I Come To Praise Rote

So Amanda’s post here last week got picked up by the BBC who thought she was “maligning a whole generation.”

Maybe she was.  Maybe she wasn’t.  I’ve long disagreed with Amanda on the “kids need more homework” but I don’t think it’s so much a disagreement on what we think the kids should be doing, as that we’ve encountered different forms of school-stupid.

My particular form of school stupid was my kids being given HOURS of homework that had no possible redeeming value.  No, seriously.

Look, I’m not the sort of parent who thinks that rote, repetitive tasks have no value in education.  On the contrary.  I learned to read and write in a village school where even the slow kids learned to read and write and cypher too: largely through never-ending repetition.  What is more, I suspect I had the same sensory and hand coordination issues as my younger son.  For instance, I didn’t start enjoying detail work, like sewing or embroidery, until after sixteen which is typical.  That type of work was incredibly difficult to me, all out of proportion to other kids my age.  And the same with you know, all clothes “itched” etc.  What’s more, when I started reading/writing I had the same issues.  BUT since my father – before I entered school – believed in rote learning, he set me to do a page copy a day (and the pages got more text as we went on.)  By six I wrote slow but not disastrously so, and by fourth grade I wrote faster than other kids.  (Mind you ANYTHING else I needed to do with my hands was a disaster.)

In fact, when younger son came home to homeschool for a year, and he was dealing with all these sensory issues and difficulty in focusing that made him write verrryyyy slow, the optometrist gave us a million exercises for him to do.  I have issues visualizing written instructions.  I was supposed to supervise his exercises and I had NO clue what he was supposed to do or in what order.  There was all this stuff with beads and string and rulers, and frankly I’m not smart enough to even know what to do.  So I ditched all the professional advice.  (eh!) Instead I set him to copy a page – increasing to three pages – a day.

By the end of the year, not only was his writing much faster (though still slow for his age, but not badly so) but he had impeccable spelling and grammar.

In the same way, I’ve taught language, and I can tell you the way they teach it in our schools, trying to make it fun and giving the kids colorful magazines written in the language, before they even know the basics is not only insane – it’s counterproductive.  When neither of my kids could learn French, I asked for their books and looked through both instructional materials and notebooks.

Guys, I TAUGHT languages.  The only way my kids could learn languages from what they were given was to be naturally gifted on the order of my brother, who could be dropped naked in the Amazon forest and would emerge two weeks later speaking the language of the nearest tribe like a native.

I’m not like that and neither are my kids, and neither are most people.  Most people NEED a basic vocabulary which includes a couple of verbs and some grammar rules, before you drop them into the deep end head first.  And the easiest way to acquire a vocabulary is to memorize lists.  Which is boring, and rote, but by gum it works.  (It is in fact all that most language learning software does.)

Now, after you have the basics, say about second year level, then you need to be dropped into the deep end head first.  I did this with older son (younger never really wanted to learn French, so he scraped by with a b, and then stopped taking it) by teaching him lists and lists and then, over summer, having him read Dumas in French (with dictionary at hand.)  Once he finished the Three Musketeers he had a very tolerable command of French.  (And an outdated swearing vocabulary.  Apparently Ventre Saint Gris said in class made his teacher – native – say “oooh, lala.”)

Anyway, I realize that because it worked for me and mine, it doesn’t mean it works for the entire population.  But kids used to come out of school minimally competent in reading and writing and now they don’t.  And in my area at least – though apparently not Amanda’s – kids do more and more homework.

I realize #2 son had issues that slowed his writing, so stuff took longer, and I won’t use him as an example, but #1 son, who was faster than average, usually had 4 to 5 hours homework.  EVERY night through high school.

Now I don’t know about you, guys, but when I was a kid my homework took at most two hours.  Three if we were ramping up for a test.  Which left me time free to read, spend time with my family, have hobbies.

But what was weird was the nature of the homework.  Part of the reason it takes so long is that it tries to be “fun fun fun” instead of just having rote memorization.

Look, let’s say you’re trying to teach your cat to fetch paper balls.  Yes, it can be done.  I did this with Pixel (best cat evah.)  — well, I had no kids, and I was bored.  Shut up – by throwing the ball, picking it up, bringing it to him, throwing it again.  Eventually a light bulb went on in his head, and he started bringing me the paper ball.

Now imagine that you’re told cats only learn if it’s fun.  So, first you soak the paper ball in sardine juice and throw it.  It seems to work better, because the cat goes to it immediately.  But then he tears it apart.  So then you fill a water bottle and spray the cat when he starts eating the paper.  Now the cat is afraid of the paperball and you must add catnip to make him go near.  Now he’s playing with it but not bringing it to you.  So you put sardine juice on your fingers.  He comes, but he doesn’t bring the paper ball…. Etc. Ad Nauseum.

As tedious as the first process is, the second, as you can see, can extend to absurd lengths.

