July 04, 2007
Daniel Greenberg taught a group of students of different ages six years' worth of arithmetic in 20 one-hour sessions.
It's an example of the learning style at Sudbury Valley School, MA, and Mountain Laurel Sudbury School, CT. The schools are democratic: staff and students vote on everything from curriculum to clothing to hiring and firing. There are no exams and no grades.
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lol. So what?
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I vote no means yes.
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lol. So what? So like maybe gazillions of kids could learn and enjoy mathematics instead of being turned into mathphobes by the school system.
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In New Zealand at present, maths is listed by primary (elementary) students as their second most favourite school subject. (I don't know what the first is because my maths lecturer is a grouch.) I've just finished a week-long intensive introductory maths class in which we basically played the sorts of games kids play during maths. It was pretty fun and I can see why they like it. And all the games actually served a purpose, which is a bonus.
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I absolutely hated math (or maths) and it was for the precise reason that storybored mentions. We were taught rote memorization by uninspiring teachers (I remember one high school teacher telling us he didn't care one way or another if we graduated or not). It's only now as an adult that I see what I was missing by reading accounts of the creative aspects of higher mathatics and algebra that I somehow feel cheated. Thank god for calculators.
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Same here.
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When I was a kid I jumped classes from the 2nd grade to the 4th grade, which landed me smack bang in the middle of the dreaded discipline division, which I was supposed to have learned in the 3rd grade, which for obvious reasons I had not. That put me off numbers, figures (exept female ones!), calculus, maths, arithmetics and similar sundry disciplines for good, and I dearly LOVED it, when small pocket calculators made their apearence. What put me off the most was arithmetics! I could not for the life of me understand why we had to fiddle around wíth x´es and Y´s and square roots of this or that! No one told me what the stuff was good for or how it might be utilised in an everyday situation. Geometry, on the other hand, was another matter! I could clearly see, that if I wanted to build a birdhouse or a soapbox racer, I needed measurements, drawings and angles to come up with a decent end result, and for that reason I got good grades in geometry - a fact that was a mystery to my long suffering maths teacher. I guess that just goes to prove the old adage, that you can lead (or drag!) a horse to the water, but you can´t make him drink unless he wants to. In Tragicles link the "horses" wanted to drink, so it was just a question of showing them the water.
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I learned the times tables by rote in second grade,and I'm eternally grateful. It was just a daily class exercise, and not a big deal, but it's never left me. When my daughter was in grammar school in the 1970s, the waty they taught multiplication made no sense to her, so I drilled her in the tables, and it worked. Now, I see my grand nieces and nephew having the same problem. I guess I really don't understand you you all learned that sort of thing so easily.
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I remember one high school teacher telling us he didn't care one way or another if we graduated or not Jeezus. Those types belong in a special circle of academic hell. I was lucky enough to have good math teachers through high school. Then my luck ran out midway through university when our algebra class was run by a terrible "teacher" who hated what he was doing, didn't like any of the students, didn't seem to have much interest in the subject...yeesh.
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I learned the times tables by rote in second grade,and I'm eternally grateful. My mom was wise (and patient) enough to make up flash cards. All the multiplication tables through ten times ten, and goddamn if she didn't relentlessly drill me on them until I had them back to front. One of those little things she did for my education that always stuck with me -- I hated it at the time (I've always loathed rote memorization), but damn if it wasn't important.
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I learned the times tables by rote in the second grade,and I'm forever grateful. I see my grand nieces and nephew struggling with math because the basics weren't drilled into their heads. I didn't have that problem till I hit algebra 2 and couldn't figure out why I should care about quadratic equasions. So, for those of you who learned math easily without the rote stuff, how did you get there?
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I absolutely hated math (or maths) and it was for the precise reason that storybored mentions. We were taught rote memorization by uninspiring teachers Everybody hates the memorization, and yet these kids wanted to do it. I don't get it. I've heard about different ways to learn the times tables that involve more of a cognitive/intuitive approach instead of memorization, but don't get them. Supposedly, very young kids can quickly grasp the concept that 4x6=6x4 so it "halves" the number of problems to memorize. I can calculate the percent for a discount or a tip, but don't ask me to try to teach someone, or to work it out on paper, because I can't remember which way the decimal goes half the time. Same with other calculations. It's like I can do the math that I need to do to get the world's work done, but I've put up this barrier against "math" that started in third grade. Lucky kids. Now what are they going to do for the next six years in math class?
