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Xon
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Post by Xon »

The Duchess of Zeon wrote: Calculators were only invented in the past few decades, and the majority of math done at even the High School level was invented long before that. Even Matrices, for that matter, somewhat predate the hand-held calculator. I grant that a normal scientific calculator might be useful for several things (like log tables) which it would be ridiculous for a student to be expected to learn in this day and age, but otherwise a student should be able to perform math that they will ecounter before college without one. Perhaps some sort of stripped down scientific calculator could be produced for the schools and issued in class. That would be especially important to prevent students from bringing in calculators with a memory function.
Doing basic number crunching when the major aim of the course it to teach symbolic manipulation (aka equation solving & rearrangement) kinda defeats the point.

Its trivial to write questions which are directly unsolvable by modern calculators or require the student to display steps the machines simple dont use.

Its pure laziness to require the students todo significant number crunching in situations which are testing their understanding of how to manipulate mathmatic equations.

The answer itself isnt important, but how you get there.
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Post by Lusankya »

ggs wrote:
The Duchess of Zeon wrote: Calculators were only invented in the past few decades, and the majority of math done at even the High School level was invented long before that. Even Matrices, for that matter, somewhat predate the hand-held calculator. I grant that a normal scientific calculator might be useful for several things (like log tables) which it would be ridiculous for a student to be expected to learn in this day and age, but otherwise a student should be able to perform math that they will ecounter before college without one. Perhaps some sort of stripped down scientific calculator could be produced for the schools and issued in class. That would be especially important to prevent students from bringing in calculators with a memory function.
Doing basic number crunching when the major aim of the course it to teach symbolic manipulation (aka equation solving & rearrangement) kinda defeats the point.

Its trivial to write questions which are directly unsolvable by modern calculators or require the student to display steps the machines simple dont use.

Its pure laziness to require the students todo significant number crunching in situations which are testing their understanding of how to manipulate mathmatic equations.

The answer itself isnt important, but how you get there.
I made enough arithmetic errors with a calculator, without one, my sums would be chaos, despite my understanding the concepts fine. Once I went through an entire problem saying that 7^2=32. I don't know why. Fortunately the 32s cancelled each other out, so I ended up with the right answer, but unfortunately, I'd finished that assignment early for a change, and everyone else in my class copied my answers, and not a single one of them noticed my mistake.

And once it has been proven that a student understands a certain mathematical principle, there's not too much point in making them repeat it again and again. We might as well go and make students solve all of their calculus problems from first principles.

Besides, the calculator knows the value of pi better than I do.
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Post by phongn »

The Duchess of Zeon wrote: Calculators were only invented in the past few decades, and the majority of math done at even the High School level was invented long before that. Even Matrices, for that matter, somewhat predate the hand-held calculator.
I'm currently taking a linear algebra class. Calculators are banned from the tests, but the professor tends to write the tests so that the arithimetic is trivial. OTOH, the maths tend to be fairly simple for linear algebra, unlike some other courses.
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Post by Edi »

Crown wrote:I believe I mentioned that the Finnish system is ranked as the best in the EU AFAIK, IIRC ...

Come on! Throw a brother some love here, I don't get to read and post here as often as I would like anymore, you could at least try! :P

:wink:
Sorry, I forgot about it it because I was too busy chuckling at the mental image of your Hellenic re-education squad showing up at Vympel's door. :lol:

I actually didn't know our system was designed by a German, so thanks for that. Funnily enough, there has iirc been some serious talk about making German school reforms to make the system there similar to ours. There have been several groups of politicians from at least Germany and the UK coming over here to see the system in action, and at least in their comments to the Finnish media they've been rather impressed.

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Post by Broomstick »

Edi wrote:The amount of bullshit about language education in this thread is fucking staggering, I just waded through 4+ pages of it, and the number of actual, worthwhile posts could be counted on one hand. Most of those were of the short variety too.
Well, Edi, it's like this - most folks in the English-speaking world know jackshit about languages outside of their own. As a result, they have a lot of mistaken notions about the difficulty of learning and the utility of foreign languages. The result, in a thread such as this, is, as you so aptly stated, bullshit

For better or worse, at this point in time English is the de facto (nice Latin, huh?) common tongue of the vast majority of the world today. It is the international language of science and aviation. If English is not your native tongue then there's a lot of very good reasons to make it your second language.

