I think a very simple, but effective way to change the attitude towards Maths would be to compel every student to read at least one popular science book. The first popular science book I read (Fermat's Last Theorem) transformed my view of the subject.

While the majority of the technical stuff was beyond my realm of understanding, it introduces the aesthetic, even romantic, element of the subject which is entirely ignored by the secondary school syllabus. It's obviously necessary to cover the technical stuff in school, but if there were even a suggestion that Maths is possibly an art as well as a science, it could begin to change the attitude that it's all about mindless calculation.

We would most likely have no hope of understanding the actual maths that mathematicians work on, but even to introduce the notion that it's an incredibly creative field; that some mathematicians spend their entire lives working on a particular problem - it could help people see the parallels between the subject and the humanities.

I read a piece (which I can't find right now) some time ago comparing the current method of teaching maths to teaching art as 'paint by numbers'. Seemed pretty interesting and accurate. You need a certain amount of rote learning for the early stages to establish the basics (although I'm not entirely sure they're even doing that anymore), but after that it should be opened up a lot more. That and remove the 'maths is hard can't do maths' attitude.

Eliot wrote:

I think all the branches of intellectual activity - maths, economics, physics, philosophy, literature, history, political theory, etc - are complementary, and a base knowledge of all leads to the most fulfilling kind of education and thus life. It's hard to describe what a fulfilling education is, of course - for me it's being able to understand a lot of the world around you (taking a broad definition of world). All these branches give you new perspectives on different parts of the human experience.

Couldn't agree more
What with reading, writing, thphys, maths, languages, actuary, being a musician - I am doing my best to cover all bases I just need to pick up art again

Count Duckula

I hate threads like this. They're usually full of clever people who can do well in every subject "despairing" at no one else doing the same.

Newsflash: most people aren't intelligent enough to do really well in every subject once the difficulty ramps up beyond junior cert. Hence you get more and more specialised as you advance through education. That system hasn't come about just for the sake of it - it's grounded in experience of the educational system that the majority of students need to specialise to achieve real academic success.

It's very easy for the more intelligent people to point to the benefits they receive from knowing everything about everything and being amazing at math, but most of the population don't have that capacity nor that inclination to learn. Frankly, linear algebra and calculus don't affect their lives at all.

But Duck, it's not capability we are talking about, it's attitude. It's giving up before you even start. You don't need to be a whiz at calculus and have the works of Shakespeare stored in your head. But to assume that proficiency in English means you shouldn't bother attempting to be good at maths (and vice versa) is the killer.
If you look at the very first post here, the OP is not scorning the teacher's ability at maths. He's talking about how she seems to be proud of lack of ability:

My current English teacher, an extremely intelligent woman, proclaims with what is almost pride that she is hopelessly numerically incompetent. In a sense, it seems to be a badge of honour.

We all have different abilities, and of course people may shine in one area and not another. But that's not really the problem being discussed here.

Count Duckula

But the "badge of honour" status she regards her lack of mathematical ability with may just be a defense against what would otherwise be quite upsetting. She's obviously an intelligent woman, and probably enjoys being regarded as such, and therefore her lack of numerical ability may bother her a bit. That being the case, rather than suggest she's no good at math despite wanting to be - and thus looking like she's not as intelligent as everyone thought - she'll instead "reclaim" her numerical inability as a badge of honour.

I am talking entirely from personal experience, I admit, but those people I knew who tended to be approaching polymathy also tended to be so aloof as to be unapproachable.

You do seem to be an exception to that rule, dear Bluewolf, but given that you seem to be playing classic instruments, writing (fantasy fiction?) and studying theoretical physics I'm not sure your academic successes are fair to compare with the rest of us

For the record, my best results at Leaving cert level (though I personally did the International Baccalaureate) were History, English, Biology and Maths, so I agree that knowing a broad basis can be nice, although I never took that wide base of knowledge to university level because it started to simply get too difficult.

I just think it's exceptionally unfair to judge those people who don't have that capability for excellence in all fields for instead choosing to specialise, when in the end that may produce far better results in the long run.

