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How Technology Changes Classrooms
Corrupt writes "Just ask 11-year-old Jemella Chambers. She is one of 650 students who receive an Apple Inc laptop each day at a state-funded school in Boston. From the second row of her classroom, she taps out math assignments on animated education software that she likens to a video game."
She is one of 650 students who receive an Apple Inc laptop each day
I wish I could receive an Apple Inc laptop each day! Sounds profitable ;)
Its not like a computer can teach you to think critically, they also stifle real research skills. Why poor though references or bother to learn the proper way to annotate them if you can just google for a text string?
Kids don't learn Latin anymore but they are learning to 'use' computers at the age of 11, get real. As a tool they are useful but in order to be a tool the user must have some basic skills that becoming computer dependent at that age will seriously retard. I really think there is no call for kids to be using computers as part of the educational experience before high-school.
"Ahh! Arrogance and stupidity in the same package, how efficient of you!" --Londo Molari
Forget flying cars; this is how the mysteeeeeerious future is supposed to be. I still remember sitting in E&M class back in the day, thinking that if, instead of static images drawn on chalkboard, the charges and fields were animated and interactive, it'd all sink in much quicker. Ditto pretty much everything that has to do with classical mechanics.
Maybe this already exists, but I'd always hoped for a good intersection of games and education that actually encourages students to learn in a lecture setting. "Edutainment" has generally been pretty awful, but I bet there's a way we could integrate learning into an MMORPG such that you can (say) use a knowledge of kinetics to advance your character.
jenious1: I now understand Newton's Laws, so I built a catapult that demolished your castle. Kekekeke!
!pnk101: o yeah??? well im still beating u up at lunch u nerd!!!!1
jenious1: Snap!
We're indie. We're working on our 14th game.
There is very little value in learning how to do things the old way when the new way is all that will ever be used.
Following your logic, we should all be hunting and gathering instead of shopping for food because now we can't feed ourselves, either.
Let us retard all progress in the name of tradition because... well, there is no good reason. But it would make you happy, I suppose.
IT in education is too young. I dont think the right models for education have been developed anyhow, much less good software that supports them.
The thing is that education is severely tied into media: from the greeks and their oral traditions, to the medieval cult of the books, to the discovery of print, education has been transformed by the media in which we store and confer information.
Today, that media is becoming a universally accessible cloud. I think current trends of education that favor the use of PowerPoint as a better tool than a blackboard are ok in terms of efficiency, and they might really convey information in a better way.
The question that I make myself is not about efficiency, but about the difference between information and knowledge. Yeah, sure, tech conveys info. it also MAY convey knowledge of SOME things that are encodable in our new tool (the net, for example).
But knowledge? Is viewwing a simulation of a physic phenomenon the same as taking the weighs in the labs and proving them yourself? Is it the same viewing a simulation of the parabolic shot, than actually going into the lab, meassuring force, launching a thingie, see how far it got and THEN using newtons tools to see if they still work.
In a word: can we ever substitute experience through tech?
Worse: do we WANT to do that?
NO SIG
I have a small issue with your argument. As tools become more complex, learning to use them becomes more complex. Reasoning and logical thinking are not harmed/hampered by having complex tools available. They are harmed by teachers who use complex tools to avoid doing the harder part, teaching kids to reason and think. Sure, a laptop or calculator makes fast work of math problems yet structuring a mathematical proof is something the calculator won't do. If kids want to copy someone else's work off the Internet, teachers need to ensure that testing requires the child to prove they know the material.
Did nailing guns make carpenters less skillful?
Did spreadsheets make accountants less skillful?
and so on....
You are blaming the problem on the tool instead of the teacher.
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Kids don't learn Latin anymore
Aside from learning one of the foundations of our language I'm not sure why you pick this of all things to be upset about. I never learned Latin and I speak the english real good.
Thanks to technology, people are graduating without even knowing how to construct complete sentences. And also thanks to technology, those same people can now go on to be "editors" for major websites. : p
This guy's the limit!
We didn't have computers, but we still played games and passed messages behind the teachers' backs.
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And following your logic we should not be teaching math at all just how to use a calculator.. See how silly following logic can be!
"Ahh! Arrogance and stupidity in the same package, how efficient of you!" --Londo Molari
Is a computer easier or harder to use now that its more sophisticated? As a tool I have little problems with computers in the class when someone can read/write/and do math and *maybe* even a useful root language like Latin at an 8th grade level..
