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  1. #81
    Quote Originally Posted by Endus View Post
    Because business and technical writing is a very specific skill for a very specific market, with very strict rules to abide by. Focusing on literature and poetry and so forth teaches students about the entire breadth of the language and its use and flexibility. It's far easier to narrow down and teach a specific sub-skill within that, like technical writing, if you've got a strong basis in the language itself. Learning those specific skills is where you start specializing, which is a post-secondary education thing.
    Agreed, however the intent and content of technical writing is pretty different than normal literature. It takes practice to translate factual/technical information in your head or that you've written in a lab notebook or something into a cohesive, understandable and logical written document that accurately encapsulates what it's meant to. The language may be the same, but the way it's used is different enough to make it a completely separate skill from normal literature.

    I'd argue that in the classes meant to prepare you for that job field should include courses in the writing style and writing skills needed for that field. It shouldn't necessarily HAVE to wait until post-secondary education.

    Students that can't follow those proofs have no business being in those classes, and should likely fail those classes as a result.
    While I get the point you're making, I don't necessarily agree. I personally never saw the point of proofs in math class. The rules have ALREADY been proven by thousands if not millions of people, why do I need to know HOW it works when I already know THAT it works? Especially since once I leave that classroom, when put into a situation where I might need to apply the skill, I'll jump to the "shortcut" and never even look at the proof again.

    I understand teaching the skill of proving your methodology and describing why and how something works, but that's somewhat separate than applying the skill to a real world scenario.

    Just because you're not so good at doing proofs, doesn't mean you're bad at applying the proven rule appropriately.

    [SNIP]

    Really, the root of all this is simple; education is not primarily job training. If you're in a professional accreditation program, then there's a component of that in there, but otherwise, you're not on an employment track to begin with, so looking at it from that angle is idiotic.
    100% agreed. Knowledge is always a good thing, you never know when you might actually apply it, but you WILL apply it. Whether it's on a persona, recreationall or professional level is largely irrelevant, though you'll likely want the skills and information you need for your professional career/life to be better polished and sharp than your recreational ones for obvious reasons, but everything you learn CAN be applied.

  2. #82
    The problem isn't the content of education as much as the methodology and the structure in which it is taught.

    Instead of focusing on understanding, the focus is entirely on achievement - as long as you can reproduce the information required of you in tests, you pass. Whether or not you truly UNDERSTAND the contents you are required to study is secondary, and indeed often falls by the wayside entirely.

    This, however, runs entirely counter to the very reason why certain subjects are taught. The purpose of teaching literature is not to produce people who can recite the members of the Transcendentalist movement or people who know The Charge of the Light Brigade by heart - it's to produce people who are capable of critically examining social-historical paradigms, who can decode and employ the intricacies of ornate language, who can reflect on the human condition in its various temporal and spatial contexts.

    Similarly, the purpose of teaching advanced math and mathematical proofs is not to produce people who can recite the Pythagorean Theorems or tell you what a LaPlace die is. It's to produce people who are aware of how mathematical relations operate; how statistics run counter to intuition but underlie fundamental empirical phenomena; who can apply structured thinking and reasoning to problem solving regardless of the concrete nature of the problem.

    In short, what you want people to learn is not how to do or fix something particular - but rather how to find and use the tools they need to do or fix ANYTHING. The reason for that is simple. Some argue that we should teach people how to do their taxes instead of teaching them advanced math. Okay. Now you have someone who can do their taxes. But what if they need a loan now? You didn't teach them that. So we teach them taxes and loans. But what if now they need to budget? And so on. If, however, you teach them how to handle numbers in general, how to work with equations, statistics, graphs - then you have people who can be faced with whatever math-based problem you didn't (and/or couldn't) anticipate and they will know how to approach it to get to a solution. And it is precisely because of that limitation that education needs to be broad. We can't know what people will need to know in particular - but we know that teaching them the general will provide them with the tools they need to tackle even the unexpected.

    The rates of poor reading proficiency are troubling; but the rates of functional innumeracy are even more staggering, and arguably even more pernicious. People that don't understand how math works and relates to the real world tend to make a whole lot of stupid decisions. And that's largely because they weren't taught the underlying methodology of math - they were taught specific procedures, but not the understanding that lies behind them. And it is that understanding of math that is crucial to connecting abstract structures to concrete phenomena.