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..No one told me what the stuff was good for or how it might be utilised in an everyday situation.. Personally, I think that one big mistake in math education is this feeling that it should need to be constantly justified every step of the way to students.
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My fourth-grade teacher has the multiplication tables set to music on 45's. He played them in the background whenever we had quiet time. It was awesome. The 5's record did tend to stick, so whenever I have to multiply 5x12 I still get that line stuck in my head, looping, for a few hours. But I highly recommend subliminal multiplication. When my cousin's kid (now 14) was learning mulitplication his teachers explicitly forbid any use of memorization or even multiplication tables themselves. As a consequence, he still has to stop and count every time he needs to multiply.
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Maths is stoopid.
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I think what's interesting is his use of an old primer. I collect old scientific books and occasionally grab an old school book if it's in decent condition. The mathematics in that stuff is freaking hard, and I passed out of college math due to completing high level courses in high school. But more importantly, a lot of it was stuff these kids were going to have to use - business math, agricultural math, etc. (I think part of the reason it was hard is that I have no idea how many feet are in an acre, or what a bushel means.)
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I started school at the tail end of the New Math phenomenon. By the start of fourth grade, I had a reasonable grasp of number theory, set theory, boolean operations, base-8 (octal) and base-12 arithmetic, etc. Then my family moved to another part of the country where they were memorizing multiplication tables. I was considered "backward" and uneducated by my teachers. Luckily, I was able to see the patterns and understand the structure of the multiplication table, so I caught up in a couple of weeks, and then went on to outperform my classmates for most of my school career. I was also the only kid in my school who enjoyed "story problems." But I hated drills and busywork, and my success rate at solving quadratic equations never got much above 70 percent. I maintain that the New Math wasn't dropped because it didn't work; it was dropped because reactionaries didn't like the idea of kids not doing mindless drills.
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Maths is stoopid. Go back to your hole, arty fartman! And there's only one of 'em! ONE!1!1!1111!!!!1!
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I alos think that a lot of it had to do with parents not being able to help their kids when they floundered in the New Math. As is geberally the case in American public schools, teachers can't (or in some cases, simply don't) give each child the individual attension he/she needs to keep up. They rely on parents to help with the homework that is intended to reinforce classwork. In this case, the parents couldn't do that.
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Do you study mathematic, eh Beardy? Do you?!! DO YOU??? bloody septics
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Kit, math is clearly stoopid, I agree, but math is plural. Just like hair, or Lego.
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You are all wrong.
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let's not start all this again... When I was a kid (about 4 years and up) and my parents took me to restaurants with them, my dad would set me Pythagoras theorem problems to solve to keep me entertained - draw a triangle on a napkin, give some values, let me figure out the missing bits. It was great. Maths lessons at school completely took all the fun out of numbers though.
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Sorry mothy. It's the only thing about maths I give a fuck about. My calculator in work is big and purple, if anyone's interested. I keep it in my drawer.
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Fair enough, kit, can't argue with you really. *inserts some pre-emptive SSSSSSSs into thread*
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(and, to take care of the argument, "maths" is a shortened form of "mathematics" - plural. "Math" would be a shortened form of "mathematic" - which doesn't exist.)
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I bet MCS's calculator isn't purple.
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mct's, obv
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Mathematics is just taught wrong(ly) in schools. When I am king, I shall decree that everyone first learn the principles of mathematical logic. Logic is much easier to grasp than arithmetic and can be taught fruitfully to preschoolers. Once they understand logic, they shall then be introduced to the lambda calculus, and then learn mathematics methodically via construction in the lambda calculus. The beauty of this approach will be that they shall always be a short step away from implementing their knowledge in a suitably advanced computerized proof-assistant. Writing proofs with pen and paper shall be outlawed, of course, except insofar as it leads directly to getting the proof accepted by a mechanical verifier. I think we are not yet able to support this plan technologically, but this shall be the state of mathematics education by the turn of the century.