Finally, polymaths were more useful throughout history than they are now, in my opinion. Scientific knowledge was at a far lesser level, where uniting differing disciplines was key to unlocking new discoveries and laying the groundwork for future discoveries. Education was also at a more limited level and fewer people obtained that high level of knowledge owing to that, meaning those that did were required to have a broad knowledge to counter that sparsity of genius. In the modern world, education produces more people at a higher level of knowledge. Fields have become so specialised that you can no longer easily delve into the very core of more than one advanced subject, and there are also so many more people in higher education that there's no need to. With the advancement of technology, too, polymaths no longer need to be one person - that same broad basis of knowledge can be obtained by pooling the resources of more than one specialist.

Count Duckula

Count Duckula wrote: »

But the "badge of honour" status she regards her lack of mathematical ability with may just be a defense against what would otherwise be quite upsetting. She's obviously an intelligent woman, and probably enjoys being regarded as such, and therefore her lack of numerical ability may bother her a bit. That being the case, rather than suggest she's no good at math despite wanting to be - and thus looking like she's not as intelligent as everyone thought - she'll instead "reclaim" her numerical inability as a badge of honour.

I understand where you are coming from, but I cannot ever agree with pride in ignorance.

You do seem to be an exception to that rule, dear Bluewolf, but given that you seem to be playing classic instruments, writing (fantasy fiction?) and studying theoretical physics I'm not sure your academic successes are fair to compare with the rest of us

I am exceptional :pac:

I just think it's exceptionally unfair to judge those people who don't have that capability for excellence in all fields for instead choosing to specialise, when in the end that may produce far better results in the long run.

But again, I don't think this is the point. It's about attitude and recognising the value in different areas of learning instead of eschewing them entirely.
There is a great divide between maths/sciences and other areas, where there shouldn't be. That is not to say everyone should excel at everything, but rather - don't assume talent in one area precludes talent in another. The other posters on this thread have shown all sorts of connections already.

This fuss about honours maths bonus points, for example, really makes the situation worse in my opinion. It is building up maths as some lofty unattainable subject which you should enter into expecting great difficulty. And then when it is taught rigidly as a bunch of uninteresting irrelevant formulae and the students lose interest - well, we did warn you maths was hard and boring! It needs to change, honestly.
Even this into report acknowledges the attitudes need to change -
http://www.into.ie/ROI/Publications/MathsPrimarySchool.pdf

opinion guy

Count Duckula wrote: »

I hate threads like this. They're usually full of clever people who can do well in every subject "despairing" at no one else doing the same.

Newsflash: most people aren't intelligent enough to do really well in every subject once the difficulty ramps up beyond junior cert. Hence you get more and more specialised as you advance through education. That system hasn't come about just for the sake of it - it's grounded in experience of the educational system that the majority of students need to specialise to achieve real academic success.

It's very easy for the more intelligent people to point to the benefits they receive from knowing everything about everything and being amazing at math, but most of the population don't have that capacity nor that inclination to learn. Frankly, linear algebra and calculus don't affect their lives at all.

Actually I disagree with this. In fact I have a problem with the whole concept of IQ......but thats another thread for another day. My point though is that students don't fail a subject, rather teachers fail to teach some students. The way to teach little johnny may be very different from the way to teach little billy, yet most teachers teach using one method of explanation. Though I must say - part of the reason for this and part of the problem here is that class sizes are way too big. It is ridiculous to think that one teacher can explain large amounts of material to 30 different kids with 30 different mindsets and reasonably expect them all to have the same understanding. Its just not possible. Some will need more help than others. Some will understand one explanation and not another. Our system of education does not allow for this.

Count Duckula wrote: »

Finally, polymaths were more useful throughout history than they are now, in my opinion. Scientific knowledge was at a far lesser level, where uniting differing disciplines was key to unlocking new discoveries and laying the groundwork for future discoveries. Education was also at a more limited level and fewer people obtained that high level of knowledge owing to that, meaning those that did were required to have a broad knowledge to counter that sparsity of genius. In the modern world, education produces more people at a higher level of knowledge. Fields have become so specialised that you can no longer easily delve into the very core of more than one advanced subject, and there are also so many more people in higher education that there's no need to. With the advancement of technology, too, polymaths no longer need to be one person - that same broad basis of knowledge can be obtained by pooling the resources of more than one specialist.