For those of us who started with English, there are still benefits to learning another language. Although English might be either the most commonly used language or damn close to it, there are still millions of people who do not speak it. From a standpoint of practicality in the global economy, learning a second major tongue - which could be Mandarin, Arabic, Spanish, etc. - makes a lot of sense, for the same reason that learning English makes sense - you can communicate with a lot more people and have access to more knowledge.

But beyond that, the exercise of learning another language - ANY other language - outside your native tongue is beneficial in children because it stimulates brain development and provides a different outlook on the world. Given the complexity of today's world, flexibility of thought and perspective is a benefit. I don't think you even need to achieve true fluency to beneift, although that is, of course, preferable to mere halting speech and elementary reading skills.

However, forcing people to learn dead languages (unless they want to learn them) or language number three and beyond, gets into dimishing returns. Unless you're in a language-specialty area, but most people aren't and never will be. It gets back to what is the best use of resources. In some areas of the world learning 3 or 4 languages does make sense - India, for example, seems to be a place where polyglots are quite common and enjoy distinct advantages - but large swaths of North America and Australia are not among such areas. There are only so many hours in the day, and an infinite numbers of subjects to study - what is the best use of time for the average student, with a slice of limited time left over for specilization?
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Post by Edi »

Broomstick wrote:For better or worse, at this point in time English is the de facto (nice Latin, huh?) common tongue of the vast majority of the world today. It is the international language of science and aviation. If English is not your native tongue then there's a lot of very good reasons to make it your second language.
True enough, and with me, you're preaching to the choir. :)
Broomstick wrote:For those of us who started with English, there are still benefits to learning another language. Although English might be either the most commonly used language or damn close to it, there are still millions of people who do not speak it.
Indeed. Just try going to Italy, for example, outside of a few specific regions like the Garda area and the high class tourist resorts like Sorrento, Capri and Positano near Napoli you're completely up the creek without a paddle if you only know English. Most people in that country don't know English, they are far more likely to know either French or German (depending on area) or no foreign languages at all. For example, a bit over a year ago when I went to Pesaro on the Adriatic coast with my gf, there were two people among the staff at our hotel who knew English, one tourist guide we met, two or three people among the various shop employees and three people in the tourist info office. And it's a fairly large town. If my gf didn't know some Italian because of language courses she took, we'd have been SO in trouble.
Broomstick wrote:From a standpoint of practicality in the global economy, learning a second major tongue - which could be Mandarin, Arabic, Spanish, etc. - makes a lot of sense, for the same reason that learning English makes sense - you can communicate with a lot more people and have access to more knowledge.
Yes, and it also gives these foreigners the impression that you respect them, because learning their language is not necessarily an easy undertaking. They will likely be more favorably disposed toward you, because there is a greater sense of equality.
Broomstick wrote:But beyond that, the exercise of learning another language - ANY other language - outside your native tongue is beneficial in children because it stimulates brain development and provides a different outlook on the world. Given the complexity of today's world, flexibility of thought and perspective is a benefit. I don't think you even need to achieve true fluency to beneift, although that is, of course, preferable to mere halting speech and elementary reading skills.
True. Didn't mean to imply that true fluency is necessary, as long as the communication is reasonably clear and you and the other person can get your points across, it's sufficient. Of course, for people who are constantly exposed and immersed, true fluency is not a question of if but when, assuming they have any linguistical talent. Because I know some people who couldn't learn a foreign language fluently if their lives depended on it, they just couldn't. On the other hand, they could solve math problems that had me completely stumped quite effortlessly.
Broomstick wrote:However, forcing people to learn dead languages (unless they want to learn them) or language number three and beyond, gets into dimishing returns.
Sing it, sister! The reason I've learned Swedish is because it was forced on me (by law, must be taught in school, because it is an official language here), I'd not have taken it voluntarily, unlike German which was an optional choice for me. The good thing was that those two are so similar that learning them at the same time fed both efforts. Having double German followed by double Swedish got very confusing because they began to get mixed up...
Broomstick wrote:Unless you're in a language-specialty area, but most people aren't and never will be. It gets back to what is the best use of resources. In some areas of the world learning 3 or 4 languages does make sense - India, for example, seems to be a place where polyglots are quite common and enjoy distinct advantages - but large swaths of North America and Australia are not among such areas. There are only so many hours in the day, and an infinite numbers of subjects to study - what is the best use of time for the average student, with a slice of limited time left over for specilization?
My personal opinion, based on my own experiences, is that learning one foreign language well and at least the basics of another is good, but beyond that it has to be through genuine interest, not forced. It's better if both the primary and secondary foreign languages are of interest to the student, but it is not absolutely necessary, and pursuing extensive studies in the second foreign language is not necessary once you have a grasp of the basics. No sense forcing even intermediate level of skill when there is no desire to learn, because that will just cause resentment which will actively hinder the process.

