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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."
Seriously, what's wrong with the abicus? Master Splinter used it quite proficiently.
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 ;)
That's a lot of apples!
She gets an Apple laptop every day?
Whilst I'm sure she's making a sweet resale profit, isn't that a bit wasteful?
...at least rewrite the summary in your own words, rather than directly plagiarizing from the article. Besides, without the first paragraph of the article, the summary makes no sense. Just ask Jemella what?
-Rob
Biblical fiscal responsibility
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
At my previous school we had a digital school board in advanced math class. It was pretty awesome because the teacher could teach much more during the 1,5 hours. Not that the lessons went faster because you always have these noobs that should have never taken advanced math ("I don't understand it!", "Can you explain that again?" -teaher: "Again?!")
Here be signatures
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.
Or maybe it's the 3rd, 4th, 5th, or 500th verse.
In the history of America, we've introduced electricity, graphite pencils, ballpoint pens, calculators, cheap paper, lighting, various audio-visual technologies, books, and I've lost track of what else just in the classroom. Telephones, computers, fast package delivery, faxes, and many other technologies used in the school office and elsewhere make running a modern school possible. I haven't even addressed labs and specialty classes and the nurse's office.
Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
Anyone seen a comparison of final test scores for kids learning via computers and kids learning the "old fashioned" way (books and paper) as in "does one group do better than the other?"
"If any question why we died, Tell them because our fathers lied."
Computers don't really help in a classroom environment... at least, not in High School or Earlier, because the kids know enough to be able to play games and email behind the teacher's back. Computers are a tool, yes, but most of the time they are misused... especially by those immature enough to put checking their myspace at a higher priority then doing their schoolwork. I just graduated High School, and it was depressing, the way that kids wasted their time in the assorted computer classes...
"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."
They receive a computer "each day"?!? And don't have to give it back?!? Hmmm... 180 school days (times) $1000 (approx price) = COLLEGE FUND!
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.
I remember when I was that young, we used Apple computers in school, which had a math flash-card type application. This concept isn't very new, however what IS new and interesting is that they're using the laptops to also completely replace books.
I guess one of the problems would be giving a student study material to take home, since they return the laptops at the end of the day. I'm usually one to assume everyone has a computer with broadband at home, but this may not always be the case.
Still, it's nice to see newer ways of passing information being embraced at such a level in the K-12 education setting.
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.
I imagine knowing Latin would assist with understanding the roots of (and perhaps learning the languages of) Italian, Portuguese, and Spanish.
Lately I have been asking accountants and financial traders that I meet if they can do long division, after all it is a skill one learns in primary school at around the age of 10 or 11. Very few remember!
So in programming we can get away with not knowing how a red-black tree works, we just use the C++ map template. Is there no validity in learning how a red-black tree works anymore? Possibly, but I think there is. At least really knowing how something works can lead to an appreciation (and better usage) of that tool.
I thought that the student was supposed to bring the teacher an apple every day...?
For that matter, why bother learning how to spell properly and use correct grammar?
She is one of 650 students who receive an Apple Inc laptop each day at a state-funded school in Boston.
What is she going to do with all those computers they are giving her? One is probably enough.
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
Modern media methods that provide interactive feedback on a student progress are a good thing IMHO. Like any other tool however, it can be utilized in a fruitful fashion, or it can be abused.
A lot of the education interaction can be automated, but I still see a need for evaluation and special needs scenarios. Some kids which need either specialized guidance to make headway, or gifted kids that could deal with an accelerated program. Seriously, some kids want to take on calculus and differential equations in the 7th grade! Rare, but true. Last year I was a judge in a local science fair and one of the kids had presented a proof for a mathematical hypothesis, gotten it published in a peer reviewed journal and was getting out of high school early to go attend Harvard on scholarship. They exist on both ends of the 6 sigma curve.
www.effectiveelectrons.com "chips that work" Analog, RF, Mixed Signal
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.
Latin is a great resource if you want to learn other romance languages, and it is the language of western science.
"Ahh! Arrogance and stupidity in the same package, how efficient of you!" --Londo Molari
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.
Aside from being politically flashy to brag about shoving technology into schools... whats the point of it? Young people write in some elvish looking scrawl nowadays, and barely have the arithmetic capacity for Su Doku. Once kids can read and write, computers can open up avenues of learning to develop other skills. I'm speaking from a UK point of view where we have no-where near the inbuilt urge of "must do well, must go to college"... sadly.
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.
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.
> "Why poor though references..."
Yeah, and why learn to spell when you have a spell checker (except those damn homophones can still get you). I suggest you pour through a dictionary to figure out the difference between the verb pour and the adjective poor.
Why should it be a problem that kids learn to use a computer instead of learning Latin? Now if an ancient Roman were learning to use a computer and not learning Latin, that would be a problem.
An example (by Asimov) is The Feeling of Power .
Great minds think alike; fools seldom differ.
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
Following your logic, we should all be hunting and gathering instead of shopping for food because now we can't feed ourselves, either.
And watch closely as he turns out to be a survivalist nut who DOES teach the wonders of hunter/gathering instead of trusting those new-fangled stores to provide food. He's probably also screaming PPP into his phone line to post comments just so that he can say how much better he is than you.
Kids don't learn Latin anymore but they are learning to 'use' computers at the age of 11, get real.
Quite the contrary, at least where I'm from Latin is a very popular language to learn. Also, having gone to several national and state Latin competitions, I can vouch that there are several thousand kids in grades 6-12 that represent almost every US state. Although I realize that, "several thousand" kids is quite a small minority of kids in grade school.
But, back to the topic: I'd have to agree with another comment that it seems to be the teachers who don't implement the technology well enough, not the technology itself that causes problems.
Is it just me or does anyone else find Taco's combination of porn and an 11 year old disturbing?
Posted by CmdrTaco on Monday July 07, @12:12PM
from the way-more-porn-for-starters dept.
"Keep at least 3-6 full bottles of hard alcohol on hand, a 2 week resignation notice,..." - Poetmatt
> "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
lol nice catch ;) I am a product of teachers who thought 'who cares about spelling, thats what spell checkers are for' So I am a victim here /sarc
"Ahh! Arrogance and stupidity in the same package, how efficient of you!" --Londo Molari
http://www.usatoday.com/tech/news/2004-12-06-complicating-things_x.htm
We must be alert to the danger that public policy could become captive to a scientific-technological elite. - Eisenhower
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.
Tom Swiss | the infamous tms | my blog
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.
If you want to correct someone, first know the right answer. The verb in question is "pore", not poor, or pour.
No, English is the language of western science, followed by German(at least historically). They're the languages the vast majority of papers are published in. Latin is mostly the language of scientific elitism, used to prevent the uninitiated from understanding specialist terms.
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.
In recent months, my children have given me a fresh perspective on games like these. My wife and I adopted two Ukrainian sister, 8 and 9, who are very bright but had not received much schooling before the came to America. They both love playing computer games, and so we thought they would love the math games their elementary school assigned them.
As time went by, they put up more and more resistance to the games and began asking for pencil-and-paper exercises. It seems the animated games over-stimulated them and caused anxiety. With a pencil and paper, they can take time to think about how to do problems without feeling that they need to throw out an answer before a timer goes off. As a result, they are thinking much more and guessing rarely if at all.
Nonetheless, computers do have a place in their math education. Every day, I run a python script I wrote that generates arithmetic work sheets, which have to be completed before the girls get their computer time.
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
A computer can't teach you to think critically, but neither can a pad of paper and a pencil. Both are just tools. Computers do not decrease the quality of learning. Finally, kids don't learn Latin anymore because it is a dead language. However, they should still be learning Latin roots which will help them decipher the meanings of many scientific words.
I don't know, because I haven't seen the software they use, but I'll bet the big stack of $1 bills in my wallet that it's all T/F and multiple choice.
And that's crap.
Such testing only tests the ability of a student to pass T/F or multiple choice tests. When you can solve a math problem when it's only you and the problem on the page, OK, then you understand what you've been taught.
If you don't know what I'm talking about, go read an old Princeton Review SAT or GRE book, they talk about it at some length.
We're training these kids not for reality, but to take tests, with the answers fed to them.
It's the intellectual equivalent of trying to teach mechanical skills with a erector-set simulator on a PC. There is a subtle disconnect between what we can learn virtually and what we can learn through real experience.