    Similarly, people have shockingly low levels of critical thinking ability. People who are taught how to dissect language, how to question and investigate claims, those are people that DON'T fall prey to things like fake news or inflammatory populist rhetoric. But if you are only taught "this book means X, that book means Y" instead of being given the tools to find out how to argue for X or Y - or Z, A, B, C, any letter you like - or how to confront claims of A, B, C then it is no surprise you tend to swallow anything some authority figure throws at you.

    Goal-oriented education is self-limiting. And here we have people who say they want to make it even MORE goal-oriented? Sure, if all you want to have is obedient, unquestioning workers who perform rote tasks on command, then do it like that. But that's not the people who produce innovation, and who can improve life for everyone.

    Don't get me wrong, though - I absolutely agree that there are deficits in the education system relating to contemporary societal demands. We SHOULD be teaching people about economics, about computers, about banking and taxes and real politics. But we should do that in a general way, too - teach them the structures, the methods, the meanings of things. Teach them how to solve any problem, and not just the solution to a particular problem. And for that, you NEED a broad education. You need literature, philosophy, science as much as you do sociology, economics, and politics, because they are all connected at fundamental levels. And without the fundamental, the specific will forever remain a hollow shell that you find yourself unprepared for.

    We need to address the structural problems of education. Don't teach for tests, teach for UNDERSTANDING; and, conversely, make tests about understanding much more so than about knowledge. Integrate subjects vertically and horizontally. Teach methodologies and principles, and how these apply to examples and applications - any examples, and any applications. That way, you'll never have college kids who don't know how to do their taxes and instead of going and finding out on their own, instead raise their hands to the skies in frustration and lament that their teachers never told them.

  3. #83
    I Don't Work Here Endus's Avatar
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    Quote Originally Posted by Katchii View Post
    Agreed, however the intent and content of technical writing is pretty different than normal literature. It takes practice to translate factual/technical information in your head or that you've written in a lab notebook or something into a cohesive, understandable and logical written document that accurately encapsulates what it's meant to. The language may be the same, but the way it's used is different enough to make it a completely separate skill from normal literature.

    I'd argue that in the classes meant to prepare you for that job field should include courses in the writing style and writing skills needed for that field. It shouldn't necessarily HAVE to wait until post-secondary education.
    I'm not saying it isn't, I'm saying that learning how to do so is part of your 3-year baccalaureate, in the same way that learning how to write a research paper is part of a history degree.

    You're not expected to know it when you start. It's what you're there to learn.

    I'm suggesting it's easier to teach technical writing to someone who already has a firm grounding in English composition than it is to someone with limited language skills, which would be the reality if we moved away from teaching literature and such.

    While I get the point you're making, I don't necessarily agree. I personally never saw the point of proofs in math class. The rules have ALREADY been proven by thousands if not millions of people, why do I need to know HOW it works when I already know THAT it works? Especially since once I leave that classroom, when put into a situation where I might need to apply the skill, I'll jump to the "shortcut" and never even look at the proof again.
    Math classes are not, fundamentally, about learning that math works. It's about learning how and why math works. That means understanding the proofs.

    If you don't understand the proofs, you don't understand the mathematics. And when something goes wrong, you'll have little chance to figure out why. You also have little capacity to understand how the mathematics could be applied to a new circumstance beyond those you've already been exposed to.

    This is the reason why they usually don't allow calculators in early math training; the entire point is to learn how to do it and why it works that way, because you can train a monkey to match symbols and punch them into a calculator. That's not comprehension.

    If you don't understand the proof of a math principle, you don't understand the principle, and you're operating at the skill level of "advanced symbol-matching monkey", not the level of someone who understands the mathematics.

    I understand teaching the skill of proving your methodology and describing why and how something works, but that's somewhat separate than applying the skill to a real world scenario.
    And that's the point; figuring out the mathematics to apply to a real-world scenario that's "new" requires that you actually understand the proofs and methodology behind that mathematics.