"Ahh! Arrogance and stupidity in the same package, how efficient of you!" --Londo Molari
Kids don't learn Latin anymore
Because it has no practical application for 99.999% of them. There's a reason it's a dead language and it has nothing to do with computers.
While I think computer usage in this particular school may be a little overboard, I don't see it as a major problem overall. Kids use computers all the time, and are starting at a younger and younger age. Computers can be a very good tool for these sorts of things, and I'm not sure how they can really retard basic skills other than possibly handwriting. In that regard, kids could hardly end up with worse handwriting than most of their parents, even if they never write anything by hand outside of their handwriting classes in Kindergarten through 3rd grade.
Most kids in my experience will use computer learning games because they're more interesting than long sheets of math problems. However, if given the choice between that same computer game and, say, a particularly interesting worksheet (maybe one of those where you color a picture different colors based on the answers to the math problems), the choice is not always so clear cut.
The basic upshot is that kids will learn best if they're engaged in the material. A computer game can engage them, but a particularly good teacher or a particularly good set of handouts can engage them just as well. A good education will come from a mix of various techniques to keep the kids from becoming bored with any one thing and disengaging from the process.
As for kids not learning Latin anymore, I think that's just because Latin is not particularly useful to anyone not in a specialized field (like medicine or law), and is thus not worth spending a ton of time on in the earlier grades. If you're interested in joining a profession that uses Latin, or planning on competing in a spelling bee, you'll learn Latin eventually. Otherwise, you're going to be bored out of your mind in a class you have no use for, and will eventually forget most of it anyway.
Seriously, what's wrong with the abicus?
The spelling?
(Disclaimer: I wish English would simplify its entire spelling system, blah blah blah.)
Information theory is life. The rest is just the KL divergence.
Funny how kids used to do a lot better when schools didn't really care about kids' self-esteem and made them work diligently on paper. The focus on using computers to make things better is just a distraction from the fact that the average public school is literally just a tax-supported daycare center that provides some education.
"Thanks to technology, people are graduating without even knowing how to construct complete sentences. And also thanks to technology, those same people can now go on to be "editors" for major websites."
Or it could be that most schools do not teach grammar or language structure at all, I know when I was in school we never got any of that crap. We got a few mentions of 'noun' vs 'verb', etc. But nothing like a lecture or classes on proper sentence structure.
At the secondary level, it seems to me that the impact in the technology itself. For instance, learning to use a teletype machine did not provide a long time marketable skill, but it did provide an opportunity to learn a novel device, which was cool. It made me learn how to learn. Likewise when one might learn to use a EEPROM programmer, vi, a drill, a saw, or even drive a car. All of these are learning the technology, and motivated students will learn how the technology works, and how it does not work, which is what we want anyway.
This continues to college until technology is mostly used to help us learn more efficiently. An computer index can be more efficient than a printed index. Typing paper in LaTeX can be more efficient that on a typewriter or in lower tech word processing program. The list goes on.
What I think is really important, though, is that kids are allowed to become familiar with technology, and it's use. I see classrooms where there is no play time with machines. I see primary school kids being taught by rote the parts of a computer, which little context of what a computer does. I see teachers telling students to open the internet by clicking IE. In this way technology changes the classroom very little, as we are still teaching facts with little context in reality.
"She's a scientist and a lesbian. She's not going to let it slide." Orphan Black
Latin is a great resource if you want to learn other romance languages
Actually they could just spend their time more wisely and directly learn the language they want in the first place.
and it is the language of western science.
Funny, since most of the scientists I've ever met or worked with don't know speak Latin. Apparently it's not as big of a deal as your conflation attempts to make it.
So I went to visit my local high school in Georgia and I spent a little time talking with some teachers. While I was there they were setting up a presentation on a projector from a PC, it wasn't using powerpoint, rather some vastly inferior-looking custom software. Anyhow, I digress...
I was struck by how much it appeared to lock the teacher into the detail of the curriculum. It seemed to me that the main point of the presentation method was to confine what the teacher could say to the class.
My impression was that the technology was being used to micromanage teachers more than to enrich the learning experience for the students.
Nullius in verba
> "The dog ate my homework" is no excuse here. Sure, now it's...my hard drive melted or the server's down. Seriously? Kids are starting too young. I love how people are worried that people are too connected to their technology and that kids aren't getting out enough anymore, and yet, we're starting them with a need for technology at the age of 11. Has anyone else been at the supermarket when the computers go down? No one knows what the hell to do. It's a madhouse. Technology can be exceptionally helpful, but I don't think this is a move in the right direction.