See I disagree with this also. The trouble these days is research has become to prescribed. It used to be that doing a phd was a creative venture - smart people were given resources to learn and come up with ideas. Nowadays it is more and more a prescribed persuit. Particularly in science/techy fields. Everything is profit driven - even in universities and every bit of research is part of a preformed plan.

This, as much as anything is why its difficult to cross fields. It used to be you would just hire the local genius to figure stuff out. Now even if you had a genuine polymath he wouldn't get the job unless he had a phd at the right university etc etc. But crossing fields is something we need. Polymaths are just as relevant now as ever.

southsiderosie

Count Duckula wrote: »

I hate threads like this. They're usually full of clever people who can do well in every subject "despairing" at no one else doing the same

Newsflash: most people aren't intelligent enough to do really well in every subject once the difficulty ramps up beyond junior cert. Hence you get more and more specialised as you advance through education. That system hasn't come about just for the sake of it - it's grounded in experience of the educational system that the majority of students need to specialise to achieve real academic success.

It's very easy for the more intelligent people to point to the benefits they receive from knowing everything about everything and being amazing at math, but most of the population don't have that capacity nor that inclination to learn. Frankly, linear algebra and calculus don't affect their lives at all.

I do not think it is not clear what the current system is grounded in, especially since this has historically not been the structure of higher ed. And even if someone tracks into vocational education early, they will still need a good grounding in math, composition, and reading comprehension.

In addition, the structure of today's labor market also does not suggest that this makes sense. The trend in less skilled jobs today is for people to take on multiple tasks, rather than one highly specialized task. So for those countries that still have a manufacturing base, most workers will need to be able to multi-task and problem solve because technology and China have made single-task workers obsolete in the West. There may be a lot of people who don't like school or only want to do one thing, but the realities of todays labor market suggest that they don't have much of a choice.

For jobs where some vocational training makes sense, but not 4-year university, I can see a case for specialized training, but this still does not suggest to me that basic skills in math and critical thinking and writing are any less necessary, especially since many of these kinds of jobs (physician's assistant, systems maintenance) have a strong science component.

At the high-skills end of the labor market, yes specialization is necessary, but it is something that should be the focus of graduate-level education, not undergraduate. Most skilled professionals will change jobs multiple times in their career, making a well-grounded broad core education more important than ever.

Finally, I think people need to get over the fact that they aren't going to be good at everything. As I've said, I am not mathematically inclined, and my grades in secondary school and university reflected that. I am also terrible at learning foreign languages, in part because I find studying vocabulary to be the most tedious, boring exercise on earth. Yet I still had to take four math and science courses and four semesters of foreign language as an undergraduate, and believe me I fought for those B-minuses in Latin and statistics!

southsiderosie

(sorry to double-post, but these were getting quite long)

Count Duckula wrote: »

Finally, polymaths were more useful throughout history than they are now, in my opinion. Scientific knowledge was at a far lesser level, where uniting differing disciplines was key to unlocking new discoveries and laying the groundwork for future discoveries. Education was also at a more limited level and fewer people obtained that high level of knowledge owing to that, meaning those that did were required to have a broad knowledge to counter that sparsity of genius. In the modern world, education produces more people at a higher level of knowledge. Fields have become so specialised that you can no longer easily delve into the very core of more than one advanced subject, and there are also so many more people in higher education that there's no need to. With the advancement of technology, too, polymaths no longer need to be one person - that same broad basis of knowledge can be obtained by pooling the resources of more than one specialist.