Well, it’s sort of like that with teaching.  Say they’re trying to teach basic French vocabulary.  They can’t give a list like “Fille->girl” because that would be rote and bad pedagogy.  (And besides any idiot can learn that way, so what’s the fun in that?)

Instead the homework will involve going through the fun fun magazine printed for French teens, finding every picture of a girl and writing down the page number of the page where the girl is.  Then looking at all the captions (without reading French, remember) and finding the common words.  Then you write all those down.  Then you write your answers as to what “girl” is in French.

Guys, writing down Filleàgirl twenty times affixes it your mind better and takes five minutes (TOPS at kid speed.)  To do the other?  An hour.  And at the end of it, the kid is tired, cranky, and has learned nothing, because girl could be fille, or it could be gamin, or jollie, or elle or…

So my kids had HOURS of homework which not only didn’t teach them anything, but didn’t leave them free to learn anything on their own.

Not only that, but because the homework wants to teach kids in ways the kids don’t know they’re being taught, most of the exercises come across as utterly pointless.

Like most kids I HATED vocabulary lists.  I HATED copies, and there is nothing more despicable than multiplication tables.  BUT I knew why I was being given these.  I was supposed to memorize them, duh.

The kids don’t.  What I mean is, no one could.  Most of the stuff makes no sense for its stated purpose. They just know they have hours after school of putting tab a in slot b and coloring tag c and they have to do it because homework now a days counts way more than it did in my day.  (I should know.  I was very good at spacing homework.)  So even if you have all As in tests but don’t do homework, you’ll fail.  (Trust me, younger son tried this.)

So what the kids are taught is that they must perform senseless tasks they don’t want to do, which accomplish nothing, or be punished…

Worse, as I found out, the teachers don’t even remind the kids that homework is supposed to be turned in.  “Oh, I told them two weeks ago.  They’re supposed to remember.”  This is used as early as elementary when most kids CAN’T remember, so unless the parents remember it for them, it’s not going to happen.  (Surely you DO remember being young and the sense of floating in timelessness?  That’s neurological.  You’re not good at keeping track of time at that age, and I was told by a psychologist friend this can persist till 14 in boys.)

OTOH when older son had to have surgery and we asked the teachers for homework for the next two weeks, we found that they didn’t know it and had no plan.  From then on our reaction to homework was “the children must plan, because I can’t.”

This too is a bad thing.  Someone in power who does what he/she pleases while the kids/peasants must scrupulously follow the rules.  Bad precedent.

My point is, calling for more homework isn’t going to fix this mess.  The teachers happily pile on more and more mind bogglingly stupid homework, designed to avoid that awful “rote” and thereby more or less utterly pointless.

Now they’re talking about year around school, because the kids just don’t have enough time to learn.  (Rolls eyes.)

Oh, and they say that “it’s because the kids have so much more to learn.”  Poppycock.  This reminds me of publishers saying that “people are reading less because there’s so much more entertainment.”  When in fact, people were reading less because they had trouble finding anything they wanted to read.

How about you teach kids to read and write and let them pick up “all that important stuff” on their own?  Because, guess what, they do to the extent they need/want to.  And if they can’t read/write, the rest won’t happen EITHER.

Guys, there will never be enough time so long as we try to teach the kids without the kids knowing they’re being taught.

I come to praise rote, not to bury it.  Sure, if ALL you learn is by memorization, you create a learning system like China’s, where people can’t reason over what they learn.  But what we’re creating is exactly the same – a sort of behaviorist hell, where we’re trying to teach people things through other actions, but which ends up imprinting the idea that obeying pointless instructions is good.

Basic skills can be acquired through memorization.  I would skip the wooden ruler on the knuckles for memorizing the multiplication tables, because all it did was make me incapable of speaking when called on (I was likely to mentally transpose and say 45 instead of 54, and then the ruler would descend.)

And after you have the basics, you should move on to more challenging things.

If you’re trying to learn the basics without rote, you’re doing it wrong.  If you have the basics and still doing rote, you’re doing it wrong.

Removing all rote from learning because it’s bad after a certain point is like making strollers illegal because kids are supposed to learn to walk.  All it does is limit people’s choices and take away the time parents should be doing other stuff.  (OTOH some parents would become Olympic lifters.  I mean, Robert weighed fifty pounds at 2. And he wasn’t fat.  I have pictures.)

Right now?  Homework or no homework?  I’d say homework is a tool for keeping your kids FROM learning, unless your kids go to an exceptional school.

Agitating for more homework without checking on content is not the answer.

In fact, the more I look at it and hear, and exceptional schools like second son’s second high school excepted, I’d say the best thing you can do, if at all possible, is bring those kids home and make them do some copies and memorize their multiplication tables.  At least they’ll be bored for a reason.

 

197 responses to “I Come To Praise Rote

  1. “You’re not good at keeping track of time at that age, and I was told by a psychologist friend this can persist till 14 in boys.)”