  4. #84
    Void Lord Elegiac's Avatar
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    I see anti-intellectualism is still alive and well.
    Quote Originally Posted by Marjane Satrapi
    The world is not divided between East and West. You are American, I am Iranian, we don't know each other, but we talk and understand each other perfectly. The difference between you and your government is much bigger than the difference between you and me. And the difference between me and my government is much bigger than the difference between me and you. And our governments are very much the same.

  5. #85
    Quote Originally Posted by Endus View Post
    I'm not saying it isn't, I'm saying that learning how to do so is part of your 3-year baccalaureate, in the same way that learning how to write a research paper is part of a history degree.

    You're not expected to know it when you start. It's what you're there to learn.

    I'm suggesting it's easier to teach technical writing to someone who already has a firm grounding in English composition than it is to someone with limited language skills, which would be the reality if we moved away from teaching literature and such.
    Fair point, agreed.

    Math classes are not, fundamentally, about learning that math works. It's about learning how and why math works. That means understanding the proofs.

    If you don't understand the proofs, you don't understand the mathematics. And when something goes wrong, you'll have little chance to figure out why. You also have little capacity to understand how the mathematics could be applied to a new circumstance beyond those you've already been exposed to.

    This is the reason why they usually don't allow calculators in early math training; the entire point is to learn how to do it and why it works that way, because you can train a monkey to match symbols and punch them into a calculator. That's not comprehension.

    If you don't understand the proof of a math principle, you don't understand the principle, and you're operating at the skill level of "advanced symbol-matching monkey", not the level of someone who understands the mathematics.
    I agree with you, however for people who are not math majors or working in a field where they truly need that in-depth understanding of how it works, they don't need to know all of that. They just need to know THAT it works and apply the proven principals to their situation.

    Advanced symbol matching monkey, as you put it, is really the minimum skill level people not in heavy mathematics fields need to be. They don't need to be more advanced than that to do basic finances, add, subtract, or even do statistics (which is honestly a whole different skill set).

    And that's the point; figuring out the mathematics to apply to a real-world scenario that's "new" requires that you actually understand the proofs and methodology behind that mathematics.
    Which is true, but in my experience, people will learn what they need to while they're pursuing this kind of thing in their professional life similar to how business and technical writing skills would be acquired. I just think this level of understanding isn't required in primary education levels (through High School), at least in math. Though it would make sense for this to be taught in AP level courses and in college.

    If someone doesn't know this information they'll contact someone who does and pay them for their expertise. If you need to know it yourself because of work, you'll research it and learn the principals you need to understand to apply it to your situation (or you will if you're a competent employee, if you're not you'll just find someone else who knows it and call in a favor or whatever).

    I agree with you on why someone would need the skill set, I'm just arguing that not everyone needs to have that skill set.

  6. #86
    Quote Originally Posted by imunreal View Post
    I have always viewed algebra as problem solving. You always hear someone saying “I don’t use algeba” but the way I always looked at it, is that algebra helps to refine your skills to problem solve, and think a bit more outside of the box instead of sticking to basic formulas.
    The problem is that, barring very few professions, it is USELESS problem solving. It's also something that (a) some people are horrible at and never get the hang of (so no "problem solving" to be learned, just makes them feel stupid), and (b) there are too many crappy teachers that understand complex math just fine, but couldn't teach a kid 1 + 1 if they didn't already know it. So, their victims don't learn algebra - which again, means they aren't learning problem solving.

    There are PRACTICAL ways to teach problem solving without torturing kids. It also drives me nuts that we have kids that get tons of algebra and calculus that they'll never use, but don't know how to balance a check book or create a budget (or wisely invest for retirement).

  7. #87
    I Don't Work Here Endus's Avatar
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    Quote Originally Posted by Tazr View Post
    The problem is that, barring very few professions, it is USELESS problem solving. It's also something that (a) some people are horrible at and never get the hang of (so no "problem solving" to be learned, just makes them feel stupid), and (b) there are too many crappy teachers that understand complex math just fine, but couldn't teach a kid 1 + 1 if they didn't already know it. So, their victims don't learn algebra - which again, means they aren't learning problem solving.

    There are PRACTICAL ways to teach problem solving without torturing kids. It also drives me nuts that we have kids that get tons of algebra and calculus that they'll never use, but don't know how to balance a check book or create a budget (or wisely invest for retirement).
    The biggest impediment to math education is people who were taught badly and think that bad teaching is the only way to teach math.