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Kit, I love you -- you're my brother, my lover, my future civil union partner -- but please, let's not bring this between us again. You're wrong. It's OK to be wrong sometimes. One day, I may even be wrong myself. The way you go on about it, you'd think you guys invented the language or sumthin'.
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Dude - my school is older than your country, so let's not go there... But what colour's your calculator?
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And, on preview, mothy, dear -- sorry. That explanation doesn't make any sense. Why would you shorten a word by taking out a middle part, and leaving the ends? Words are shortened by making them shorter -- that is, by cutting off an end entirely. FACT.
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SEIZE HIM!!! HE CRITICISES THE MOTHY!!!!
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Do we have 'arts' class or 'art' class? We study more than one art, don't we? Same goes for studying several 'sciences' in 'science' class and several 'histories' in 'history' class. Math. ...and it's not stoopid
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Dude - my school is older than your country, so let's not go there... How'd you figure that out? With your maths? *snicker*
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Um...in art class we study art, you know, painting, drawing, that kind of thing. Other arts, like dancing, music, raffier work etc have their own classes. Do we study physics in physic class?
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Sorry for derail. I'm leaving now!
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Actually, turns out I was totally wrong with the above attempt at logic. My bad! The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural τα μαθηματικά (ta mathēmatiká), used by Aristotle, and meaning roughly "all things mathematical".[8] In English, however, mathematics is a singular noun, often shortened to math in English speaking North America and maths elsewhere. So apart from my spurious explanation (this is why I love this place, I learn something new every day), *everybody* is right. So let's stop arguing. Group hug! although obv 'maths' is more right than the s-less version, cos like kit says, we've been saying it for, like centuries longer and most of the world says 'maths' so pffff
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My calculator is a big, bank-y style adding machine. And it's BEIGE! Top that!
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I think the purple calculator is a strong argument.
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My calculator in work is big and purple I would have guessed it was tame and bland.
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That got an 'Arf'. Well done.
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'Tragicles'... heh...
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It's an abbreviation - whether you decide to abbreviate "September" "Sept." or "Sep." it still refers back to the same full word.
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So apart from my spurious explanation (this is why I love this place, I learn something new every day), *everybody* is right. So let's stop arguing. Group hug! Just the sort of thing someone who is WRONG! would say.
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Regarding new math. I too was educated in new math for the beginning of my school years, then right around the middle of grade school they changed the curriculum and went back to old math. You wanna talk about a mind fuck?!?! In retrospect, that's probably one of the reasons I did so poorly in the subject.
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I hate you all.
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At least people who say "Maths" end it nicely rather than spitting all over whoever they are talking to.
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squidranch, the same thing happened to me. Very confusing to switch mid-stream. And yet I grew up and got job in banking, and everyone knows how great my math(thshthshshshts)skills are!
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*mops floor*
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My calculator is a big, bank-y style adding machine. And it's BEIGE! Top that! Well, my desk calculator is a big grey and beige plug in the wall model from 1972 with a nixie-tube display and reverse logic operator input (to subtract 3 from 4 you input "4+3-", etc, confuses the heck out of my coworkers). So there.
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I went to a private Catholic school until grade 4. I think all of our texts were at least 50 years old. Math was all rote memorisation and drills.
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So, for those of you who learned math easily without the rote stuff, how did you get there? I pretty much sailed through until the second half of college calculus, when a bad teacher and an even worse textbook combined to break my spirit. As to how... combination of mostly good teachers and, as fuyugare (half?)-mockingly got at, having the sort of brain that instinctively picked up on the underlying logic of it all. It just made sense to me in the same kind of way that artistic people get artistic stuff (yay for words!). Which is of no help whatsoever, I know. Just lucky for me I didn't have to pass four years of art to get out of high school. Mothy, my dad used to give us math problems at the dinner table too, but they mostly involved how many chickens Farmer Brown had, not the freaking Pythagorean theorem. Jeez. Overachiever.
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fimbulvetr, mine has the same logic. That's how all bank machines, and I think all adding machines, are. 4+3- I can't use a regular calculator now without having to stop and think. It also plugs in the wall. I had a circa 1972 one with bright orange keys, but I stole this better one from the desk of someone who quit, and substituted my own. It's the law of the jungle.
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I used to work for a bank but I was exposed as a counterfeit and forced to withdraw.