Just because you've played CSS, that doesn't mean you can be trusted with a rifle.
"Old man shouts at cloud."
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.
Can you be Even More Awesome?!
Following your logic, we should all be hunting and gathering instead of shopping for food because now we can't feed ourselves, either.
Not at all. I'm not sure that we should go back to hunting and gathering, but, I am sure that more knowledge of basic survival and emergency preparedness procedures would be of benefit to society. There are far too many people who'd be completely lost if there was even a short interruption in services such as electricity or cell phone service.
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.
There's a useful quote here: "There are two types of fools. One says, 'This is old, and therefore good.' The other says, 'This is new and therefore better.'" While I'm certainly not advocating a wholesale abandonment of modern methods and technology, I do think there's something to be said for teaching kids to think critically before letting them loose in the ocean of raw data that is the Internet. As anyone who's read blogs or looked at Wikipedia for a significant amount of time knows, there's a lot of information out there that's biased, misquoted, or just flat out wrong. I think its a mistake to think that greater access to this information will solve the issue of people not thinking critically about this information.
We all know what to do, but we don't know how to get re-elected once we have done it
Kids don't learn Latin anymore but
Kids don't learn COBOL anymore, either (or, for my generation, Pascal). Latin is great for cunning linguists and those interested in Etymology, but schools these days have enough trouble passing on the PRACTICAL things to students that focusing on marketable job skills is more important than reading the Illiad in it's original format.
My college experience was modeled after your thinking. After I graduated I spent some time working by myself on a project for my employer at the time. I had learned all the basic data structures but had not been informed there were standard, tried and true data structures available. I wasted hundreds of man-hours and introduced countless errors just because I didn't know standard, free, industry-accepted tools existed to do what I needed. A tool is not an excuse to gloss over the critical thinking needed to reach the conclusion, but denying your students the practical tools to solve problems is a fast track to employment uselessness compared to people who can use the tools to do it both fast and correct.
I wouldn't go that far but I do believe that certain experiences make us better people. There are some basics to life that shouldn't be skipped. If you eat, it's important to understand that something had to die so that you could live. If you're a vegetarian, growing some of your own food can give you an appreciation of the cycle of things, how dung and dirt and seeds can become the sustenance for your body. If you eat meat, actually taking a life is an educational moment like almost no other, a time when you discover, for real, not via a computer simulation but with blood on your hands, that other beings must die so that we can live.
There's individual, spiritual power and wisdom in knowing those things, really *knowing* them by experience rather than making do with the pale reflection of reality provided by a book or a digital simulation.
This is a big subject, though, and I can't do it justice in a short comment. I strongly recommend "Meditations on Hunting" by José Ortega y Gasset.
no.
From the irony dept. The phrase you are looking for is not "poor over", nor is it "pour over" but in fact "pore over".
PORE -verb (used without object), pored, poring.
1. to read or study with steady attention or application: a scholar poring over a rare old manuscript.
2. to gaze earnestly or steadily: to pore over a painting.
3. to meditate or ponder intently (usually fol. by over, on, or upon): He pored over the strange events of the preceding evening.
[Origin: 1250-1300; ME pouren ]
None of them can see the clouds; The polished wings don't care.
As I said, I have no issues with kids in HS using those tools, just grade school..
"Ahh! Arrogance and stupidity in the same package, how efficient of you!" --Londo Molari
Overhead projectors were touted as technology that would revolutionize the classroom.
And filmstrips, too. (beep)
I know I'm a better person for it and kids will get just as much out of computers in the classroom.
And how much are the used? Most about once or twice a year - does this really warrant £800 per classroom (we have 30 or 40) or taxpayers money.
The school also recently bought £800 laptops for all the teachers - decent core 2 duos with 2GB ram, large HDD, 17" screen - the real deal. What does a teacher do with 2.6GHz of dual core to-of-the range processing power? Online registers and MS Word - both highly resource intensive.
So yes, technology does change classrooms - by taking money from important areas of the curriculum and giving the teachers gaming class laptops which they can take home and use as they like.
In my calculus courses, we always started out with an "intuitive" explanation, which made perfect sense, and then dealt with deltas and epsilons. Most of the long-windedness was in the textbook, and the teacher was quite good at explaining things in plain English.
Why should learning be fun? So that kids want to learn?
Math is a particularly interesting instance of this, as it is the area I am currently studying. I see two parts to learning mathematics (this may be generalized to learning anything): 1) understanding and, 2) execution. The understanding part is where a good teacher (and perhaps teaching aids, such as software) makes the difference. This is what gives a student the mental framework to be able to do the math. I think that the execution, is incredibly specific to the student. Some students need to work hundreds of problems to be capable to solve that class of problem. Others might not need to work through any problems! Still others find it easier to audibly talk themselves through the solving process. So even if computers (software, really) can impact the first part of the process, the second part is still required. And guess what? It's the second part that requires the most important realization and skill: learning isn't fun nor easy, and it requires a lot of hard work.
-- Humans, because the hardware IS the software.
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.
From the article: "Why would we ever buy a book when we can buy a computer? Textbooks are often obsolete before they are even printed"
Nothing holds its value like a computer. That's why I threw out my obsolete copy of Strunk and White and got out my Babbage difference engine.
I suggest you pour through a dictionary to figure out the difference between the verb pour and the adjective poor.
That would just make the ink run. Do you perhaps mean he should pore through a dictionary to learn the difference between the verbs pore and pour? ;)
"16MB (fuck off, MiB fascists)" - The Mighty Buzzard
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.
Growing up, my school system always had Apple computers. I remember hearing that that was the case in most school district, thanks to a subsidy program offered by Apple. For 15 years, that didn't seem to win Apple much market share, but it seems to have experienced a boom now that my generation (late 20s) has gone off to college and gained disposable income. Unfortunately for Apple, that growth hasn't expanded as quickly into businesses (has it?). However, the program seems as healthy as ever. With the next generation (as in 20 year periods) starting off on Macs, is it possible that Apple's long term strategy will pay off on the next level once I'm sending my kids off to college?
Memorizing multiplication table was always outdated. On the other hand, understanding how numbers and arithmetic operations work and what can you do with them is a skill that cannot be replaced by a calculator or computer. Gaining this understanding can, IMHO, be aided by a use of calculator or computer, however that is not what seems to be happening at most of our schools.
AccountKiller
Because Google would never have allowed you to butcher "pore through" like that.
'a';DROP TABLE users; SELECT * FROM DATA WHERE name LIKE '%'... if you're reading this, it didn't work.
Any school which hands me an Apple computer is not one I would want to go to.
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.
Ever since computers have been introduced to schools, they've simply provided an evolution to exercises and rote learning. The transformative, revolutionary potential of the use of computers in education - getting students to think, explore, discover, realize, and synthesize - has not been widely developed. Unfortunately, this is largely due to how we educate, not how we use computers.
Won't that ruin their teeth?
No, English is the language of western science, followed by German(at least historically).
Really? I agree that English is the current lingua franca of science, but I'd argue that the previous common tongue was French, not German.
We all know what to do, but we don't know how to get re-elected once we have done it
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
Pencils don't teach you to think critically, they also stifle real research skills (not to mention causing you to write sentence fragments).
You said it later: a computer is a tool, just like any other. Its a really useful one though, and very prevalent in our civilization. Kids learn to use pencils at age four, why not computers?
At least you can write full sentences and spell correctly, unlike the Latin-knowing original poster.
Thanks you. Very well said.
English is the language of global science. Certain sciences just borrow words (and letters) from Latin (or make up Latin sounding words) either to adhere to tradition or because they want unique words.
I'm a working scientist and nobody has ever asked me to have a technical conversation or give a presentation in Latin.
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.
Wrong. The word "computer" from Merriam-Webster online:
one that computes; specifically : a programmable usually electronic device that can store, retrieve, and process data
And "compute":
Etymology: Latin computare
Latin is the root of many modern words. A major argument for studying it is to understand words' roots, so that you can figure out their meanings without resorting to Google/Wikipedia/etc. I think some amount larger than .001% of them take the SAT, for example. And AFAIK they still aren't allowed to bring a computer.
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. Try saying that to a historian or an Archaeologist. There is actually a lot of value in learning how things were done "the old way". Take photography for example. I learned Photoshop. Then I took a darkroom class. I understand concepts in Photoshop better because of my experience with earlier technology. Similar, just because I can program in Java, C++, or any other modern language, it doesn't mean that knowing assembler or hex are useless. I program better because I am familiar with them. Little value in the old ways? That's a very nearsighted view.