-MelRom
Nail guns allowed less skillful people to work as carpenters, to do an adequate job in situations where they would have not been able to do so before. Nail guns also allowed skilled carpenters to do simple jobs more easily and quickly.
If all you need is a wall frame of 2x4s, a carpenter of limited skill with a nailgun will do. But if you want fine furniture built, you need someone with more skills, who knows the properties of different sorts of wood and different types of joints and fasteners. Before nailguns, every carpenter knew these things.
I notice that TFA - like most in praise of computers in the classroom - makes no mention of test scores or any other metric that demonstrates that students are actually learning better ithis way than in more traditional classrooms.
I recommend Cliff Stoll's books Silicon Snake Oil and High Tech Heretic.
Worse, this system doesn't just use computers, it is totally reliant on them.
Says the principal in TFA, "Why would we ever buy a book when we can buy a computer? Textbooks are often obsolete before they are even printed." But that's not true: fundamental fields change slowly, a ten year old geometry or physics or art textbook will do quite well. And students can take them home, read them on the bus or under a tree, do homework anywhere - apparently this system pretty much requires kids to have computers at home. Grandma, who's uninterested in all these modern gadgets, picks you up after school and you stay at her house until your mom gets off work? Can't do homework while you wait, no computer.
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You cannot wash away blood with blood
I recently saw a demo of a classroom tool. It played upon the peer aspect of a classroom, rather than teacher-to-student. It allowed the professor, with a tablet PC, to actively write on powerpoint slides, save the edits, etc. Nothing new there. But from the student perspective, anyone with a tablet could take their own notes the same way, watching along with the slides on their own computer (those without a tablet could type as it was web-based).
In addition, there was a blogging feature -- a few students with tablet PCs could become "bloggers" for the class, and students could tune their browsers to the blogging students' pages, and watch what they were writing.
Peer respect kept it mostly to good notes but the professor said that even if she heard the class laughing at something the blogger wrote (she never actually looked at the blogs), at least the kids were awake and possibly engaged in some part of the content. More than that, it let others consider parts of the lecture they might not have before -- sort of a group collaboration, but without the professor. A blogger might note something on a slide you hadn't thought of yet, or do a quick visible search on a word you hadn't really focused on, but upon reading the definition, more made sense.
It was really interesting and I felt a very different way of performing in the classroom. Kids staying engaged is professor's number one concern -- not every teacher is dynamic and exciting. Using a tool like this kept the kids interested because it was what they were used to: reading other kids' notes and perspectives on topics.
The tool was put out by UC San Diego:
Ubiquitous Presenter
And following your logic we should not be teaching math at all just how to use a calculator.. See how silly following logic can be!
Its not that teaching math is outdated. Its that memorizing multiplication tables might be outdated.
The main point of modern math class is how to translate real life problems into numerical equations. Once you can do that, solving those equations is rather trivial.
I was 'gifted' on the computer (as I am sure most of the people on here who are around my age were). I used the computer for things I was not supposed to. I circumvented the "deep freeze" lock they had on their systems in grade 5.
I as banned from school computer use until High School (which is grade 9-12 here).
I would have performed the exact same with or without a computer. In high school it pained me to use their computers so I did most of it the old fashioned way. When it came to looking up obscure things I couldn't find in the Library I'd have a look see at home on my own computer in my "comfort zone" of Linux.
I graduated two years ago. I've been self-employed since and making pretty good money. I incorporate Linux and open source software into everything I can... as long as it's the right tool for the right job, that is.
Yeah, yeah... Linux shill. Be on the lookout.
most of the technology here goes to complete waste in normal classes because the students generally know more about the machines than teachers. Now, if they incorporated COMPUTING instead of computers, that would be sweet. Imagine using a geometry class and Object Orientation to simultaneously teach two things -- better? Students will KNOW those definitions because they will have taught them to the computer, and they will have some background in different methods of programming -- which is a useful tool no matter what field you go into.
My neighbor's kid was suspended from school for refusing to use his school-issued laptop to take notes. He preferred pen and paper.
He was telling me that several times per class, instruction grinds to a halt because of computer problems, or from the kids having difficulty drawing diagrams on the laptops amidst the text notes. It was also damn-near impossible to write down equations in math class, so he gave up and started using paper. When he refused to use the laptop, other kids followed, and he was ultimately suspended for insubordination and "gang activity" for trying to organize a civil protest to the policy that requires that they use the laptops.