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You're not a loan.
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We bankers do not find bank humor funny. In fact, we do not find most humor funny.
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I used to work for a bank but I was exposed as a counterfeit and forced to withdraw.
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I used to work for a bank but I was exposed as a counterfeit and forced to withdraw.
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omg, sorry about that.
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it was a good joke, tho :)
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Thanks moth! ....but i killed it with my little keyboard (snif)
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StoryBored used to work for a bank but was exposed as a counterfeit and was forced to withdraw.
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And then we lost interest.
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...out of principal.
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Nope, still not funny.
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You're too close to it. Were you not a banker, you'd see that it really is quite funny, dear.
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Well how about the time when a bank draft blew me out the window and deposited me on the sidewalk? it's a lot funnier when randomaction tells it
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Yeah, his account is much funnier.
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Nope, still not getting anything. Speak up or something.
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All your jokes don't make any cents to me...
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So the third priest says "I'll take two tickets to Pittsburgh, and I'd like the change in nickels and dimes, and if you don't stop dressing so provocatively, young lady, when you arrive at the Pearly Gates, Saint Finger's going to shake his peter at you."
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That's not a safe joke for mixed company. But it cracks me up anyway. To his credit, the man tried. MCT steals the show with his combination of spoonerisms and sex. I trust you found this last post rich, Lara?
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I think she's going to have to cheque it over again.
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Why did he want the change in nickels and dimes?
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It was part of his RRIF.
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Q: How many bankers does it take to change a lightbulb? A: A quarter.
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Now THAT'S funny!
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Well, our heirs will have to pay a high monthly fee to know.
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Actually, Lara, a priest will only take change in pennies and quarters when buying two pickets to Tittsburg. It's a bishop that wants his change in dickles and nimes.
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I read that as "a priest will only take change in penises and quarters". *giggles*
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nipples and dimes is how I've heard it.
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Oh, that's enough. I'll charge a bus pass to Denver.
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So, for those of you who learned math easily without the rote stuff, how did you get there? I found that having a grasp of what's actually going on with numbers means that you don't have to spend nearly as much time memorizing stuff, because you can just see it. I did well in math(s) until I hit trigonometry. And then my Dad, bless his heart, told me, "Here's all you need to know about trig: Oscar and Oliver have had algebra." Which is great mnemonic for remember the derivation of sine, cosine, and tangent.That said, I'm not really a math guy, so I left off there. Although, I've found that, as a trumpeter, a basic understanding of wave functions is a big help when dealing with practical acoustics. For the last 12 years or so, my day job has been documenting high-end engineering software, and it's nice to be able to grasp some trickier mathemetical concepts without necessarily being able to solve them. For that matter, set theory and logic are great skills to have when deciding how to describe complex technical subjects. Like I say, the "new math" wasn't abandoned because it didn't work; it was abandoned because it was insufficiently tedious and awful.
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MonkeyFilter: it was abandoned because it was insufficiently tedious and awful Alex, I'll take maths and veg, for 200!
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Which is great mnemonic for remember the derivation of sine, cosine, and tangent I learned it as "Soh Cah Toa!", shouted out like "Sock it to me!". I did the multiplication tables by rote. The teacher helped us with flash cards and setting up a game show-like multiplication contest. Alright! High school math was a mixture of rote and understanding. Talking about it now though, what do we mean by "rote" anyway? Because even with intuitive understanding you need a *lot* of mechanical practice with the techniques to do it right. And getting the practice is essential because higher mathematics builds on the practices of the lower maths.
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When I am king, I shall decree that everyone first learn the principles of mathematical logic At our school we all learned maths through a close reading of the Principia Mathematica. Unfortunately I got bored with it at about page 370 so I never found out what 1 plus 1 equals.
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Well, since you won't be needing it, please send me the the 50% off coupon for the MathBlaster Parabolator on page 371.
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Hey, do what I did! Knit a lovely multi-colored cover for your Principia! Makes a dandy door stop and covers that unsightly maths book! Don't forget to remove the coupons first! You're local BigBoxGrocer will honor all coupons on produce! Get !!!$$$$!!! off on your veg! Special sales on !!!!! today!
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Plus some grocers will double them! Figure that out, math freaks!