    See the whole outcry against "Common Core" mathematics. Nearly everyone complaining about it is doing so because they don't understand math, really, so because it teaches different approaches, they can't see what those approaches are getting at, they just know their monkey-brain "put numbers in machine, get result" techniques. Like memorizing times tables, which are a godawful system that impede comprehension.

    I'll emphasize I said "nearly everyone". Common core has some issues, but they aren't the "why did they change math?!" type things that are usually the main target.


  8. #88
    College is basically a four year vacation from life where most students partake in unhealthy activities and don't develop a work ethic or any form of real world experience. That trade off might be acceptable if we received an extensive liberal education but the vast majority of universities lack rigor in the vast majority of their programs which seem to seldom relate to the jobs that students end up having.

    If you're going to make college free, you need to make it much harder so not everyone gets out with a degree they didn't earn. No more passing easy liberal arts classes without doing the readings and no more graduating in 6 years because you took 9-12 credits per semester. College athletic programs would need to be overhauled and de-emphasized. Greek life and the level of alcohol/drug use on campuses is already completely unacceptable and it would be downright throwing money down the drain to give free tuition to fraternity brothers who skid by in their classes and instead focus on completely hedonistic activities.

  9. #89
    Quote Originally Posted by Endus View Post
    The biggest impediment to math education is people who were taught badly and think that bad teaching is the only way to teach math.
    I'd like to add to that... the biggest impediment to education (imo) is people who think that there is only one correct way to teach someone. I've had some great teachers and some bad teachers, but the ways they taught may have had the opposite effect on other students. (except for one teacher I remember, he was just awful and shouldn't have had a taxpayer-funded job)

  10. #90
    Higher education is a must IMHO. The results remain nearly invisible but it is very important.

  11. #91
    Void Lord Elegiac's Avatar
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    Quote Originally Posted by Knadra View Post
    College is basically a four year vacation from life where most students partake in unhealthy activities and don't develop a work ethic or any form of real world experience. That trade off might be acceptable if we received an extensive liberal education but the vast majority of universities lack rigor in the vast majority of their programs which seem to seldom relate to the jobs that students end up having.

    If you're going to make college free, you need to make it much harder so not everyone gets out with a degree they didn't earn. No more passing easy liberal arts classes without doing the readings and no more graduating in 6 years because you took 9-12 credits per semester. College athletic programs would need to be overhauled and de-emphasized. Greek life and the level of alcohol/drug use on campuses is already completely unacceptable and it would be downright throwing money down the drain to give free tuition to fraternity brothers who skid by in their classes and instead focus on completely hedonistic activities.
    Sounds like you're basing your "policy" suggestions under the assumption that tertiary education in the US resembles a college movie as opposed to, you know, reality.
    Quote Originally Posted by Marjane Satrapi
    The world is not divided between East and West. You are American, I am Iranian, we don't know each other, but we talk and understand each other perfectly. The difference between you and your government is much bigger than the difference between you and me. And the difference between me and my government is much bigger than the difference between me and you. And our governments are very much the same.

  12. #92
    I Don't Work Here Endus's Avatar
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    Quote Originally Posted by Halicia View Post
    I'd like to add to that... the biggest impediment to education (imo) is people who think that there is only one correct way to teach someone. I've had some great teachers and some bad teachers, but the ways they taught may have had the opposite effect on other students. (except for one teacher I remember, he was just awful and shouldn't have had a taxpayer-funded job)
    I've mentioned I'm a licensed and certified teacher before.

    Standard practice with mathematics is that you should teach it in at least two different ways, and ideally, three. Precisely because of what you're saying. If I'm teaching a bunch of kids about multiplication, we'll be going over it on the board visually and verbally, and I'm also gonna get you to play with the physical clip-together blocks or whatever the school has available. And that's a minimum, if I'm not getting imaginative, which I always try and do. I also believe in pushing kids a little further than they think they're ready for; I'd probably introduce this topic by putting two 4-digit numbers on the board, to be multiplied together. And by the end of that class, they'd be able to work through it with me, as a class. Because once you understand the principles, the size of the numbers doesn't matter, and I like to make that point consistently; in my own grade school experiences, they always acted as if things got progressively more complex as the numbers got bigger, but it's just more work. It takes longer, but it's not harder.