I would argue that the specialization of many fields is actually pulling attention away from the kinds of big, paradigm-shifting breakthroughs that we had in the past. Certainly in social sciences, the combination of overspecialization and fetishization of quantitative modeling has led to a flood of academic papers that account to nothing more than arguing about how many angels can dance on the head of a pin. If I read one more ridiculous economics paper that justifies its importance on the basis of using a quasi-natural experiment, my head will explode. Political science is no better; when you look at the kind of work that was produced in the 1960s by the likes of Barrington Moore and Samuel Huntington versus what is being produced today...well, it is a sad commentary on the field. To be fair, this phenomenon is partly driven by the fact that most departments will got give their students the luxury of taking 8-9 years to finish, and I do not think that graduate students in the 1960s spent 30% of their time writing futile grant proposals for outside funding. But I think that social sciences and the humanities in particular have specialized themselves out of relevance in a lot of areas, and this is why they are in such a vulnerable position today: if these scholars have nothing to say on the big questions that continue to challenge us today - citizenship, ethics, the role of the state in a globalized world - then what use are they? Plus it doesn't help that many of them don't even teach undergraduates, so they aren't exactly adding value in that regard either.

nyarlothothep

southsiderosie wrote: »

(sorry to double-post, but these were getting quite long)



I would argue that the specialization of many fields is actually pulling attention away from the kinds of big, paradigm-shifting breakthroughs that we had in the past. Certainly in social sciences, the combination of overspecialization and fetishization of quantitative modeling has led to a flood of academic papers that account to nothing more than arguing about how many angels can dance on the head of a pin. If I read one more ridiculous economics paper that justifies its importance on the basis of using a quasi-natural experiment, my head will explode. Political science is no better; when you look at the kind of work that was produced in the 1960s by the likes of Barrington Moore and Samuel Huntington versus what is being produced today...well, it is a sad commentary on the field. To be fair, this phenomenon is partly driven by the fact that most departments will got give their students the luxury of taking 8-9 years to finish, and I do not think that graduate students in the 1960s spent 30% of their time writing futile grant proposals for outside funding. But I think that social sciences and the humanities in particular have specialized themselves out of relevance in a lot of areas, and this is why they are in such a vulnerable position today: if these scholars have nothing to say on the big questions that continue to challenge us today - citizenship, ethics, the role of the state in a globalized world - then what use are they? Plus it doesn't help that many of them don't even teach undergraduates, so they aren't exactly adding value in that regard either.

Thats an interesting argument, the problem as I see it in the social sciences and humanities is that as soon as you expand your research scope to explain a bigger phenomenon you end up missing out on small details which contradict your findings, in other words its easier not to make mistakes if you keep your research topic small and well defined. I think though that one learns more from making mistakes in addition to making some new insights, rather than just trying to be fully correct on a very small area of knowledge, but obviously the ratio between the two should be favourable and this would be attributable to the nature of the topic at hand.

amacachi

I personally don't believe that insisting on having classes of as mixed ability as possible helps anyone, whether it's the higher achievers or those with aptitudes and interest in certain areas while others at the other end of the spectrum hold back those students and/or lose interest as the level being taught isn't suited to them. The one-size-fits-all attitude to education irks me greatly and I imagine contributes to the system of rote learning we have now.

RandolphEsq

Eliot Rosewater wrote: »

Specially about maths (I have to defend my corner ). A good maths education gives you critical thinking skills. I challenge any University debater to take a pure pure maths module and actually fully understand it - then they can talk to me about critical thinking.

As an example,

One of the key concepts in maths is the axiomatic method, by which one starts from a certain small number of assumptions and deduces everything else from that. When engrossed in a pure maths subject I find I'm constantly thinking of the root of everything. This theorem is true, but why? Why are the things that make it true true? What are the key switches, the key facts of the theorem, that turn it to absolute truth? How can we trace the pillars of this theorem back to the core assumptions of the system?

I find myself constantly applying this method when reading peoples' views on politics and other issues. When I'm confronted with a view, say "the government should make Irish compulsory", my first instinct is to head for the root, to determine exactly which assumptions that person's moral system is operating under so that the statement "the government should make Irish compulsory" could be produced. If you're analysing a person's broad views you start to find contradictions, as when you head to the root you find exclusive assumptions. And so on.

The point is that there's more to maths than boring formula and methods. If you devote some time to the really pure conceptual stuff you develop sharp critical thinking skills. And it's not a one way relationship, either. Philosophy can enlighten maths. I took a course in Linear Algebra last year, and I remarked to a friend how many of the proofs bore resemblance to the kind of discussion found in Plato's Republic. (Make statement, accept objection, account for objection, accept next objection etc etc until objections are exhausted.)