    14? Dang, I must be a late bloomer.

  2. We’ve forgotten how to teach, I’m afraid.

    Especially boys. Most especially, boys.

    It all stems, to my mind, from allowing the second- and third-rate dolts to run the education system. Good teachers teach, poor teachers become administrators. And, worse yet, educational theorists.

    I’m a fairly switched-on person when it comes to figuring things out. Give me a manual, and very little time, and I’ll figure it out, even if I’ve never seen the process, tool, equipment, or technique before. The number of times I was called on at the last minute to conduct training with no prep time in the military was legendary–If some instructor didn’t show up, the bosses always just went and got me, gave me the manual and said “Hey, you’re giving the class on this, right now…”. It’s a knack. And, kinda a curse.

    I’ve always been able to do this, too.

    Now, what’s screwed up? Our so-called “educational system” took a kid like that, and bored the shit out of him to the point where he could no longer tolerate being inside a classroom, period. And, on top of that, they managed to destroy any interest in math, mainly because they never, ever showed me what you could do with it.

    If I’d have had the epiphany I had about the time I was 22, when I first realized that math wasn’t just a bunch of silly-ass word games with no real use, at some point before high school, I think the trajectory of my education and the rest of my life would have been a lot different. Had I run into a decent teacher, as opposed to the hacks I had, things wouldn’t have gone the way they did, either.

    The best math teacher I ever had was a former West Point instructor in mathematics who hadn’t had a day of “education degree” training. He was a math major, pure and simple, and he taught math the way he learned it–With passion and conviction. Not to mention, a clear eye to what you could do with it. I wish I’d run into him when I was 14, not 26. Amazingly? He was then, and I suspect even now, remains “unqualified” to teach in any of our schools below college level. Go figure.

    • If I’d have had the epiphany I had about the time I was 22, when I first realized that math wasn’t just a bunch of silly-ass word games with no real use, at some point before high school, I think the trajectory of my education and the rest of my life would have been a lot different. Had I run into a decent teacher, as opposed to the hacks I had, things wouldn’t have gone the way they did, either.

      That, plus incoherent organization– putting “easy” equations with “easy” multiplication, rather than letting people get good at multiplication and then expecting them to reverse-engineer an easier one. (What else is “find X”?)

      Really wish we’d had classic logic, too, would’ve made high school math much nicer.

      • I think the biggest issue for me was that everything was abstract, taught in a sterile classroom environment.

        What triggered my enlightenment, if you will, was realizing late one night while carrying a hundred-plus pound ruck some ten-odd miles up (it’s a law of nature–targets you have to walk to are always uphill, and the ones you can drive up on are on nice, level terrain. Downhill targets will always be held by the enemy…) to a demo target, that my squad leader and platoon leader had done their demo calcs wrong–There was a way to do the job with a much smaller quantity of explosives. That, and then the next day having to go out and do recon work figuring out how much gravel and other fill was available at a local quarry…

        There’s a huge difference between showing someone on paper that “You can figure out how tall that flagpole is, with the wonders of trigonometry…” vs. “Hey, dumbass… If you’re smart, you won’t have to carry so much weight tonight…” out in the real world.

        • Dangerous to say it this way these days, but you sound like you would’ve done wonderful in a “vocational” class. I learned to appreciate multiplication while stacking hay bales.

        • While I agree with what you’re saying, you’re talking about classes beyond the level that is generally considered applicable to rote memorization.

          I definitely do like real-world examples, but sometimes those are hard to find in a simple enough form to be readily solved by the average students, so “how tall is the flagpole” is generally one which can be used for most people. Nothing is going to work for everyone, and if you’re an outlier, you have to look out a lot for your own examples. For instance, perhaps it would have worked better for you to be given surveying examples, where the objective is to determine the property line for land in dispute. I don’t know. But a lot of people wouldn’t care about that example, either.

          • I think the key thing is to make the use of math concrete, and “real”. You don’t get an appreciation for the utility of things from word problems, or at least, I didn’t. It took going out into the world and trying to do “real things” that required math for me to make the connection. I’m not sure that if my schooling had included a trip out into the front of the school to try to work out the height of the flagpole, that that would have worked the same magic with me.

            Now, if someone told me I had to figure out how much rope to buy to re-do the flagpole’s halyards, and that I’d get to keep the change I didn’t spend on the rope… Maybe. I’m inherently a lazy person, and I’ve found that if I can figure out an easier way through math, I’m fascinated by the math involved. There’s also a bit of greed there, too, sooo… You’d have to engage all three drives/motivations.

            You never appreciate the uses of a tool until you have to actually do something with it that you’re personally engaged in. I think the difference is summed up in regards to the old saw about chickens, pigs, and breakfast: The chicken is involved in the creation of your bacon and eggs, but the pig is committed

            • There’s a lot of math that works well for people if you give them pennies, or blocks, or bundles of crayons to do it with.