Back in my day, we were lucky to get one free laptop a week. But one each day? These 650 kids sure have it easy.
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 !
I concur. Why, of all things, does it seem you are egregiously disturbed about children not erudite Latin?
After all, I took Latin and my own English is no better than the parent's.
Then how come the vowel in the first syllable is pronounced different from the vowel in the second one, yet they're spelled with the same letter?
Are you adequate?
It's funny that the majority of the highly rated comments are just the same comments posted every Slashdot article about technology in the classroom: "Students rely entirely on computers these days, get off my lawn!" and "Back in my day we had to program an OS in assembly -- for CS101!"
After hunting around the webs for the actual product referenced in TFA ("FASTT Math"), I found it's actually designed to help kids memorize their multiplication, division, addition, and subtraction tables. The company's infomercial is here:
http://www.tomsnyder.com/fasttmath/tour.html
So yes, they're using technology to teach math, but no, they're not making kids more dependent on calculators or computers for doing math.
I suppose it is pointless to explain, but anyone who thinks calculation is what mathematics is about does not have any understanding of the subject. Often it is necessary to be able to perform or follow a calculation, but it is nowhere near the essence of the subject. For example the proof of Fermat's Last Theorem was great mathematics but it was not related in any way with some super duper calculator. The Riemann hypothesis is an area of great mathematical ferment with not a calculator in sight. Long division never has been a summit of mathematics. It is repeated guessing and correction just like extracting a square root. The quadratic formula (i.e. completion of the square) comes up so often it is useful to have it memorized but it is Galois Theory that matters (mathematically speaking), not a calculator that has the quadratic formula built in. Calculation relative to mathematics could be thought of as roughly analogous to spelling relative to literature. Mathematics is a creative intellectual pursuit, not calculation.
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.
The history is full of "new ways" which used to be "all that will ever be used".
The reality is that a given technology is adopted only when it is better.
And as far as doing mathematics is concerned, there's no evidence at all that using software fares better than pen and paper.
Forgive me, I seem to have misplaced a word ("in") between "erudite" and "Latin".
And you had to learn Latin to understand and know how to apply those prefixes and suffixes right? Those are borrowed from Latin and were borrowed a long time ago; they are now a part of modern English, no Latin required.
"I use a Mac because I'm just better than you are."
I highly recommend the kitten cannon!
Or, for those that want a 'you can try this at home version:the edutaining squirrel catapult!
Disclaimer: I do not acknowledge the concept of 'politically correct'.
Down With Slashdot BETA!!! I've been around the corner and seen the oliphant; you can only abuse me from your perspecti
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.
You claim that you have not memorized the multiplication tables. Can you tell me what 8 times 7 is without the use of a calculator or counting on your fingers? If you can, you have memorized the multiplication table.
Rhapsody in Numbers
True. However, after memorizing "the tables", how much space is there to make connections?
Plenty. Memory space is cheap, and acting as if it was otherwise impoverishes learning.
We all know what to do, but we don't know how to get re-elected once we have done it
Back in the 90's I was on a team that set up the first computer lab in our local elementary school. The lab had rudimentary equipment by today's standards, but it could run educational games and word processors, for instance.
When the lab was complete, I suggested that we study the available software and come up with lessons/modules that teachers could use on these PCs. The parents and teachers looked at me like I was crazy. They were not interested in figuring out how to use the PCs for teaching. They were only interested in what new technology they should bring into the lab for the next project.
I quit the team, having learned that people were more interested in procuring and showing off their educational technology than figuring out how it could be used effectively.
This still holds true today.
"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"
I think learning Latin can make you a better person. I think by learning Latin you not only develop your own mind just by learning the language, which is a very demanding one, you also see how the influential writers in this language developed the universe of thought that is common to us all, by reading their works; you not just getting a clearer picture of their ideas by reading it in the original, you are also seeing how the language itself influenced them. I think you learn significant things by reading poets like Ovid or Lucretius. I don't think you need to know Latin to come to the same knowledge (there are translations, and different writers can you teach you the same things), but a framework in which you learn Latin and read some of these famous works themselves I think is a good framework for personal development.
8 times 7 is a particularly tricky one. I would either do 70 - 14 (the 10 tables and 2 tables I have mostly memorized), or 40 + 16 (the 5 tables are rather easy, too, you first divide by 2 and then multiply by 10). So it seems that 8 times 7 is 56, but no, I am not able to recall that without doing one of the above (or some similar such) calculations.
AccountKiller
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.
"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"
Through high school, I really struggled with Calculus. When my teacher explained something to the class, I did great. However, when I was assigned a lesson from the book (which also had references to help material on the publisher's web site) I would find that I just couldn't understand what was going on until the following day when my teacher explained it. So I went to my grandfather (electrical engineer and former math teacher) for help. He gave me his old college calculus text*, which was about the size of a standard hard drive, compared to my math book which barely fit in my backpack. After using it, I found that I could understand the older book much better then the newer one. Why? I believe the reason is 'fluff.' Here is an approximate example because I don't have ether books anymore:
Old book: A limit can be used to find y when x1 approaches x2 at Y. This is useful for finding y when there is a hole in the graph. [Example problem or two, closely followed by 20 problems to be assigned]
New book: Do you remember the limits we learned in chapter 3.2? Did you know that they could be used to "solve" holes in a graph? [show example graph, but don't explain how to solve it] What we can do is take the limit of an equation and find the missing hole. Remember that with a limit you are not finding a true answer but a close approximation for it. [big picture of the approximation symbol] For example.........[and so on until the next page].......This is how we are lead to theorem 3.6: "A limit can be used to find y when x1 approaches x2 at Y." [two example problems followed by 100 problems to do on your own]
There was also a difference in the problems assigned too. The 20 from the old book were more in-depth and challenging, truly testing how well you had learned whereas the newer book's 100 problems were extremely repetitive and almost never challenging.
When I began to do much better on my assignments, my teacher asked me why. I showed him my grandfather's book, and he smiled and showed me his own copy of it. It turns out that he created his lessons from the old book because he felt that the teacher's edition of the new one was "worthless."
*This was so old that I found in it a love letter from my grandmother to my grandfather when they were still dating.
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
Memorizing multiplication table was always outdated.
Seriously? Are you saying that never in your life have you needed to know off the top of your head at 6 X 7 = 42? Or would you have used your knowledge of numbers and arithmetic operations to do "6 + 6 + 6 + 6 + 6 + 6 + 6"?
What's outdated is not memorizing times tables, but learning the algorithms for long multiplication and long division. Speed is no longer of value when performing arithmetic by hand, because you can just use a calculator, and all these algorithms do is teach children that math is a horrible process of rote memorization that they don't understand. Let's teach children to multiply conceptually, by breaking a large problem into smaller problems. 23*47 = 23*(40 + 7) = 23*40 + 23*7. We have two easier problems now. Let's do 23*7. It's equal to (20 + 3)*7 = 20*7 + 3*7. Again we have easier problems. This approach takes longer, but children can actually UNDERSTAND it and ENJOY it, and learn to think like mathematicians rather than memorizing finger motions.
Why should we expect more tech in the classroom to change much of anything, beyond students' comfortability in using such? The classroom itself and the larger schooling paradigm in which it sits remain unchanged from a hundred years ago when they were producing industrial factory workers.
We're still going to get students who struggle to think for themselves because they've been trained to wait for teacher to tell them what to do, and how to feel about the quality of work they did; Grads who feel powerless and fatalistic because they've watched an inexorable institution control them for twelve years with little to no input. It also shouldn't be a surprise when these kids don't care much for civil liberties or privacy, when they grew up inside buildings that don't afford them these rights. They need permission to use the bathroom, for fuck's sake.
When we see multiple schooling paradigms become widespread, Montessori schools etc, and compete for students with poorly run government schools, then maybe we'll see some change.
The distinction that's relevant in the case of the intransitive verbs is unaccusative vs. unergative. (IIRC, it is often argued that the use of être in reflexives is related to this.)
Are you adequate?