If I ever have kids (and I probably won't because it would be cruel to bring a child into the world in its current state of affairs), they're either going to Montessori school, or be home-schooled.
When I was a design engineer, I was a better CAD draughtsman because I understood the underlying principles of geometry that you learn best when working with a pencil and compass. Similarly, if you want to be a better linguist in any one or combination of European languages, a grounding in Latin would greatly improve your chances. And if you want to be a better cook, you'll stand a much better chance if you go back to basics and learn how to cook something from the raw ingredients instead of putting a TV dinner in the microwave.
Drill baby drill - on Mars
Memorizing the multiplication table is not outdated yet. It might never be. Me being able to quickly, accurately estimate totals in the grocery store is quite a benefit. Being able to factor polynomials without having to use my calculator was also handy.
My state (Utah) dropped the times tables from the 3rd and 4th grade math core for a couple of years. Disaster ensued immediately.
I cried real tears when Li Mu Bai died.
Indeed it is... IF you've got the multiplication tables memorized...
Learning is about making connections. Memorizing is about having the bits in place to connect. Education requires both.
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Nail guns allowed less skillful people to work as carpenters, to do an adequate job in situations where they would have not been able to do so before. Nail guns also allowed skilled carpenters to do simple jobs more easily and quickly.
If all you need is a wall frame of 2x4s, a carpenter of limited skill with a nailgun will do. But if you want fine furniture built, you need someone with more skills, who knows the properties of different sorts of wood and different types of joints and fasteners. Before nailguns, every carpenter knew these things.
A master carpenter would have this knowledge, a journeyman carpenter might have some insights and limited experience, and an apprentice carpenter might know how to hold a hammer. It is the same today, an apprentice carpenter with a nailgun is still an apprentice carpenter. With over 30 years experience as a carpenter in trades from housing to furniture to scenery, I can tell you that very few carpenters know what you mention until the end of their journeyman training. Few people hiring carpenters believe that a carpenter without training and experience is anything but a noob.
Like any other learning experience, whether trade or academic, what makes it engaging enough to want to learn is what matters.
No incumbents, not no where, not no how.
Vote them out every term.
I was part of my school's IT Department, and we had those computers locked down rather well. Each teacher could see what was happening on each student's monitors, and we had the net access very limited. However, the students kept finding new proxies, new ways of getting around the firewalls, and, most of all, they kept bringing in games on flash drives.
As a high school English teacher I only have one (sad thing) to contribute here. We're strongly discouraged from teaching grammar... since the administration "knows" it is boring and cannot hold student interest. If a subject or lesson cannot (or does not) keep every child in the classroom entertained, no matter how diverse the population, then the teacher is faulted.
On the other hand, be glad they've got laptops to keep them entertained. Yay!
Meh.
Nothing the government does in Massachusetts is wasteful.
Its = possessive. It's = "it is"
The main point of modern math class is how to translate real life problems into numerical equations. Once you can do that, solving those equations is rather trivial.
While that is the point of the math classes I took in high school, I'm not at all sure that's the best method to be teaching mathematics. My high school used the "Chicago Math" method of teaching, which focuses heavily on "real-life" examples and encourages heavy use of computers and calculators to ease computation.
It seemed like a pretty good method at the time, but when I got into the electrical engineering program in college, I found myself woefully under-prepared mathematically. I found that the de-emphasis on computation had caused my basic knowledge of mathematical formulae to atrophy. And, since math is cumulative, I found that I had a very difficult time catching up (especially in calculus), since my knowledge of basic algebraic principles was never developed properly. Indeed, this lack of basic skills led me to switch to the computer science program, since I found that discrete math and set theory were easier to learn, as I was learning them from first principles, making my lack of algebraic preparation less of a hindrance.
So, while its tempting to say that computation and practice are irrelevant, the fact remains that these things do matter, because its the practice that fixes the knowledge in the student's head. My father learned math in India, which has a much heavier emphasis on practice, and, even now, he's still much better at algebra and calculus than I am, because he's practiced it so much more than I have.
We all know what to do, but we don't know how to get re-elected once we have done it
As an engineer and a teacher,
Some people think doing long division is somehow better than using a calculator. Yet, I question this as you all 95% of people do is memorize the steps. You memorize the steps on what buttons to press on your calculator. You memorize the steps on how to do long division. Neither gains you any insights into division as a concept.