              My mom had a great multiplication table toy with sliders. The whole multiplication table up to 12 x 12 was on this giant matrix square encased in super durable plastic, and the colored sliders with the numbers on them slid out on the side and top and uncovered a little door with the right answer. I just liked playing with the sliders myself, but my brothers found it very helpful.

              But yeah, we had to memorize our times tables. Mom and Dad drilled us everywhere we went, and it didn’t matter that us younger kids weren’t actually studying multiplication yet when our older brother started in it.

              • Yep. This is why I’m anti-ruler. I usually got the dang things right at home, would get to school, look at the ruler and CHOKE.

                • The ruler/knuckle thing reminds me of my grandpa at the dinner table. If you reached for something instead of asking to have it passed, when sitting at the table with him, you could expect to get a butterknife handle across the knuckles. This may not of been proper table etiquette, but a couple of applications of the knife handle certainly promoted proper table etiquette!

            • As a mathematician, this “we need to make math real” thing drives me somewhat nuts. Mathematics isn’t about reality, it’s about beauty. Would you ask “What use is a Shakespearean Sonnet?” or “Why should I go see this movie? What real-life use will it have for me?” or “Why should I do this crossword puzzle?” Indeed, I decided to become a mathematician when reading Jurassic Park introduced me to Chaos Theory, which in turn introduced me to the attitude that mathematicians do what they do, not because they expect it to be useful, but because they want to do it.

              Yet mathematics can be applied to “real life” in beautiful ways. I remember a music professor who was working as a computer graphics programmer for movies. When he was in high school learning vectors, he said in frustration “When will I ever use this stuff?” Now, he uses that stuff every day. To me, though, this is more “engineering” and “physics”. (And it’s morally wrong to teach physics without introducing a little bit of calculus where it would simplify things! Calculus and physics developed symbiotically, for crying out loud!)

              Having said that, mathematics education, even before it had been heavily messed up, could use a hefty dose of appreciation of beauty. Perhaps the best call for that is “A Mathematician’s Lament” by one Paul Lockhart. And I certainly don’t trust the modern education system to do it right…

              • Would you ask “What use is a Shakespearean Sonnet?” or “Why should I go see this movie? What real-life use will it have for me?”

                Actually yes, but then I have been watching the entire collection of the AGI gunsmithing videos for relaxation and entertainment, so I may not be typical.

        • Although I know exceptions to the rule, a lot of teachers have too little experience in “real life” to design useful example/word problems. They in particular tend to use the teaching materials they’re given or can find (on line, etc), so often don’t even learn much themselves from the lesson-planning.
          We didn’t do educational quality a favor when we started making teachers spend all summer going to school for advanced degrees instead of getting seasonal jobs…

        • Heh. You just reminded me of kneeling with a stick, and deriving the angular mil system for some dunderhead who was trying pass off his ignorance as knowledge.
          Worse, he was FDC. (Fire Direction Control). A mere gunmonkey schooling him got as many knickers in a twist as any of my deliberate mischief did.

    • Yeah. I’ve often wondered why we don’t teach ASVAB style questions in High School. Figuring fuel usage and ammunition required, or ever whatever polite BS the lefties would like to convert it to, might help. I’ll never forget sitting in math class in HS listening to another kid FIRST state that he wanted to be an engineer THEN complain about taking math because, “I’ll never use this in life.”

      • Bob the farmer has five pigs. Bob sold two pigs to Bill the butcher. Each pig was sold for $1000….

        wait…. we’d offend the vegetarians..

        Dee had a vegetable garden. She grew 100 carrots. Betty grew 80 carrots. Both sold all their carrots for $1 each. How much more did Dee make than Betty? How did this make Betty feel?

        • Traumatized? Discriminated against? er… jealous?

          Capitalism is an evil tool of the patriarchy*, why should Dee make more money than Betty, just because she worked harder and grew more carrots?

          *Obviously a tool of the patriarchy because Bob made more money off of one pig than Dee and Betty made combined off of all of their carrots.

          • Funny story.

            I was recently at a “Triad” college near Asheville NC that stresses “Service” and hands on work, and they raise farm animals among other things. (Side note – the place was a weird combination of as hippy as you’d expect from the extensive vegetarian fare in the cafeteria and the girls who made no effort to be presentable, and very workmanlike on the farm)

            Anyway, we’re looking at the pig house where they have a bunch of big porkers, and a bunch of chickens the guy with the inset ear hoops described as “broilers.” Since they did raise and sell off the pigs to butchers, I asked if “broiler” was a breed of chicken or a job description….

            • Apparently “fryers” is no longer PC?
              Of course now that I think about it fryers were what we called the chickens that buy as chicks, raise for about 3 months and then butcher. Possibly those were “broilers” because they were older and need to be cooked differently to be tender, rather than due to cholesterol concerns?

              • I was going to point out that my father used to raise fryers, but I hadn’t thought about the possibility of them having different destinations based on growth time.