  13. #93
    Quote Originally Posted by Knadra View Post
    College is basically a four year vacation from life where most students partake in unhealthy activities and don't develop a work ethic or any form of real world experience. That trade off might be acceptable if we received an extensive liberal education but the vast majority of universities lack rigor in the vast majority of their programs which seem to seldom relate to the jobs that students end up having.

    If you're going to make college free, you need to make it much harder so not everyone gets out with a degree they didn't earn. No more passing easy liberal arts classes without doing the readings and no more graduating in 6 years because you took 9-12 credits per semester. College athletic programs would need to be overhauled and de-emphasized. Greek life and the level of alcohol/drug use on campuses is already completely unacceptable and it would be downright throwing money down the drain to give free tuition to fraternity brothers who skid by in their classes and instead focus on completely hedonistic activities.
    All the relaxed computer science majors. All the relaxed history majors writing 30 page papers.

  14. #94
    Quote Originally Posted by Stands in the Fire View Post
    I've always felt this about education. Education should teach students how to live better, like useful stuff for the workplace, or how to prepare a healthy meal.

    Do you think higher education is beneficial to students? A lot? Or just a little? How often do you use calculus?
    The education system is designed and ran by people who haven't worked much outside the education system, they have no idea what real work needs.

  15. #95
    Quote Originally Posted by Didactic View Post
    Sounds like you're basing your "policy" suggestions under the assumption that tertiary education in the US resembles a college movie as opposed to, you know, reality.
    I'm basing it around my experience in college as well as trends that I know are true from general reading and the experiences of others. Most students (understandably) want to get by with doing as little work as possible. When I was in school, good professors knew this and structured their classes in a way that you either did the work they wanted you to do or you simply failed. Students today can go on ratemyprofessor and dodge these types of professors in favor of easy As. Some professors when I was in school had reputations so word of mouth could have an effect on your registration but I recall mostly picking classes based solely on the content and times it was offered.

    Easy classes really do no one any favors. It is demoralizing to be a hardworking student knowing that your lazier peers have the same grade as you. Making tests easy, papers and essays lax, and readings non-essential for passing completely subverts the learning process. This started in high school but so many people go to college now that it has spread. Also considering the number of PhDs that we graduate and the average size of classes, the fact that TAs often end up teaching classes is really absurd.

    These aren't arguments against making college cheaper or free, they are just reasons why I think it should be harder. As for the other things I mentioned, yes they are based on reality. 59% of students graduated in 6 years in 2012 and almost a third of college students admit to binge drinking in the previous two weeks in 2016.


    - - - Updated - - -

    Quote Originally Posted by Themius View Post
    All the relaxed computer science majors. All the relaxed history majors writing 30 page papers.
    I don't know why people like you have a hard time understanding that some programs being challenging doesn't mean that the vast majority of them are not. A standard college paper today is going to be 5-10 pages, nowhere close to 30 unless they get the entire semester to write it or something which takes the rigor out of it.

  16. #96
    I Don't Work Here Endus's Avatar
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    Quote Originally Posted by Knadra View Post
    I don't know why people like you have a hard time understanding that some programs being challenging doesn't mean that the vast majority of them are not. A standard college paper today is going to be 5-10 pages, nowhere close to 30 unless they get the entire semester to write it or something which takes the rigor out of it.
    In a history degree, pretty much any 3rd-year level course is going to require a 25-30 page paper. And no; you usually get a month to write this, from the time the subjects are assigned. You know the timing of the workload, but you don't get the actual assignment until later in the term.

    The only time you'd get a full trimester (Canada's system runs on three terms, a semester is two half-year terms, so semesters are a few weeks longer than a trimester) for a single paper is if you're doing an independent study or an honours thesis or the like, and those generally run 50+ pages.

    It also bears noting that these are minimums, and holding to that minimum isn't a great way to try and get top grades.