Didja have a computer in school?
poor = no money, pore = careful study; microscopic hole, pour = to flow freelyI am not talking about space in terms of memory. I meant space in perhaps more abstract form. Perhaps better way to put is this: After memorizing the tables, you have this pile of pretty much useless facts, sort of jumbled together, and you have to go back and sort through them to discover any connection. If you instead memorize only some basic facts and several basic rules, you will have something that I would liken to a clean table with just few objects on it, with plenty of space to draw connections.
AccountKiller
Issac wrote this short story about a technological culture divided into two classes: those who could use computers and those who could make computers. There's a nifty plot twist in the story which I wont go into. But this story made a big impression on me as a young student, and I vowed to be a member of the latter class of "makers".
You is masterful student of language of english. Can I be teach from you-sensei?
I know that half of 7 is 3 and a half, that's easy, because half of 6 is three. Multiplying by 10 is easy, very little memorization required there. That will give me 35 + 7, and I do have sort of memorized that 5 + 7 is 12, I am pretty sure about it because 5+5 is 10, and then there is 2 more.
I will probably remember 6x7=42 for several days now, but I guarantee you that after a short while I will forget it and have to derive it again.
AccountKiller
Bullshit.
Used to know an old guy, a house carpenter par excellence - he could build a house from the ground up with nothing more than a simple sketch of a floor plan. But he couldn't build furniture worth a damm because that isn't what he did.
His brother the cabinet maker on the other hand...
Indeed! In fact, I was able to completely ignore the fact that while you can spell, you are apparently incapable of choosing your words correctly. "poor though" Both words are spelled correctly, though they are used in the incorrect context. Perhaps you meant,"pour through".
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.
Laptops are an essential part of the learning experience for students. The essentials they have learned in my district include sending e-mail of their classmates in various states of undress. The administration continues to think that laptops are the greatest things since toast. The students disagree. Never mind the high cost -- both direct outlays, additional staff, and training time.
So true. Why, kids today don't even know the difference between "poor" and "pore."
Because those 'crummy old textbooks' really are crummy and old after a year or two of being tossed in lockers, hauled back and forth in a backpack, doodled and annotated in, etc., etc.
I suspect if schools went back to the old policy of charging for damaged textbooks kids would learn to treat 'em better and schools wouldn't have to replace them every couple of years.
I'm not at all convinced giving middle-school students their own laptops does much good. Giving them to younger students seems less useful.
Look into the Maine Laptop Initiative, http://www.mainelearns.org/, for the sugar-coated version of how wonderful it has been.
A slightly irreverent flavor of our Governor's view of it is at http://www.andycarvin.com/archives/2006/06/angus_king_a_brief_h.html.
Then again, some of the less-considered issues include student damage, as discussed at http://www.raymondmaine.org/jsms/Tech/Rules_Consequences.pdf, for example...
And for a fair list of issues that can cause such a program to fail or succeed less than hoped for, look at http://www.ncsu.edu/meridian/win2008/tenlessons/02.htm and read carefully. Much of this is actually common sense, which explains how it is overlooked so easily. Note also many of the recommendations here cost more money, so they easily get lost in the budget hearings, and outcomes suffer because of it.
You won't find much in the way of criticism of the MLTI. While I wanted to offer an alternative to using iBooks, this was never possible - the MLTI is a joint venture with Apple, the State of Maine, University of Maine, and even IBM (it leveraged the MSLN network). But serious criticism of the MLTI is discouraged, and is usually found in school system meeting minutes, the rare disagruntled blog, and private comments by teachers...
And I'm not sure that there is a lot of genuine data on success, though I am pointed to many sites that claim good to great results. Mostly by adminstrators so proude that they survived the NCLB testing and reporting.
I'm not convinced that laptops do that much for studnets, if you compare the effort and integration with making the same effort with more conventional tools, or even a part-time lab.
Of course, this all may be colored by my age, remembering school in the late 60s - early 70s, and my no longer being an Apple outlet. Hey, I'm human.
deleting the extra space after periods so i can stay relevant, yeah.
Indeed, you have found a subset of the multiplication table which is sufficient for you: as much as you want to remember, and the calculations aren't slowed down too much.
Just because many would atrophy down to the same subset as you does not mean that drilling the tables was not useful to them or yourself. It merely means that once you made the connections you needed, you allowed the less useful data to fade away.
If someone were to learn your *exact* method, they'd have to memorize not only your abbreviated tables, but also your ad-hoc ruleset for mixing the tables to get the rest.
It might be easier to learn than memorizing 100 (or 144 or whatever) numbers, but that ignores the fact that learning to memorize itself is a useful tool.
Can you be Even More Awesome?!
if you dont know how something works, then troubleshooting becomes a series of endless guesses until you find the correct "solution".
this goes for mechanical processes as well as computer processes.
I always thought it was odd that my dad (and his generation - baby boomers) had Latin as a required course in public high school.
NOBODY I know, sans the medical field, has had Latin classes, except by choice (and usually in college).
How many High Schools even teach Latin anymore? I just checked...my old HS doesn't.
I have had the opportunity to teach at the college level (physics) from both the traditional blackboard approach and from the so called modern approach (so called by its fans), with powerpoints, concept tutorials session taught from a special book by a TA, yada yada yada... The students with the "modern approach" do better on standardized tests, woohoo, which means they can use 7th grade algebra and trivial calculus to solve 3 minute problems. The standardized tests don't test genuine problem solving skills, but you can bet my finals do! The cold hard fact is that most of the people in college today belong in the class I call infrastructure, and my opinion is that all that a computer learning class, or standardized tests (a la no child left behind) is develop the infrastructure people; it does not and cannot develop the more serious problem solving skills of your innovators, and in fact would probably be boring as hell and piss the innovators off (I know I would have rapidly become dissatisfied with computer learning and standardized tests back in the day). This is training for the service desk or technician level jobs in the tech world, which unfortunately is probably all the state legislatures understand the need for.
But my point is, as far as I remember, I did not spend any significant time drilling multiplication facts at school. There was some small amount of drilling, but we spent far more time actually exploring numbers and discovering ways how to avoid drilling. Which is, at least at that level, what math is all about.
I definitely do not suggest that everybody learns my exact method of multiplication. I believe that the best way to learn multiplication is, with some guidance and help, figuring out your own way how to do it.
On the other hand, I agree that learning to memorize is a useful tool, which I have never really master. I am notoriously bad at remembering names, phone numbers, addresses etc. That's one thing I have never learned. Not that I was not really required to. In many subjects at school we were supposed to memorize whole bunch of stuff. Most of those subjects I barely passed. Fortunately, math was not one of them.
AccountKiller
I'm surprised there hasn't been more discussion on this key sentence from the article:
"There is, however, one concession to the past: a library stocked with novels."
Why is it that I can go to the library and check out physical copies of books for free, but I can't read them digitally over the internet for free? And yes, before everyone starts, I'm aware of the Gutenberg Project but basically these are all old works.
The library, with all it's overhead for electricity, janitorial staff, and library staff could be reduced to a closet with a server in it. And one such "library" could serve dozens or even hundreds of schools.
Even textbooks can be checked out from the library. Imagine if digital copies were available - no more buying text books.
This, of course, is exactly what the content producers don't want to happen.
A work that expires before its copyright never enters the public domain and thus enjoys eternal copyright protection.
I haven't memorized the multiplication tables either. But 7*8 is easy, since 8 is a power of 2. Hence, 7 * 2 * 2 * 2. Simple as that.
Schools are a large enough consumer of books (enormous amounts of resources are spent by the publishers to make sure they meet schools' demands) that they could easily pressure their publishers to supply copies of their already-being-used edition, if they were so inclined.
Any sufficiently simple magic can be passed off as mere advanced technology.
But that's all the algorithm does. 23*47 is the same as 3*7+3*40+20*7+20*40. Now we have 4 super-easy problems. Maybe you learned a different algorithm.
Plus, if I have my times tables memorized, then all of those 4 problems become much easier.
I cried real tears when Li Mu Bai died.
Looks to me like "technology reshaping classrooms" hasn't progressed much past Number Munchers.
return EXIT_SUCCESS;
After memorizing the tables, you have this pile of pretty much useless facts, sort of jumbled together...
Except that no one learns like that. Learning is not "just like" throwing objects into a box. Study after study has shown that humans learn by taking facts and drawing connections between those facts and other facts that they already know. In this sense, the more facts you have, the more connections you're able to make.