                • I don’t know how universal it is, but when I was going through mom’s chick catalog a few weeks back, fryer was listed seperate from broiler; I believe the difference was that fryers grew very quickly but had to be butchered early, while broilers were slower and could be butchered later. Broiler was more common in dual use breeds.

                  • Good to know, I wasn’t sure if there was a difference or if they were simply called broilers now because fried chicken is no longer considered healthy. Haven’t raised chickens since I was in grade school (did work on a chicken farm catching fryers and cleaning barns after they were shipped every three months or so during high school) so my knowledge is out of date, but I had simply never heard of broilers before. I wonder how long that term has been in use? Is that a new term, or did they have it back then and all those I was around simply chose to raise the faster growing ones?

                    • I think it use to be like the idea of someone going to the store to buy mutton, or rabbit.

                      ehow.com says fryers are 7 to 13 weeks, and roasters are three to five months old. Fryers are more tender, roasters have more flavor.

          • Even worse, Bob collected the carrot tops and other wastage from Dee and Betty’s stands after the farmers’ market on Saturdays and fed the veggies to the pigs, thus reducing his feed expenses while providing a valuable community service! And had the gall to market the porkers as having been “fed on single source organic produce.”

        • Oh no! Like that common core problem that had Suzie divide stickers between her friends and which number of stickers left over and you think… uh… wouldn’t you just cut the sheets up to make it even or leave the remainder out for yourself?

          It’s not math but we had a question on the Petrology lab I handed in today that make me boggle a bit… you see, the question was how could you use the reaction rim thickness of hornblende crystals to predict explosive volcanic events. Well, the reaction rims on hornblende in the extruding lava would all but disappear before the volcano blew but using that to *predict* events? How exactly would that work? So I got to lab and the professor chuckled and asked us if we all had fun imagining scurrying geologists taking a sample of new lava out of the cauldron and running back to the lab to test it in order to issue the warning that it was all going to blow. Of course you’d never ever DO that. And I suppose it was funny that the “right” answer was utterly impractical and she had her little joke on us, but I had trouble getting past the real-world disconnect and I’m nearly 50. Kids, particularly those young enough to think in a concrete way often CAN NOT answer an illogical “real world” problem.

          You walk 12 blocks to your grandma’s house, every three blocks you find an abandoned puppy… how many puppies do you have when you reach grandma’s house? Either “my mom won’t let me walk 12 blocks” or “I can’t carry four puppies all at once” is the right answer.

          • And if you answer “two, one under each arm” or “none” because your parents won’t let you have a dog, that is wrong.

        • Dave has an empty room that is ten feet by fourteen feet. If a single pot plant requires eight square feet of floor, how many pot plants can Dave grow in his spare room?

          If a single fluorescent light unit is four feet by eighteen inches and requires six inches of clearance around all sides, what is the maximum number of such lights Dave can install? If each light uses 150 watts of electricity an hour and is on for twenty hours a day and it takes twenty-six weeks for Dave’s pot plants to reach maturity, how much is Dave’s electric bill increased, given that electricity averages fifty cents per kilowatt?

          If each plant produces eight pounds of reefer, what price per pound must Dave receive if one plant is enough to pay the increased electricity expense?

      • Well all the engineer does is drive the train, so how much math do you really *need* for that?:-P

        • Everytime I finally start to believe that I have the skills mastered, that I’ve put in the time, that I am finally the greatest the world has ever seen…

          Someone here comes along and out smart-alecks me.

          *SIGH*

          I’ll keep working on it.

        • Well he has to make sure he doesn’t make a wrong turn at the wrong time.

        • I’m not allowed to run the train
          The whistle I can’t blow
          I’m not the one who designates
          How far the train will go
          I’m not allowed to blow the steam
          Or even ring the bell
          But let the damn thing jump the track
          And see who catches hell.
          –Unknown

          • *laughs in delight*

            I love all the variations of that which come up– supports my mom’s theory that it was a folk poem.

            Ours was:
            It’s not my job to steer the train
            The whistle I can’t blow.
            It’s not my job to say how far
            or fast the train may go.
            It’s not my job to let off steam,
            nor even clang the bell–
            but let the d’m thing jump the tracks
            and see who catches h’l.

            One of the first poems I memorized, in the bus barn when mom was subbing.

    • I caught “Mew Math” in the neck when I was in third grade – up until then I was slow, but adequate, with yes, memorizing the multiplication tables and doing long division. I still firmly believe that the New Math absolutely wrecked any interest that I might have had in doing mathematics for a minute longer than getting through algebra in high school.
      I might have done much better, if there had been some kind of teaching regimen using it to solve real-world stuff … like how many squares of tile to cover a room so many feet square. As it is, I got all the way to the age of 43 until I knew how to figure percentage – in a job I had in a department store fur salon, where the prices dropped 10% a week as the store came closer to the day it was going to close.