There is a 5% of more gifted students who actually understand how long division works and take some conceptual aspects from it in terms of number theory... but most don't.
One of the sad things is that using a calculator SHOULD permit teachers the time to drive home the concepts. This enables the students to know what they're doing when they're dividing and how they should apply it in real life. It's like teaching kids multiplication. Yet, they don't understand when to use it and they don't *grasp* the connection to say calculate the sales tax on something.
I personally spent much more time with number theory, number lines... than most do precisely because teaching to use a calculator is trivial... which BTW it is not :P I was amazed at the number of kids who have trouble with a calculator.
That is, I think, one of the most eloquent and succinct comments I have seen about memorization, and its role in education. Do you mind if I use it in the future?
Rhapsody in Numbers
Bi-nary, Dec-imal, Hex-a-dec-imal... Right. Latin has nothing to do with computers.
Indeed it is... IF you've got the multiplication tables memorized...
I have a PhD in math, and I still don't have the multiplication tables memorized. I can multiply without problems, because these things are very easy to figure out. In fact, I thing that should my school require me to memorize the tables, I probably would not choose to study math. And if I did, I would probably be worse at it.
Learning is about making connections. Memorizing is about having the bits in place to connect. Education requires both.
True. However, after memorizing "the tables", how much space is there to make connections? There are number of fascinating connections related to multiplication that can be discovered after memorizing just a few simple rules. And after kids spend several months memorizing and drilling multiplication tables, how much time and how much desire is there to make connections?
AccountKiller
Or it could be that most schools do not teach grammar or language structure at all, I know when I was in school we never got any of that crap. We got a few mentions of 'noun' vs 'verb', etc. But nothing like a lecture or classes on proper sentence structure.
I am 26 years old, with a degree in English, and I have taught English at the high school level in the past (I now teach computer courses for various reasons).
What does that mean besides the fact that I will invariably overlook a grammatical mistake in my own post? We don't teach grammar or language structure at all. Since about 1990, the trend in American English instruction has been the so-called "whole language" method. It is essentially based in a belief that immersion in proper English methods will result in more effective grammar instruction.
In practice, it means that children should be taught grammar through, say, correcting their own papers (where the changes and differences have more meaning than a drill) and through reading.
The fifth grade (1989-1990 for me) was the last time I had instruction in sentence diagramming. I did have one hold-out 9th grade English teacher who insisted on rote memorization of irregular verbs and their tenses, but who didn't provide much guidance for what distinguished "future perfect" from "past participle." Having sat through those courses, it's easy to understand both sides of the grammar education approach/
Like several other posters, it took foreign language instruction in middle school and high school before I started understanding the concept of infinitives, conjugations, tenses, etc. Coincidentally, it was also immensely frustrating when certain parts of foreign language instruction had to "dumbed down" because most students wouldn't have understood the terms being thrown around. In French, for example, you create the past tense of a verb by conjugating either avoir (to have) or etre (to be), then using a special ending for your action verb. Whether you use avoir or etre is determined entirely by whether or not your main verb is transitive or intransitive (one that has vs one that doesn't necessarily need a direct object). It's a simple distinction, but even at university level we were reduced to memorizing an mnemonic device (DR AND MRS VAN DER TRAMPS) to list the few intransitive verbs. Had the students received even minor direct grammar instruction, the distinction between the two would have been easy; as it is, there was much hand-wringing from students over the fact that a few uncommon verbs were not in the mnemonic but were intransitive.
So, to summarize, there are valid arguments for both teaching approaches. I am personally of the opinion that we learn grammar much more through absorption than rote memorization; this also makes it one of the most difficult subjects to teach to minority groups or recent immigrants who aren't immersed in the "proper" grammar 24/7. I can see why "whole language" grammar learning has its advocates - immersion methods are generally considered the best way to learn a foreign language, so why not apply them to our native language? On the flip side, though, ignoring the more technical instruction can substantially weaken a student's performance in other subjects. In the end, it's really a philosophical debate, like many in education, that boil down to personal or institutional preference.
An Apple Inc. laptop a day keeps the Norton Disk Doctor away...
perl -e "eval pack(q{H*},join q{},qw{70 72696e74207061636b28717b482a7d2c717b343 637323635363534323533343430617d293b})"
The tech approach to raise a generation of retards. These institutions rock !
Abacus is spelled phonetically.
No it isn't.