If you instead memorize only some basic facts and several basic rules, you will have something that I would liken to a clean table with just few objects on it, with plenty of space to draw connections.
And you miss all of the connections that could be created by having a proper library of facts to draw from.
This view of teaching (simple facts + basic principles) is very attractive as a theoretical model, but there's very little data to support any view of that being the way people actually learn.
We all know what to do, but we don't know how to get re-elected once we have done it
I concur. I'm a techy, I'm a geek, but I'm also an educator and my experience (and the experience of others) says that computers are not needed in the classroom.
I would much rather read poor penmanship and misspellings than allow students the opportunity to cheat by using a computer or the internet as a crutch.
Would we allow students to use calculators in elementary school?
Incorrect. One must learn how to do things the original way or they will be doomed to fall when they do not have their crutch.
Also, your parallel is flawed. It's not that we should be hunting and gathering, but we should be taught that drinking still water is dangerous and what poison ivy looked like.
Your 'conceptual' approach appears to be an exact replication of the long multiplication algorithm. In fact I'm sure that is pretty much how long multiplication was explained to me in infants school, back in the 60s.
I think it depends on how good the teacher is, mine made it clear exactly why we were doing what we were doing.
I don't think that rote learning of tables aids mathematical understanding to any great degree, BUT it is still a worthwhile thing to do. I mean, 100 numbers (or 144 or whatever); at age 7 or 8 that stuff sticks in a week or so and stays there. Well worth the investment in time just for things like shopping bills, playing darts, settling bets, buying timber and any number of other day to day tasks.
[ ]Half Empty [ ]Half Full [x]Twice as big as it needs to be
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),
You could say that about many other fields as well, though, most notably math. Beyond basic arithmetic and decimals and maybe, maybe a bit of basic geometry, most people have absolutely no use for it. At 28 I can honestly say I've never had to factor a quadratic equation, calculate the volume of a sphere, or solve a linear equation outside of a classroom setting. Ever. I'd wager this holds true for the vast majority of the populace.
What's more, since I haven't had to use this stuff in ten years, I am quite incapable of doing it now, which makes me wonder what point was served by all the forced marches through years and years of class.
You only need mathematics more advanced than this stuff if you're planning on going into a field which requires it, like architecture or physics or engineering. For everyone who isn't, sitting through math classes beyond age 13 is a waste of time and resources, teaching children how to memorize things they don't really understand, have no use for, and are guaranteed to forget shortly after they graduate. Unless you can come up with a reason anything beyond rudiumentary algebra is particularly useful for people who aren't going into technical fields, let's drop that as well.
mirrorshades radio -- darkwave, industrial, futurepop, ebm.
No no, I said that memorizing times tables is NOT outdated. And yes, even though what I described is in fact all the algorithm does, it is easier to understand (and takes longer to execute) when presented in this more conceptual way. The fact is that most students don't understand why the long multiplication algorithm works, or why they are putting extra zeroes in certain places. It is just a memorized process to them. And that is the kind of thing that makes them hate math.
The school district I used to work for started doing this at one school. Crapton of apple laptops, one for each student. All of the elementary schools were primarily Mac. Once you hit middle school, they started mixing it up a bit. All the high schools are primarily pc (Dells) with a few Macs thrown in. The theory was they would carry that laptop from the 6th grade to graduation. The reality was Apple dropped the ball, so now the laptops stay with the school. It basically just put a crap load more work on the computer techs. We gained around a thousand new computers, but no more help. The math programs seemed to me, to be helping. The kids really did want to play them, which I though wouldn't happen. Anything to get kids interested in math helps. I sucked at math in school, never made it past algebra. My brain just isn't wired to add a+3. Give me something physically in the real world and I can figure it out though.
I don't think that anyone was necessarily suggesting that one must spend time drilling in order to memorize. For me, that was the easiest way to memorize things, but others may have other methods. The point is that some amount of memorization is necessary. You have to have information before you can start drawing connections between the individual pieces of information. At some level, that must be memorized.
Rhapsody in Numbers
Or as point out above maybe pore through as pour is still the wrong verb, but thanks for playing..
You're converting a simple multiplication problem into an algebra problem, and a decently complex one if you were to write it out. While this may be fine for adults with a good grasp of algebra and equation manipulation, we're talking about children. I personally learned algebra in about 7th grade, and the times tables in 3rd. While memorization isn't the optimal solution for all cases, it's definitely a good and necessary stepping stone towards the best way.
I think you learn significant things by reading poets like Ovid or Lucretius.
Of course, to get the most out of these poets, you need to read them in the original Klingon....
(Sorry, couldn't resist).
A lot of important scientific works were also written in Latin, albeit a debased and bastardised form. I only did a year of Latin in school, so I can't say if there is a richer experience in reading Newton's 'Principia' in Latin as opposed to Motte's near-contemporary translation. 'Axiomata, sive leges motus' still sounds cool, though.
[ ]Half Empty [ ]Half Full [x]Twice as big as it needs to be
Nobody replied to this question yet? I say the "$39.99" per square yard carpet is more expensive than the $1.95 per square foot carpet. My liberal public school education is paying off :)
Not the best analogy.
Framing is not cabinetry or home finish work.
Newer construction methods and tools have have aided both sets of skills. Regardless, house framing can be accomplished with a reduced set of skills, but the latter requires much more experience, knowledge and patience.
Not that I am necessarily disagreeing with your point, but I do believe that everyone should at least know how to gather their own food, whether that means hunting or foraging. One day those little conveniences like cheap produce and precut, skinless/boneless chicken might not be readily available.
"He who can destroy a thing, controls a thing." --Paul Atreides, Dune
The difference is, I made my mistake on purpose. To see if you were paying attention.
So you're saying they should be TAUGHT the algorithm instead of just be required to memorize the algorithm. Assuming that the definition of teach includes understanding. I'd agree with that.
I cried real tears when Li Mu Bai died.
And there I was thinking it was supposed to be "pore over". The ambiguity of poor English...
I think some amount larger than .001% of them take the SAT, for example.
And yet interestingly enough most people taking the SAT aren't fluent in Latin and seem to do just fine on it.
Most people will never need to do long division with symbols in their entire life. Heck, I'm a geek with a real interest in math, and I've still never found the ability to factor a polynomial useful even once in real life. Perhaps teaching of the manual method should be moved to where it will be immediatly helpful to math students, and therefore of some interest to them, instead of being taught in elementary school?
Socialism: a lie told by totalitarians and believed by fools.
Most people will never have any practical use for mathematics anytime in their life, but they'd find the ability to do calculations useful quite regularly. Which makes sense to teach in elementary school?
At some point we have to teach students "abstract thought and logic", and certainly math is one approach to this, but most non-geeks are going to be far more receptive to learning this skill in a good English class than a math class.
Socialism: a lie told by totalitarians and believed by fools.
But "simple" multiplication is a decently complex algebra problem. And when I was in 3rd grade, what I described is how we have learned multiplication. We simply studied numbers and organized things in rectangular patterns, we discovered and subsequently memorized some rules, and eventually learned how to multiply. Some of us, those that were better at memorizing rather than derivation, memorized most of the facts, others learned ways similar to the way I described. Later, in 6th and 7th grade, we just formalized all the intuitive ideas about properties of numbers and operations we actually discovered and learned in the second and third grade.
AccountKiller
I stopped reading here.
Except that no one learns like that. Learning is not "just like" throwing objects into a box. Study after study has shown that humans learn by taking facts and drawing connections between those facts and other facts that they already know. In this sense, the more facts you have, the more connections you're able to make.
There are also number of studies that seem to suggest that people learn better by discovering things rather than being told facts to memorize. Also, there are more useful interesting facts and less useful and interesting facts. As far as multiplication goes, the facts that 3x5=15 is pretty useless by itself. The fact that you can arrange 15 pieces in a rectangle with 3 rows, and if you take 1 row away you will have 10 pieces left, is in my experience and opinion much more interesting and useful (and I don't mean useful for "practical" applications, I mean useful for drawing connections).
And you miss all of the connections that could be created by having a proper library of facts to draw from.
This view of teaching (simple facts + basic principles) is very attractive as a theoretical model, but there's very little data to support any view of that being the way people actually learn.