  3. Without rote, I wouldn’t have learned multiplication tables. Spelling lists– not such a problem for me. When I was first learning to read, the teacher would send word lists home– that was hard at six for me, but became easier as I went through a few. And back to the multiplication tables, I still have to go through them to remember them. I just don’t have an affinity to numbers as much as to words.

    • Ditto. Some nights I lay in bed and run through the times tables, or two digit by three digit multiplication, just to make sure I still have the memory and knowledge fixed.

      Re. Language. I learned Latin first, at the same time we were doing “fun” worksheets in basic Spanish. I stuck with Latin for several years before going back to Spanish, and then soaking up German like a little sponge. Ye German Prof was Olde School and pounded grammar, rote vocabulary, and chanting verb forms, just like my Latin instructors had. German took, Spanish still floats around. Rote stuck, and with the basics of Latin grammar, I can tack on other languages to the basic framework (French, survival Czech and Hungarian).

      • I learned all languages by rote EXCEPT German. I had as much German as French and at one time was nearly as fluent in them as I am in English — but twenty years with not using either, and my French is good enough to read for research AND I could get it back in a week. German? Gone.

      • Reminds me– the “fun” way tends to implant as synonyms, not a different language.

        So I royally confused folks in Japan by randomly switching in badly done Mexican Spanish!

        • I flop from Spanish into German. Depending on where I am, the other person might just follow, even though there’s a pretty large dialect difference.

          • You can actually control it? For me, both come out in the same sentence. And once that started, mixing German and Spanish has only gotten worse.

            • I think that is what they are saying, that they don’t control it.

              I used to know a little Spanish, or rather Mexican, that I picked up from working around them. I took 2 years of Spanish in high school, but never learned anything there (of course it is possible that if I would have showed up for class more than once every week or two I might have learned more, but knowing the teacher that was unlikely). Now I can recognize words if I am around someone speaking Mexican, but may or may not remember their meaning, and only recall a couple phrases to speak myself. Mainly, “No hablo Espanol.”

            • I know I’m sliding between the two, but I worked for several years around Mennonites for whom Deutsch-pañol worked. More precisely, Plaat-pañol, but we communicated and no one got killed. Now I have to stay ready to stop the German and flip to English or Spanglish when I lose a word.

              • And now all those Mennonites are my neighbors (seriously, like 3/4 of the rural population growth in the last five years has been Mennonite immigrants from Texas). Maybe I’ll have to learn Plaat-panol.

  4. Heh.

    I strongly second the “fun” project BS – having watched my kids spend hours putting together a poster for something, finding the right pictures, etc., when they could have written out a bullet list in 20 minutes.

    … and while I strongly believe that time spent focuses one, time spent hunting pictures for a collage is time spent hunting pictures, not time spent on the subject at hand. Ditto most dioramas, etc.

    I’m bothered by the many people I run into – uncomfortably many my own age – who think that my skill at adding/multiplying two and often three digit numbers in my head is some special ability. I “get” that many may not grok how powers relate and how to use them as shortcuts to mentally work with larger numbers, but the number of people, and especially kids these days in HS, who can’t fire back “81″ if asked 9×9 (I often enough, with larger numbers do 10x-x, that I often take that slower route with the times table, but *shrug*) is disturbing.

    So yeah – we need rote for stuff that is the BASICS on which all the more abstract stuff hinges, and while homework is necessary, if the teacher was really doing her job, it should be just a few more rounds of practice to make sure you can do what you were taught on your own, or do research.

    • A lot of kids miss a lot of math classes, too, because they’re being moved around. But boy, did I get in trouble when I volunteered to help tutor kids in reading, and I ended up explaining math instead to my tutoring kid one day. Especially since I was imparting the easy way to do math that involved tens.
      Sigh. As if there’s only one subject.

      • I taught Robert to do long division. The method they were trying to teach him made no sense to me, as it involved “guessing”. it made no sense to him, either. So I taught him how I was taught. Got sharp note that it was “too advanced.” Didn’t care. Neither did Robert. He still does long division that way, including the old Portuguese symbols which DO throw people.

        • Guessing? What the …, excuse me, what does guessing have to do with math? Outside of estimating how many bad guys are in the horde about to overrun your position, guessing…jeez, I just figured out some of the crazy answers I would get when I’d ask my nephews math questions. There is a reason that math is called a science, for crying out loud!!! The only time you should be guessing at math is if it’s a multiple choice test and you have more questions left than minutes to answer them!

          • marycatelli

            One of my cousins in a class on estimating used her own techniques which got more accurate results so they were marked wrong.

          • Guessing is, in fact, how long division has always been done. There isn’t any other way to do it, barring subtracting logarithms or some such, and is part of why division is difficult. You guess what the next number in the answer is and then see if your guess is correct by multiplying it out and then you correct the guess if it’s wrong. The technique in question leaves out the “correct the guess” step and does something else.