If I'm correct (I'm not a native English speaker) the first a is an 'a' while the second a is 'ei'. There are several more than 5 vowel sounds in English. It's just that you use only 5 characters for them. Even simple words like "race" are mind-boggling - the a is actually an 'ei', the c is actually 's' and the final e is mute!
For nearly-phonetic writing look at Slavic languages (there are some exceptions, like word-final w, but those are at least consistent), or at relatively modern scripts like Vietnamese.
Those who would give up liberty to obtain working drivers, deserve neither liberty nor working drivers.
Oh! But there IS something a "free computer" can teach you, and that's loyalty to the brand. That's probably the main thing I can think of right now.
I had the opposite experience, to my benefit. I went to a Catholic HS which was very traditional, and the highest level math class was "Elementary Mathematical Analysis", which was heavy trig with some differentials near the end. No calculators allowed except for particular items. Mightily we bitched, not being able to take "Pre-Calc", but the nun said "Trust me - this will better prepare you for what you will face in college calculus". So we learned what all the trig functions meant from the most basic level: First day "This is a circle".
Fast forward 1 year, and I get to Lehigh for engineering and am in Calc 21. First third of the course is...analytical trig, and the test started with "Put away your calculators; if you know what you are doing you should not need them." Followed by wails of protest, and a few smiles from me and some fellow classmates.
Similar was 7th and 8th grade math - we memorized decimal equivalents of ever fraction from 1/2 to 1/12, and selected ones up to 1/32. We hated it at the time, but I probably use those more than any other bit of grade school math.
"As God is my witness, I thought turkeys could fly." A. Carlson
Actually they could just spend their time more wisely and directly learn the language they want in the first place.
I would disagree somewhat, partly because you make the assumption that Latin is just a stepping-stone to the language I REALLY want to learn. Don't forget that, although Latin is dead, there's a nearly endless back catalog of Latin literature that's worth reading (from as recently as the 19th century). Of course, if you master basic Latin, you'll have general reading knowledge of many other languages.
Your statement also implies an either/or approach -- either learn Latin or be 'wiser' and learn the language I really want to learn. The language I really wanted to learn was German, and I did. But my 4 years of Latin allow me to travel in Europe relatively painlessly. Would it have been 'wiser' for me to just learn Italian and try to extrapolate that to French, Spanish, or Portuguese? Maybe, but I would've missed out on some great literature.
Really, who's to say which is 'wiser'?
I remember reading of a program that studied the effects of teaching Latin. Not only did they do better in English, they also did better in history. Naturally, the program was cancelled.
The problem is that your response displays reason, which has little place in the bureaucracy and money sink that is the modern public school system. After all, why use a crummy old textbook when you can get a new one for only $35-50 (times the number of kids, times how many books each needs).
I remember reading a truly mind-boggling article about the textbook development and selection process, but I can't find it now. If somebody else knows about this, please post a link.
As to the "bureaucracy and money sink" stuff, I highly recommend that any parent read the free online book: The Underground History of American Education. It gives a very interesting perspective on the whole public school system, and raises some compelling and disturbing issues about it.
Any sufficiently simple magic can be passed off as mere advanced technology.
Yet, I question this as you all 95% of people do is memorize the steps. You memorize the steps on what buttons to press on your calculator. You memorize the steps on how to do long division. Neither gains you any insights into division as a concept.
Its true, that, when learning long division, all you do is "memorize the steps". However the steps are more generalizable. For example, if you know how to do long division with numbers, its a fairly simple jump to get long division with symbols. Yet, if you're doing division on your calculator, you'll have a much harder time figuring out how to divide with symbols, since you've never been exposed to the actual division algorithm (all your division took place inside of a black box).
In other words, learning to divide using a calculator would be fine if nothing else depended on long division. But we both know math doesn't work like that. Math is cumulative - advanced topics build off basic ones. If you don't have an adequate grasp of long division with numbers, you're going to have a hard time factoring equations using that method.
We all know what to do, but we don't know how to get re-elected once we have done it
Yes - if you know how to do basic arithmetic. Almost all the arithmetic I do in real life, I do in my head -- usually just approximated to two significant figures.
I worry that kids who don't learn multiplication tables will become paralyzed by an everyday question like "which carpet is more expensive, $1.95/square foot or $39.99/square yard?"
Ultimately, the point of translating real life problems into mathematical equations is to get a solution. If someone can't at least get a ballpark solution on his own, I submit he's functionally innumerate.
[Sir Garlon] is the marvellest knight that is now living, for he destroyeth many good knights, for he goeth invisible.