Some native talent in languages is also desirable, it greatly eases things. I have a good head for linguistics, both sides of my family have it. My mother is a teacher of two foreign languages (English and Swedish) and speaks fluent, unaccented Spanish. My father knows German, English, Swedish and some Estonian. The younger of my two uncles knows six or seven languages, four of them fluently. The older one knows at least three foreign languages, and all of them relatively well. So no surprise that I've no trouble with this. We all suck at math, though...

Edi
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Post by Gil Hamilton »

The Duchess of Zeon wrote: Calculators were only invented in the past few decades, and the majority of math done at even the High School level was invented long before that. Even Matrices, for that matter, somewhat predate the hand-held calculator. I grant that a normal scientific calculator might be useful for several things (like log tables) which it would be ridiculous for a student to be expected to learn in this day and age, but otherwise a student should be able to perform math that they will ecounter before college without one. Perhaps some sort of stripped down scientific calculator could be produced for the schools and issued in class. That would be especially important to prevent students from bringing in calculators with a memory function.
Unless you are doing trignometry, in which they never made students ever do trig functions by hand. Back before calculators, they had big tables in the back of math books which listed the values for all the trig functions for 360 degrees. Why? Because you can do trig functions by hand, but it's a huge bloody pain in the ass and more to the point, a giant waste of time, thus making them do it for every single trig function wouldn't teach them anything but it would make them take 4 hours to do 15 minutes of work.

Let me give you an example (straight from my Trig textbook). Say you've got a submarine that's sighting a moving target at a distance of 820 m. A torpedo is fieded 9 degrees ahead of the target as shown in the drawing and travels 924 m in a straight line to hit the target. How far has the target moved from the time the torpedo is fired to the tme of the hit?

Please do that by hand, Marina, without a calculator or a cosine table. That means for the cosine you've got to do the Cosine Infinite Series:

cos(x) = 1 - (x^2 / 2!) + (x^4 / 4!) + (x^6 / 6!) + ...

Have fun. :)
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Post by Broomstick »

Edi wrote:
Broomstick wrote:For those of us who started with English, there are still benefits to learning another language. Although English might be either the most commonly used language or damn close to it, there are still millions of people who do not speak it.
Indeed. Just try going to Italy, for example, outside of a few specific regions like the Garda area and the high class tourist resorts like Sorrento, Capri and Positano near Napoli you're completely up the creek without a paddle if you only know English.
Absolutely.

When I went to France I had a lot of people tell me "Oh, everyone speaks English". Um... no they don't. Not even in Paris. Sure, if you stick to the tourist areas and the high-rent districts someone will be able to speak English, but personally I enjoyed being able to wander off into the quieter areas. No, my French wasn't fluent but I could communicate well - like just about everyone my comprehension of the spoken language was much higher than my ability to speak, but slightly broken works just fine in the real world.

In Paris there were a few people who took offense at my "murdering" of their language but what the hell - you have jackasses everywhere. MOST people appreciated the effort, even when their English was better than my French. And outside of Paris there were entire days when I never encountered an English speaker and if I had had no knowledge of French I would have been up to my neck in merde.

The only place my French didn't work was in the Paris Chinatown - their Chinese accented French and my American accented French collided horribly and lay twitching spasmodically on the floor. But we all had a good laugh over it. At that point in my life I was eating enough Chinese food that I could recongize the characters for certain ingredients like "chicken" and "pork", which oddly enough meant that I could read some Chinese, although I couldn't speak it. And I couldn't order in French because I don't know how to say gai kow or chop suey in French! (For some reason, Chinese food was never mentioned in my high school French textbooks) Everyone had a good laugh over our mutual mangled French, we tourists ordered by pointing at the Chinese side of the menu, and my first dinner in Paris was Cantonese and delicious.