            • ??? No that is what the multiplication tables are for. If you know your multiplication tables backwards there is no guessing involved.

              • With multiple-digit values, it’s not so easy to get exactly the correct next digit, and you have to correct up or down one after you multiply it out for the next level. The number of digits required to make this necessary varies from one person to another, of course.

                • 7/510, 7 obviously doesn’t go into 5, but if you know your multiplication tables you know that 7 goes into 49 7 times so that leaves you with 20 and 7 goes into that 2 times and leaves you with a remainder of 6.

                  That isn’t the way that I would do it in my head, but that is the way I would teach someone to do it, once they get the basics down then if they are talented at math they can do such problems in their head, but anybody who has memorized their multiplication tables should be able to sit down with a pen and paper and break things down into simple enough steps to do it, whether they are any ‘good’ at math or not.

                  • And I meant 510/7, oops.

                  • Ah, but you’re still using a single digit. Try 6348/787. Is the first digit of the answer 7 or 8? It’s very close to the border, and most people won’t be able to tell automatically.

                    • That’s when, over on the “show your work” area, you write “787+787=A+787=B=787=C” until you get a number bigger than the first three you’re dividing into.

                      The “guessing” is what you do when you already have a feel for the math.

                    • Yeah, my comment a little further down says that when I was taught, it was supposed to be an educated guess, not a wild one.

                    • Ah, joys of semantics– I had a half-dozen teachers get quite snippy that an educated guess was an estimate, not a guess.

                      I now feel better that it wasn’t my imagination that it generally meant the other way!

                    • Foxfier described it well, it is still basic multiplication done backwards. IF you know your multiplication tables, you just need to know how to break it down into small enough pieces for you to be able to handle (this will vary, person to person). Once you are taught how to do that, the size of the number doesn’t matter except in the time it takes you to do it, and the more steps you have, the more statistically likely you are to ‘fat-finger’ something and make a stupid mistake.

                      Some people will be able to do 6348/787 in their head (just over 8, I didn’t bother to go out into decimals or figure the remainder*) while others will fill have a page with figures, but anybody who has their multiplication tables memorized and is taught how to break a problem down into manageable pieces can do it. The problem is that they don’t teach either of those well in school any more.

                      *I hesitated to explain how I did that in my head, because it borders on how you are saying to use educated guesses, and is not the basic way that should be taught first. But it is an alternative method of using multiplication tables, not a guess, so I’ll try to explain it. I looked at that and said 8*8=64 8*13=104 6400-104=>6348 by a much smaller number than 787, therefore 787 goes into 6348 8 times with a small remainder.

                    • I was taught that an estimate was not a guess, but generally done by using rounded numbers. For our example you would round 6348 to 6300 and 787 to 800 and…. come up with the wrong answer. :) This is why I later learned when doing cost estimates that you ALWAYS round up.

                      Gotta love semantics. An educated guess would be to look at that and say, well 8*8=64 so yeah, the answer is somewhere around 8.

            • Not the way I was taught… for, say, 571/3, you’d look at the first number and say “does 3 go into four? Yes? Does six? No?” and write 1 over the four, write three under the four, and subtract, write the two under that. Write seven next to the two. Go through the same “Does three go into twenty seven” thing.
              Ad nausium.

              I frequently got marked down for NOT writing the calculations for the three, six, nine part.

              • I got marked down for “not showing my work” frequently in grade school. I used to get in arguments with teachers over this because I did show my work. (Now I can imagine how irritating it is to a teacher to have a fourth grader explain to them that, “any idiot can see that 3 goes into 571 190 times”). I never learned long division until I was long out of high school and was attempting to teach someone else math.

                I learned many of the basics later, when trying to teach others. Because I found out that explaining that 3 goes into 600 200 times and 10 times less than that is 570, so so 3 goes into 571 190 times with 1 left over, tends to get a “huh?” response and glazed eyes.

                • Mom helped me a lot by explaining that the dumb questions were supposed to let the teacher find out if I knew how to do the work, and if I didn’t what part was screwy.

                  Surprisingly, I was a very polite kid. I never confronted except by being blindsided.

              • Just the way I was taught long division, except that I was taught to put an x under each digit as I pulled it down. For clarity I guess.

          • I think I understand it, if you work from the “logic” they use elsewhere.

            Just as they go, “those who succeed have a deep desire that happens at an early age, thus we will tell people to make a desire at an early age” they are going “folks who are good with math have an idea what the answer is before they solve for it– so we’ll try to teach people to have the idea before we teach them to solve it.”

          • The division I was taught relied on a certain amount of guessing, but it was methodical, and you were supposed to make an educated guess on what the next digit should be, then correct it if you missed.

        • Susan Shepherd

          The “too advanced” rebuke reminds me of a teacher I had back in high school… He taught math to ESL students at one point, and there was a very specific method he was supposed to use, but it wasn’t intuitive and a lot of the students were having trouble. So he switched teaching methods, and the kids started getting the material and doing far better.