Having a larger library of facts is not necessarily helpful. I highly doubt that memorizing all known zeros of the zeta function will take you any closer to proving the Riemann hypothesis. I may be wrong, and you may discover a weird pattern that everybody missed so far, but I believe that general consensus is that to learn about the Zeta function, you need to learn much smaller number of much simpler, but more essential facts.
AccountKiller
If I wanted some fine furniture making, I would want a cabinet maker and not a carpenter. Totally different jobs.
Think about it: A superextra cool desktop enviroment, say compiz fusion, is deffinietelly more advanced than the plain old console, it has a lot of eyecandies and cool efect 3D efects and you can play forever with the wiggly windows. But if you are supposed to do something on the server you will be faster with the console than clicking thru windows with the special effects distracting you. Basicaly it gives you a method to solve the problem, a method which maybe be fast, and that everyone ca learn but it is very limited... Let's say another example, making fire: You need to spend weeks in order to learn how make fire out in the wild using just what you can find, and it works almost always. Than you can spend a few minutes to learn how to make fire with a lighter, hey it's cool and easy and fast and every last dummy can learn it...And only works when you have a lighter...And the lighter ain't damaged...And for as long as you have lighterfuel...And so on. Basically if you know how to make fire with two sticks you can use a lighter to do it faster and return to the old methods when you have to. When you only know how to use a lighter you can't do it any other way, probably you can't do it when given matches, magnesium block or a looking glass either. The technology you've been teached to depend on is a limit.
You are probably referring to Feynman's essay about his experience in participating in a school book review committee.
http://www.textbookleague.org/103feyn.htm
I learned Latin, you insensitive clod!
How does he know 6 + 6 = 12 without a calculator?
He'd have to at least memorize by ROTE learning (there's that dreaded word again) that 6 x 10 is 60. Ok, maybe not memorize since you can simply add a 0 to 6. But how does he figure out what 60 - 6 - 6 - 6 is without memorizing some subtraction tables?
Oh I see, we do need some level of ROTE learning, but we must not be permitted to memorize a simple multiplication table so that we can be forced to go through the exercise of new math even if it requires a calculator. I'm sure this MIGHT be useful for some of the smarter types out there who are in love with numbers, but it scares the living daylights out of normal people and they end up going through life not knowing basic multiplication and hating/fearing math.
You even got the right answer. Congratulations. :-)
($1.95/sq. ft. = $17.55/sq. yd.)
"True. However, after memorizing "the tables", how much space is there to make connections?"
Exactly how big you think a human mind is? You think memorizing multiplication tables somehow prevents someone from eventually becoming a good mathematician?
You're effectively advocating the use of higher-level algebra to derive a simple 8 x 7 problem. This might have positive effects for some elite math types though memorizing more tables is more harmful, but what is undeniable is that the methods you advocate is disastrous for the masses who end up hating/fearing math.
"Why poor though references"
You talk the talk, but I can see you are relying on the spell checker yourself.
"in order to be a tool the user must have some basic skills"
So now you want the user to be a tool? I don't think that requires any skills.
I suspect if schools went back to the old policy of charging for damaged textbooks kids would learn to treat 'em better and schools wouldn't have to replace them every couple of years.
Also, have the teachers stop requiring the kids to take the textbook to class everyday (unless they really do need the textbook everyday, like a math class). Not only would it reduce the wear and tear on the books, it will also help save the kids' backs.
"You're effectively advocating the use of higher-level algebra to derive a simple 8 x 7 problem. This might have positive effects for some elite math types though memorizing more tables is more harmful"
Should have read
"You're effectively advocating the use of higher-level algebra to derive a simple 8 x 7 problem. This might have positive effects for some elite math types though I DOUBT memorizing more tables will prevent those elite students from achieving higher learning. But what you advocate is undeniably disastrous for the masses who end up hating/fearing math."
Why? Because most of the technology in the classroom are Ipods or similar devices. As far as computers go, they are more of a distraction than aid to teaching.
Are you kidding? Mathematical multiplication tables have at most 100 items to memorize. Your mind is able to memorize a lot more than that.
Exactly how big you think a human mind is?
As I have already explained in a reply to another post, I was not talking about memory capacity here.
You think memorizing multiplication tables somehow prevents someone from eventually becoming a good mathematician?
It will obviously not prevent anybody from becoming a mathematician, however, it will not help either. In fact, it may give you a slight handicap, as it will give you a completely wrong idea about what math is.
You're effectively advocating the use of higher-level algebra to derive a simple 8 x 7 problem. This might have positive effects for some elite math types though memorizing more tables is more harmful, but what is undeniable is that the methods you advocate is disastrous for the masses who end up hating/fearing math.
Come on, do you really believe this is higher-level algebra? Sure, you can formulate it in terms of group and field axioms etc, but in fact all you need to use is commutative, associative and distributive properties of real numbers. I don't know if you ever had a chance to teach introductory algebra, but pretty much the only problem with teaching these "laws of real numbers", how the textbooks like to call them, is to explain the students why they should even bother with such an obvious stuff, and why should we give these simple and obvious properties such fancy names. As a matter of fact, I have yet to see an introductory algebra textbook that manages to explain this in a good way.
Do you really think that 3rd graders will have trouble realizing that if you organize bunch or rocks in 7 rows with 8 rocks in each, you get the same number of rocks as if you do a 5 by 8 rectangle and another 2 by 8 rectangle?
As for hating or fearing math, I know a number of people who hate or fear math exactly because it evokes in their mind an image of endless memorization of useless facts. The funny thing is that stuff like that has actually nothing to do with math. If I was required to memorize my multiplication facts in third grade, I would probably ended up hating math as well.
AccountKiller
It's hard to explain the difference between an adverb and an adjective
I don't think it's that hard to explain the difference between adjectives and adverbs. Adjectives modify or qualify an object, a noun, whereas an adverb can modify or qualify a verb, another adverb, or an adjective.
Falcon
Should there be a Law?
Anything that can be done with a couple button presses on a calculator isn't real math anyway. It's good to understand how division works, but when was the last time that you needed to solve a long division problem by hand? I remember spending months in 3rd grade doing the same damn math problems over and over again.
I loved British Lit in high school. I read some of my favorite books in that class, "Beowulf" and "A Tale of Two Cities" among them.
I got As in English up until 8th grade when they turned to literature. I got a great score on the English portion of the SAT, ACT, and GRE, even better than my math score. Yet I've gotten Cs or worse in every literature based class I've ever taken.
I did just as well in Lit as I did in composition, and I had more fun in Lit. In both American Lit and British Lit, which was an elective, we'd do different things. We'd memorize parts of a book, play, and then perform it. For one project we had to do in British Lit I baked and brought into class a cake in the image of one of the characters. Several others baked something as well so we ended up having a party during class.
Falcon
Should there be a Law?
Did spreadsheets make accountants less skillful?
The punchline to the joke I'm thinking about is, "What do you want it to be?".
But if you want fine furniture built...
That's called a cabinet maker or ebinistre, not carpenter.
Its true, that, when learning long division, all you do is "memorize the steps".
In fact, if you learn long division properly, there is very little memorization required. The algorithm follows very simple logic: You start with a large chunk of the dividend, ignoring all the digits at lower position to make it simpler, and see how many times can you fit the divisor in there. That will give you a partial quotient. Then you figure out how much of the dividend is covered by this partial quotient. You subtract that, as it is already covered, and repeat the process with the remainder. Nothing mysterious there.
AccountKiller
Following your logic, we should all be hunting and gathering instead of shopping for food because now we can't feed ourselves, either.
No, just being able to garden can help a lot though if you're a meat eater you should hunt or fish and clean what you get at least once. Admittedly I haven't fished or hunted in years but I grew up doing both. I used to fish freshwater and saltwater. And for hunting I've used bow and arrow, firearms, and built and set traps. Some people have called me mixed up because I love and wanted to be a scientist but at the same tyme I love the Society for Creative Anachronism.
Falcon
Should there be a Law?
"Higher algebra" wasn't what I meant. I meant the fact that it was algebra makes it higher level with respect to arithmetic. By forcing people to learn this way, the majority of American students end up learning neither methods because memorization was shunned and they weren't able to easily grasp algebra concepts at an early age. Maybe it wasn't hard for you and it wouldn't have bothered me personally, but it's clear that the majority of people can't handle this elitist method of teaching math.