    Liberal arts programs are based on an assumption of about 40-50 hours of work per week, on average, at the BA level. The amount you spend specifically in class really isn't relevant; you spend as much time on readings and research as a Chem student is spending in lab time. It's just not scheduled, because you don't need to schedule your access to specialized equipment and materials.
    Last edited by Endus; 2019-04-01 at 08:38 PM.


  17. #97
    Pandaren Monk wunksta's Avatar
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    I agree with the view that education shouldn't only be focused on labor skills. It should encourage people to think critically, learn about the world around us and how to interact with other people. Even stuff like art can be beneficial towards personal development. People aren't cogs to be put on an assembly line.

  18. #98
    Void Lord Elegiac's Avatar
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    Quote Originally Posted by Knadra View Post
    I'm basing it around my experience in college as well as trends that I know are true from general reading and the experiences of others. Most students (understandably) want to get by with doing as little work as possible. When I was in school, good professors knew this and structured their classes in a way that you either did the work they wanted you to do or you simply failed. Students today can go on ratemyprofessor and dodge these types of professors in favor of easy As. Some professors when I was in school had reputations so word of mouth could have an effect on your registration but I recall mostly picking classes based solely on the content and times it was offered.

    Easy classes really do no one any favors. It is demoralizing to be a hardworking student knowing that your lazier peers have the same grade as you. Making tests easy, papers and essays lax, and readings non-essential for passing completely subverts the learning process. This started in high school but so many people go to college now that it has spread. Also considering the number of PhDs that we graduate and the average size of classes, the fact that TAs often end up teaching classes is really absurd.

    These aren't arguments against making college cheaper or free, they are just reasons why I think it should be harder. As for the other things I mentioned, yes they are based on reality. 59% of students graduated in 6 years in 2012 and almost a third of college students admit to binge drinking in the previous two weeks in 2016.
    So, basically anecdotal evidence and correlations. Okay Felicia.
    Quote Originally Posted by Marjane Satrapi
    The world is not divided between East and West. You are American, I am Iranian, we don't know each other, but we talk and understand each other perfectly. The difference between you and your government is much bigger than the difference between you and me. And the difference between me and my government is much bigger than the difference between me and you. And our governments are very much the same.

  19. #99
    Quote Originally Posted by Endus View Post
    In a history degree, pretty much any 3rd-year level course is going to require a 25-30 page paper. And no; you usually get a month to write this, from the time the subjects are assigned. You know the timing of the workload, but you don't get the actual assignment until later in the term.

    The only time you'd get a full trimester (Canada's system runs on three terms, a semester is two half-year terms, so semesters are a few weeks longer than a trimester) for a single paper is if you're doing an independent study or an honours thesis or the like, and those generally run 50+ pages.

    It also bears noting that these are minimums, and holding to that minimum isn't a great way to try and get top grades.
    In Florida, third year level courses and higher are called 3000s and 4000s so for example American History for a junior would be called something like AMH3500. I was a philosophy major and these upper level courses were usually just reading a few books with a few papers to write and a midterm and a final. The first two years are intro classes and general credits, you don't really get into your major until you are junior. Semesters are roughly 4 months each in the US so Fall is late August to December, Spring is January to early May, and Summer is early May to late August.

    My program didn't even have a mandatory thesis. They only made you do that if you wanted to go to grad school since philosophy majors usually feed into law schools instead.

    - - - Updated - - -

    Quote Originally Posted by Didactic View Post
    So, basically anecdotal evidence and correlations. Okay Felicia.
    I just gave you two sources. I mean if you are really going to sit here and tell me my own college experience is irrelevant in my judgement and that liberal arts programs at the hundreds of state schools in this country are actually really rigorous, then I don't know what to say to you. You either didn't go to college or you went to a top school that is actually difficult.

    Also if you went to any school besides a Mormon or Quaker university or something, you know that college students drink and smoke a lot. Way too much. They eat like complete shit even for American standards. They don't sleep enough because they procrastinate, get stressed, drink, and have inconsistent schedules and workloads. If you're going to push for free college, you need to push for a total overhaul at the same time because they don't encourage healthy life habits at an age where you form your habits for the rest of your life.
    Last edited by Deletedaccount1; 2019-04-01 at 08:59 PM.