I'm not sure what all that is supposed to mean, other than picking up any bit of any language might be potentially useful and international travel is an adventure.

And by the way - there is the additional problem that while there are many people in France who speak English, it's almost always British English, which is not my native dialect. That, too, can be an obstacle to understanding.

But I tell you, a working knowledge of French proved invaluable when I was in a bar in Clermont-Ferrand were no one spoke English but me, I needed the bathroom badly, and the path to the nearest one involved a trip through maze-like medieval streets. Trying to remember instructions given in a foreign language, in a dialect of that language you are not very famillar with, and trying to remember it while inebrated is a far greater test of one's language skills than anything I did with pencil and paper in a classroom.
Broomstick wrote:From a standpoint of practicality in the global economy, learning a second major tongue - which could be Mandarin, Arabic, Spanish, etc. - makes a lot of sense, for the same reason that learning English makes sense - you can communicate with a lot more people and have access to more knowledge.
Yes, and it also gives these foreigners the impression that you respect them, because learning their language is not necessarily an easy undertaking. They will likely be more favorably disposed toward you, because there is a greater sense of equality.
Indeed. I found that out myself personally. No doubt my efforts to speak the language is a large part of the reason I found the French hospitable while I was over there.
Broomstick wrote:But beyond that, the exercise of learning another language - ANY other language - outside your native tongue is beneficial in children because it stimulates brain development and provides a different outlook on the world. Given the complexity of today's world, flexibility of thought and perspective is a benefit. I don't think you even need to achieve true fluency to beneift, although that is, of course, preferable to mere halting speech and elementary reading skills.
True. Didn't mean to imply that true fluency is necessary, as long as the communication is reasonably clear and you and the other person can get your points across, it's sufficient.
True - however, I have encounterd many people over here who seem to feel that if you can't achieve native-speaker fluency you might as well not bother. Nevermind they're surrounded by immigrants speaking less than perfect English who nonetheless mange to get by quite successfully in this country.

I insisted on starting a foreign language as early as possible - which in my case was 12. I was willing at 8, and wish I had started then. Even so, many people asked me what was the hurry, I could study a language in college. No! Not good enough! It is always easier to acquire language skills prior to puberty and I wanted at least one non-native language "installed" prior to then.

When I later studied Irish Gaelic (now there's an obscure language!) the class was entirely adult and there was a definite difference between those of us who had been heavily exposed to a second language early in life vs. those who took up the study later. Those of us with earlier experience learned to recongize and pronounce unfamilar phoenyms (yes, I probably misspelled that) much quicker than the others - English has about 40 sounds, Gaelic 60. That's 20 new noises you have to learn to recognize and make. We picked up the grammer quicker - and Gaelic grammer is quite different from either Germanic or Italic branches of Indo-European. As an example, the sentence the "the girl is walking" is literally "is the girl at walking", and it takes getting used to a word order that is a question in English being a statement in Irish (and Irish never changes the word order to make it a question, the verb changes to indicate that). The language has two difference alphabets in use, and two different spelling systems (and you thought English had problems with spelling....!) But after the first year I could carry on simple conversations (never learned to read it much - the classes I took emphasized speaking over writing). I really think Irish would have been MUCH more difficult if I hadn't had French first - and not because the two are related. They're pretty distant.

Now I mutter about taking something like German or Spanish - and people tell me I'm too old! Bullshit. You're never too old to learn. Yes, it will be more difficult for me than if I were six, and my accent will most likely always be heavy... but there's absolutely no reason I can't acquire the same proficiency in German or Spanish that I once had in French. If I am motivated to do acquire it - and that's a huge factor. You can not force someone to learn a foreign language, they have to want to learn it. You can mandate exposure, not comprehension.
My personal opinion, based on my own experiences, is that learning one foreign language well and at least the basics of another is good, but beyond that it has to be through genuine interest, not forced. It's better if both the primary and secondary foreign languages are of interest to the student, but it is not absolutely necessary, and pursuing extensive studies in the second foreign language is not necessary once you have a grasp of the basics. No sense forcing even intermediate level of skill when there is no desire to learn, because that will just cause resentment which will actively hinder the process.
Agree again - once you know how to ask for the bathroom and say "I'm hungry" or "I'm thirsty" without causing offense you've tackled the really essential real-world items...
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