This isn't just my opinion; it's a fact that so many of our public school students suck so badly that they get stuck in arithmetic their entire lives even through high school. That's what hurt me so badly early on because I had learned enough math in China in first and second grade to last me until the 6th grade in the USA. I was bored out of my mind through 5th grade and pretty much flunked every math class because I was so bored by it and completely ignored the teacher. I didn't start doing well until I got in to Algebra and Geometry and then started really excelling by the time I got to Calculus because it was so powerful and exciting to me. Heck, I couldn't put that Calculus book once I started but heck, according to you, memorizing the multiplication tables ruined me.
This "mindless" memorization is a one-time deal and I had my single-digit tables for addition, subtraction, and multiplication memorized by the time I was 6 such that I could do everything lightning fast. Once that memorization was out of the way, everything else was challenging word problems where memorization didn't help you other than the fact that you didn't need a calculator or some other tool to compute the single-digit results. I never suggested that everything or even the majority of education should be based on memorization. What I am suggesting is that memorization should be a tool used in conjunction with challenging the kids with problems that force them to think. Forcing the kids to derive single-digit multiplication at 6 and 7 years old is simply too much to handle and it's a bloody shame American kids are still wasting time learning basic arithmetic when they're in the 9th grade which other countries have mastered by the 3rd grade.
The bottom line is that new math (elitist math) only works for the elite and it doesn't work for the masses. While it might be conducive to future PhD candidates; it's highly ineffective for the majority of 6-7 year olds and it's totally ineffective at producing productive graduates who can get jobs. Watching 15 year old kids struggling with basic arithmetic new math is a national shame when most of those 15 year olds should be well on his way to pre-calculus courses. If you can't recognize the problem with this teaching method, you're out of touch with reality.
How does he know 6 + 6 = 12 without a calculator?
Simple. 5 + 5 = 10, I know that, I have two hands, 5 fingers on each, that gives me 10 fingers. If you don't know that you have a serious problem. 6+6 means you have add two more fingers.
He'd have to at least memorize by ROTE learning (there's that dreaded word again) that 6 x 10 is 60.
6x10 is 60 by a simple definition of the number 60. That's what 60 is. What in the heck is there to memorize?
Ok, maybe not memorize since you can simply add a 0 to 6. But how does he figure out what 60 - 6 - 6 - 6 is without memorizing some subtraction tables?
That's addition up to 10. 10 - 6 = 4, I can do that on my fingers.
Oh I see, we do need some level of ROTE learning, but we must not be permitted to memorize a simple multiplication table so that we can be forced to go through the exercise of new math even if it requires a calculator.
1) I have never said that there should be no ROTE learning at all. I am just claiming that most of such memorizing as it is done in our schools is pointless, at least for some students.
2) I never said that people should not be permitted to memorize their multiplication tables. Some people don't find memorizing things hard. In my third grade class, I believe number of people simply memorized the tables and were done with it, but those of us who had problems memorizing things did not have to do that, since we were taught how to find other ways. And we probably learned more actual math while doing that. I am complaining about a typical American fourth grade classroom, (and I have seen a number of them) where the kids spend more than half a year drilling times tables, without ever realizing that there is more to multiplication that bunch of pointless facts. Than, two years later they are given a calculator and told that they can happily forget all that stuff they have learned before.
3) I don't know where you got the idea I am talking about any type of "new math". The way of learning multiplication I am talking about is over 100 years old. In fact, couple years after I finished the elementary school, it was declared too old, and was replaced by some sort of new method, where students spent first several years of school learning about something called "sets", and spent tons of times memorizing stupid terminology like "empty set" and so on. In first grade. Never mind that what they called "sets" had actually nothing to do with any notion of set in any possible set theory in existence.
4) Exactly how does anything I described here require a calculator? I was under the impression that what I said was that you don't actually need to even memorize the tables in order to be able to do multiplication reasonably fast. It would seem to me that a logical conclusion would be that one does not need a calculator even if one has trouble memorizing things, like myself. I don't let my students use calculators until they get to advanced calculus or diff eq. By that time most of them actually don't need it.
I'm sure this MIGHT be useful for some of the smarter types out there who are in love with numbers, but it scares the living daylights out of normal people and they end up going through life not knowing basic multiplication and hating/fearing math.
I don't have any statistics on this, but it does not appear to me that in the countries that use (or used in the past) the "method" (if you want to call it that, I personally consider the term "teaching method" idiotic) I described had significantly larger percentage of people hating or fearing math than the US.
AccountKiller
Mathematical multiplication tables have at most 100 items to memorize. Your mind is able to memorize a lot more than that.
There may of been 100 items on the multiplication table where you went the school but there was 144 where I went. We had to memorize 1X1 to 12X12, why I don't know when 10X10 will work. Like you say though most people are able to memorize a lot more data than that.
Falcon
Should there be a Law?
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.
My (gasp!) girlfriend is learning latin this summer, and the way she describes it gives me an understanding as to why latin is nearly a dead language. TOO DARN COMPLICATED. Language needs to be simple, concise and easy to learn, not full of extraneous rules and details and situational caught-ya's.
Honestly, I think learning how to use and adapt to the latest tools to gather information as efficiently, effectively and rapidly as possible is far more important than learning an overly complex method of communication.
ERROR: SIG NOT FOUND (A)bort, (R)etry, (F)ail?:
That's what hurt me so badly early on because I had learned enough math in China in first and second grade to last me until the 6th grade in the USA. I was bored out of my mind through 5th grade and pretty much flunked every math class because I was so bored by it and completely ignored the teacher
In a way I went through something like you. At the end of my 6th grade I met a counselor from the jr high I would go to for 7th grade and he said I should take algebra in 7th grade but he couldn't let me take it because I didn't know how to do square roots. So I went from 7th to 10th grade taking as advanced a math class without taking algebra without ever learning how to do square roots. A couple of months after 10th grade started for me my math teacher did something that caused me to loose my cool. Every day when the bell rang for the start of class all of the students had to be sitting down. Students in rows behind the front row then handed the homework to the front and he'd walk across the front row to collect it. Several weeks after the year started he did this, then he leafed through the homework papers and took one out. He held it in front of the class, it was mine, and proceeded to rip it up right there in front of class. I started yelling then grabbed my books and walked out of class. I went right to my counselor's office, I'm glad she was someone different than the first counselor, and told her what happened. I then told her I had to get out of that class. When she looked at my records she said I should be in algebra. I stammered I didn't know how to do square roots, then my stack blew again when she said you learn to do them in algebra. It was too late in the year so she didn't want to put me in algebra but she said a new class, pre-algebra was being offered so I agreed and she put me in it.
Falcon
Should there be a Law?
Most people will never have any practical use for mathematics anytime in their life
Does anyone (other than authors and editors) have any practical use for literature? Why would we bother having English classes beyond spelling and grammar? The answer is that it is part of a liberal education.
My point about calculators and mathematics is that it is entirely appropriate to explain how to use calculators in preference to tedious and error prone pencil and paper calculations. That sort of instruction doesn't teach mathematics in any case. People with nostalgic attachment to "the good old days" when students learned to extract square roots don't have a clue what mathematics is about. Explaining to students why the square root of 2 cannot be expressed as the ratio of two integers has mathematical significance but no insight into that is obtained by using pencil and paper rather than a calculator.
"But to speak a language, especially a first language that has been learned since birth one needs to know little more than elementary grammar. Intransitive verbs, for example, are likely outside of the scope of what 90% of the population needs to know to use a language."
People don't go to school to learn how to speak. Writing, however, most certainly requires a good knowledge of grammar. One could argue that 90% of the population does not need to be able to write with correct grammar. Indeed, I doubt that over 10% of U.S. adults can consistently write without making grammatical errors. Almost everyone I know socially has a college degree, but few of them can write at a level acceptable for publication.
For what it's worth, the move away from formal teaching of grammar started way before the early nineties. I attended grade school in the late sixties and early seventies, and my school had already done away with formal grammar instruction. In high school, a one-semester "grammar workshop" was available, and I found it to be the most valuable English course I ever took. Most of my classmates opted out of it, saying they didn't need to review basic grammar. They were wrong.
So, while I agree that 90% of the population can and does "get by" without really knowing grammar, it strikes me as a cause for national embarrassment.
If I wanted some fine furniture making, I would want a cabinet maker and not a carpenter. Totally different jobs.
Perhaps GP used the wrong profession, try this, would you rather a competent carpenter or someone who can use a nailgun building your home?