  20. #100
    Quote Originally Posted by Biomega View Post
    The problem isn't the content of education as much as the methodology and the structure in which it is taught.

    Instead of focusing on understanding, the focus is entirely on achievement - as long as you can reproduce the information required of you in tests, you pass. Whether or not you truly UNDERSTAND the contents you are required to study is secondary, and indeed often falls by the wayside entirely.

    This, however, runs entirely counter to the very reason why certain subjects are taught. The purpose of teaching literature is not to produce people who can recite the members of the Transcendentalist movement or people who know The Charge of the Light Brigade by heart - it's to produce people who are capable of critically examining social-historical paradigms, who can decode and employ the intricacies of ornate language, who can reflect on the human condition in its various temporal and spatial contexts.

    Similarly, the purpose of teaching advanced math and mathematical proofs is not to produce people who can recite the Pythagorean Theorems or tell you what a LaPlace die is. It's to produce people who are aware of how mathematical relations operate; how statistics run counter to intuition but underlie fundamental empirical phenomena; who can apply structured thinking and reasoning to problem solving regardless of the concrete nature of the problem.

    In short, what you want people to learn is not how to do or fix something particular - but rather how to find and use the tools they need to do or fix ANYTHING. The reason for that is simple. Some argue that we should teach people how to do their taxes instead of teaching them advanced math. Okay. Now you have someone who can do their taxes. But what if they need a loan now? You didn't teach them that. So we teach them taxes and loans. But what if now they need to budget? And so on. If, however, you teach them how to handle numbers in general, how to work with equations, statistics, graphs - then you have people who can be faced with whatever math-based problem you didn't (and/or couldn't) anticipate and they will know how to approach it to get to a solution. And it is precisely because of that limitation that education needs to be broad. We can't know what people will need to know in particular - but we know that teaching them the general will provide them with the tools they need to tackle even the unexpected.

    The rates of poor reading proficiency are troubling; but the rates of functional innumeracy are even more staggering, and arguably even more pernicious. People that don't understand how math works and relates to the real world tend to make a whole lot of stupid decisions. And that's largely because they weren't taught the underlying methodology of math - they were taught specific procedures, but not the understanding that lies behind them. And it is that understanding of math that is crucial to connecting abstract structures to concrete phenomena.

    Similarly, people have shockingly low levels of critical thinking ability. People who are taught how to dissect language, how to question and investigate claims, those are people that DON'T fall prey to things like fake news or inflammatory populist rhetoric. But if you are only taught "this book means X, that book means Y" instead of being given the tools to find out how to argue for X or Y - or Z, A, B, C, any letter you like - or how to confront claims of A, B, C then it is no surprise you tend to swallow anything some authority figure throws at you.

    Goal-oriented education is self-limiting. And here we have people who say they want to make it even MORE goal-oriented? Sure, if all you want to have is obedient, unquestioning workers who perform rote tasks on command, then do it like that. But that's not the people who produce innovation, and who can improve life for everyone.

    Don't get me wrong, though - I absolutely agree that there are deficits in the education system relating to contemporary societal demands. We SHOULD be teaching people about economics, about computers, about banking and taxes and real politics. But we should do that in a general way, too - teach them the structures, the methods, the meanings of things. Teach them how to solve any problem, and not just the solution to a particular problem. And for that, you NEED a broad education. You need literature, philosophy, science as much as you do sociology, economics, and politics, because they are all connected at fundamental levels. And without the fundamental, the specific will forever remain a hollow shell that you find yourself unprepared for.

    We need to address the structural problems of education. Don't teach for tests, teach for UNDERSTANDING; and, conversely, make tests about understanding much more so than about knowledge. Integrate subjects vertically and horizontally. Teach methodologies and principles, and how these apply to examples and applications - any examples, and any applications. That way, you'll never have college kids who don't know how to do their taxes and instead of going and finding out on their own, instead raise their hands to the skies in frustration and lament that their teachers never told them.
    Excellent post. Well said.
    I can only add that in the fast moving world we live in, learning things for a particular job only, can be a recipe for disaster.
    You will keep needing full re-training!

    Learn all the broad general knowledge to function properly.
    Then specialize on your masters or with professional certification(s)
    That is how it should be
    and the geek shall inherit the earth

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