My primary fear about current maths education in Ireland is that it spends so much time on the formula stuff (solve this quadratic; find centre of this circle; find probability of this coin toss) at the expense of the conceptual and philosophical stuff, where the real rewards lie for applying maths outside the subject, in my opinion.

EDIT: I'm sorry if this post is too long and self-indulgent! :pac:

You are right about applying real life to maths (or maths to real life, whichever), in fact I did a module in my philosophy undergraduate degree which dealt with argument deconstruction using algebra! Breaking down arguments to their premises and conclusions. It was all reductive but quite interesting!

I never actually heard of that UC curriculum they have but it sounds mightily wonderful! If I was to go back and redo my CAO (4 years ago), I would have thrown myself into a pure Arts degree (instead of law and philosophy), in order to get a more grounded intellectual experience. What is it they say, you go to college to get a degree, not an education? It is so true unfortunately,

red_red_wine

It's very easy for the more intelligent people to point to the benefits they receive from knowing everything about everything and being amazing at math, but most of the population don't have that capacity nor that inclination to learn.

This wasn't my point though. As bluewolf pointed out, it's an attitudinal problem. Although most of us don't have the capability to become Olympic athletes and are perhaps hopelessly nonathletic, that doesn't mean that we can't recognise the importance of going for a walk every evening and indeed, encouraging people to do their best athletically.

I just think it's exceptionally unfair to judge those people who don't have that capability for excellence in all fields for instead choosing to specialise, when in the end that may produce far better results in the long run.

Obviously, at some point, most people are going to have to specialise somewhat and narrow their field of study, even if they maintain an interest in many subjects. This is an issue applicable not just to university study, but also to secondary and primary school, where a student is prevented from true specialisation because the core subjects are compulsory. Yet, you have this huge divide between the departments within the school, which is primarily attitudinal, because the differences between the areas of study are not as great as are perceived.

This problem pertaining attitudes is fostered by the staff, i.e. the English teacher in question. Maybe she is embarrassed by her numerical inability, but that's not the worrying issue. It's her dismissive attitude towards the subject. For example, she would often make disparaging comments about how 'poetry isn't maths. It's not just about plugging values into a calculator and getting a definitive answer.'

That being said, this attitude is echoed in some of my science teachers, e.g. my Maths teacher who talks about how she is useless at English. Both departments appear to believe that their own is more important than the other; or at least that it is completely removed from the other.

I can't help but think that this attitude is then absorbed by students, perhaps more so the younger ones. For example, supposing a student has her first English test and your first Maths test around the same time in First Year. She gets an A in the Maths and a C in the English. She's heard her Maths teacher talking about how she is dreadful at English, she's heard the English teacher talking about how she is dreadful at Maths, the student infers that it is impossible to be excellent at the two subjects. Thus, instead of trying to get an A in English as well as in Maths in the next test, she becomes complacent and rather than trying to better herself in English, assumes that the C is the cost to pay for the A in Maths.

Obviously everyone can't be outstanding in every field. That doesn't mean that we should indirectly discourage them from trying to do their best in every field.

TaraFoxglove

bluewolf wrote: »

It's interesting how many people combine maths & music though - there is hope yet

When I hear maths and music spoken of together, I think of this lady:

http://en.wikipedia.org/wiki/Delia_Derbyshire

TaraFoxglove

TaraFoxglove wrote: »

When I hear maths and music spoken of together, I think of this lady:

http://en.wikipedia.org/wiki/Delia_Derbyshire

That's funny - I love dr who!

That reminds me of:
http://www.youtube.com/watch?v=PdrqdW4Miao

DublinWriter

As the late great Kenneth Williams said, people are getting better and better at less and less.

red_red_wine

Although very much the obvious choice, there's no song that says Maths + Music to me more than this one:

https://www.youtube.com/watch?v=6FLGZtwfV3Y

opinion guy

red_red_wine wrote: »

Although very much the obvious choice, there's no song that says Maths + Music to me more than this one:
<vid snipped>

I beg to differ:

https://www.youtube.com/watch?v=3e7yYBDHOgg