Falcon
Should there be a Law?
And yet polygamists continue to multiply.
"I believe in Karma. That means I can do bad things to people all day long and I assume they deserve it." : Dogbert
You only need mathematics more advanced than this stuff if you're planning on going into a field which requires it, like architecture or physics or engineering.
When my sister was working on her BA in Accounting she had to come to me because she didn't understand some of the concepts in her calculus class, yes a calculus for business class was required for her degree. Fact is is math is more important than many admit or realize. Here's a problem anyone should be able to do by the tyme they are an adult, how much should you save for retirement starting today if you want to retire in 40 years with enough income so you can retire on a comfortable income? Algebra and the equation for Present Value will give you an answer once you know how much you will need later. Actually it along with Future Value and other formulas are used quite a bit in fields like accounting, economics, and finance.
Falcon
Should there be a Law?
Oddly enough, a great many people learn critical thinking and the ability for abstraction from literary analysis in their first "hard" English class, not from math or logic (which they find impenatrable beyond what can be memorized). As a geek, I find this mind-boggling, but it's true nevertheless.
Teaching "real" mathematics to those who aren't interested is thoroughly pointless, and does nothing but waste the time of everyone involved. We definitely need to teach the logical reasoning process by some method by high school, obviously, but for most abstract Math won't do anything to accomplish that goal. As a byproduct, it sure would be nice to actually teach some abstract math to high school students who are interested - anything beyond basic Trig may be unavailable these days, being "too hard" for most, which is really a shame.
Socialism: a lie told by totalitarians and believed by fools.
Me being able to quickly, accurately estimate totals in the grocery store is quite a benefit.
Ah, the joy of working out your total and handing the checkout operator the correct amount, just so that you can see that stunned look on their face....
I jumped onto #olpc at freenode a year ago when the idea that giving kids (whos bones are still developing) laptops to use 6 hours a day 5 days a week for years might not be a great idea.
I asked the people there at #olpc: 'Have you guys considered the physical ramifications of this?' I also sent a similar question to the minister for education in Australia at the time. From both sources I got the same answer 'I don't think its a big issue, not we have not done any studies but we think the benefits are greater than the risks'.
Don't get me wrong, I'm a programmer by profession not a ludite, but ffs I have CTS, so do most people in our industry, you turn over a kbd and there are health warnings in big letters, is noone thinking this through?
Well, there is always:
23 * 47 = 35^2 - 12^2 = 1225 - 144 = 1081
But the multiplication table up to 10*10 or perhaps up to 20*20, should probably be memorized. There isn't much memorization required in mathematics from that point on though.
Grammar needs to be reinforced in the other subjects where appropriate. A social studies teacher for instance, should mark down when students don't use proper grammar.
I urge anyone who is interested in this to read "The Flickering Mind: Saving Education from the False Promise of Technology" by Todd Oppenheimer. It is a thorough book and starts out that computers are the only the latest thing that will 'save' education. The same was said about radio, films and of course TV. Bottom line: NOTHING beats solid teaching by real people and technological solutions are money pits. Please, before you criticize me, read the book. It was a real eye opener for me.
There are 25 cows grazing in a pasture, all but 9 cows go into the barn. How many cows are left to graze in the pasture?
I disagree with this wholeheartedly, memorization doesn't teach you anything, it makes you a tape able to play back the sound, 'facts', without hearing the music, 'concept'. I believe it is more important to teach people how to learn than to teach them to memorize pages of trivial dates and such.
Don't teach the data teach the abstraction.
Most people will never need to do long division with symbols in their entire life. Heck, I'm a geek with a real interest in math, and I've still never found the ability to factor a polynomial useful even once in real life.
It all depends on how you define "real life", I guess. Does college count? I know that having the ability to quickly work out the factors of a polynomial via long division would have been of immense help to me in college.
The argument, "Well, I'll never use this on the job," is somewhat of a straw man, since you'll need to get a college degree to get that job. And, in college it is useful to be able to do algebra and basic calculus in your head quickly.
We all know what to do, but we don't know how to get re-elected once we have done it
I know the squares. 6x6 is 36. Add 6 to that. Seperate the 6 from the 36, add the new 6 to that (=12), add the 12 back onto the 30, (=42). That's fast enough and less wasteful of valuable education time in childhood.
FGD 135
You entirely missed the point. Either that, or you are trolling (which seems likely, given that you are posting anonymously). You need to memorize some things -- basic arithmetic, spelling, &c. (honestly -- do you sound out every word phonetically when you spell? -- given that your spelling is spot on, I imagine that you don't). You have to have some facts before you can start making abstractions, or give meaning to those abstractions. To paraphrase the above, critical thinking is about connecting the dots, while memorization is about having the dots to connect in the first place. No one is suggesting that children should not be taught abstractions or critical thinking. Rather, it is being suggested that some level of memorization is necessary in order to facilitate higher level abstractions.
Rhapsody in Numbers
Online gym class.
I suppose I've been clear enough in my defense of the use of calculators in K - 12 education. The points being that calculators are better suited to the tedious details involved and my claim that there is almost no mathematical significance to the displaced memorized routines.
I probably have not been as clearly insistent about the value of mathematics education in K - 12 (I wouldn't distinguish it as "real" mathematics since the current curriculum is mainly about arithmetic and tediously artificial "word problems"). Mathematics was understood by Plato as an essential part of a liberal education and should be recognized as such even more today. In other words it is not to be justified by being practical or specifically useful on a daily basis. Mathematics is justified as part of the curriculum because it is among the most remarkable of all human achievements and it is worthwhile trying to impart some of it to anyone who wishes to be educated.
But however one feels about that thesis I wish we could get past the idea that rote calculation is significantly about mathematics and that as a result calculators somehow interfere with something important. It isn't, they don't.
My wife teaches at a state funded school just south of Boston and they don't even have a photocopier that works properly, never mind a Mac per student.
It all depends on how you define "real life", I guess. Does college count?
No, pretty much the definition of "real life" is "that place you go when you leave school". :)
Oddly enough, I took many years of math classes in college and don't remember ever factoring a polynomial there either.
Socialism: a lie told by totalitarians and believed by fools.
I certainly agree with you on the lack of value of rote calculation. I'm extremely good at doing math in my head, and learned many helpful tricks while doing repetitive calculaion in school. While this is nice for impressing coworkers in meetings, I *still* use a caclulator or spreadsheet any time the math actually matters.
OTOH, while i agree that (abstract) math is a part of a liberal education, I completely deny the value of that liberal education. It was a great idea a couple of centuries ago, because it equipped you with genuinely useful skills, and a common base of knowledge that gave you a framework for a discussion with anyone else so educated. Today it has no practical value. Different skills now form the core of what you need to do well in the world.
Of course, for the brightest few %, a liberal eductaion is quite useful precisely because it makes one "well rounded", but the vast majority of people need skills that will be useful in earning a living, instead.
Socialism: a lie told by totalitarians and believed by fools.
I know a couple of guys who do structural, home- or set-building type carpentry, and also do furniture, sculpture, and other arts and crafts in wood. They all call it carpentery; occasionally the term woodworking is used for the finer work.
I have never heard any of them use the terms "cabinet maker" or "ebinistre". I've never heard anyone use "ebinistre", and Google turns up only a handful of hits, only one of which is in English.
The only person I've heard use the term "cabinet maker" is Dan Fogelberg, in his song "Leader of the Band".
According to the wik, "A carpenter (builder) is a skilled craftsman who performs carpentry - a wide range of woodworking that includes constructing buildings, furniture, and other objects out of wood," with various specializations thereunder. This is consistent with the use in the handful of shop classes I took, where "carpentry" referred to both framing a wall and building a stool (both of which, I found, I suck at).
So, I stand by my usage.
Tom Swiss | the infamous tms | my blog
You cannot wash away blood with blood
Depends on what you mean by "fine furniture", I guess. I'm referring to the higher-end stuff that I'll never be able to afford and wouldn't buy even if I could.
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.
You've hit the nail right on the head! What are you going to connect if you haven't learned the bits. The more knowledge you have, the more connections you can make. Knowledge is power.
A series of opinions isn't a series of facts. Just asserting your belief doesn't make it true. Personal anecdotes don't provide any support. I'd say that happily heartily grounded education didn't teach you too much about how to think critically or articulate facts instead of baseless subjectivity.