          The administration caught him and told him to go back to the approved teaching method. How did they catch him? His students were doing too well on state tests, compared to ESL students taught by the official method. The mind boggles.

          This was in California, by the way. I can only imagine the situation has gotten worse since.

  5. Looking at the diversity of ideas here, it’s obvious that there is no optimal teaching method, unless your metric is a ‘best fit’ compromisory method that does well for most… which is where the value of ‘leveling’ kids comes in. I was shocked to find that my boy’s school lumps the kids in together en masse and teaches at the speed of the lowest common denominator. When I pointed out that my boy was miserable and bored out of his trees (I got some dirty looks for referring to the slow learners as the ‘cabbage patch’), the teacher mentioned some behavioral complaints- Sarah’s comment the other day about how boys don’t learn well in group settings was certainly enervating… and countering that my kid was there to learn, not to teach his peers out of boredom was ignored. I never did exercise the nuclear option (“you don’t have kids, do you?”), but it certainly was tempting.

    My dad, a marine engineer, taught me basic math with a dartboard- rapid mental calculations in the basic operations goes well with a physical component for boys. The Catholic school I went to taught multiplication tables while playing catch with a wiffleball. Yet our educators went the other way and completely removed any freeform exercise from our kids’ days.

  6. I think there’s more wrong with current education than you’ve covered here, and some of it is now full of mean-spirited contempt for a big segment of the nation’s citizens. Common Core was defended by a government official who actually said something like, “Now the white suburban parents will see their kids aren’t that smart after all, heh heh heh.” Favored students can be led through the maze, those they want to fail can be left to founder.

    By the way, I’ve seen Sarah’s sons’ writing in their school notebooks, and it’s startlingly good. Nineteenth-century professional quality handwriting, as legible as print with a good clear font.

  7. masgramondou

    Basic words and sums can (IMHO) only get learned efficiently by rote repetition. I mean I’ve seen the poor kids these days who are taught subtraction by some method that looks almost as complicated as long division and it is sad. Moreover because they never had the basics thay have no idea that 7 – 4 = 3 or 14-9=5 etc. and have to struggle through calculating each partial subtraction instead of just writing the thing down.

    It gets worse of course. The same limit means they have no idea of how to do estimation and approximation well.

    E.g. a task we had at work recently (numbers modified slightly)
    It takes the computer an average of 1 second to do this task. We have a million in the queue and we get half a million more a week. Will the computer ever catch up? If so how many days will it take? And if not, how many computers in parallel do we need to get it to catch up? etc,

    I could see right away that a single computer would be able to gradually whittle away at the task and would be able to keep up once the backlog was eliminated, but that it would take a couple of months to be up to date. OTOH if we chucked 3 computers at the backlog we’d be done in about 4 days.

    The person who asked me had no idea why the single computer was taking so long to “process the backlog”

    • I have seen time and again how “calculator kids” have no concept of approximately what answer to expect and so have no sense check as to whether they may have inadvertently miskeyed their data entry and generated a totally bogus result. It came out of the calculator so it must be correct.
      Same thing at countless registers and checkout counters. I get the strangest looks from clerks when I hand them cash and coins in what to them appears to be a totally random amount. To their credit it does become clear to most when they return my change of two quarters instead of a handful of coins, but sometimes even that doesn’t cause them to get it. It’s gotten so I will either pay the exact amount or accept that I’ll carry around a pocket full of small change rather than experience yet again that hurt look when a checker seems to think I’m messing with them. After all, the one thing that they’ve all been taught is that math is hard. In many cases it would appear that your average public school graduate considers it on a par with magic.

      • masgramondou

        But adding/subtracting 25 is hard…

        yes I’ve done the same thing. that’ll be $19.87 so I give them 12 cents and $20 . and the cashier hands me back the 12c then hand me another 13c change

        • It’s worse when you calculate it out to get back a $5 bill plus nice change.

          “That’ll be $16.84 please.” Hand them $22.09…

        • marycatelli

          OTOH, I heard professors ridiculing us at college for using a calculator to add one to a seven-digit figure. In the middle of a long chemistry/physics/whathaveyou problem. (Not math, though; you used your calculator less in math classes than in any other.)

          Apparently they managed to get tenure without noticing that “+1=” is three keys, and the sum was bound to be seven-digits, so it would take longer to key it in than to just add the sum.

      • marycatelli

        My prize was the time where the cashier’s manager actually had to come over and tell her to ring up the amount I had given her.

      • I’ve found that with some people, they’re simply exhausted and focused on entirely different tasks. Sure, for you it’s obvious– because you are dealing with “money” in your head.

        If they’re running the register, they’re dealing with sorting, grouping, codes to enter, checking for coupons, checking for fake bills, switching over to “handle money” because most people use plastic…. even the lady at my coffee place is in a totally different mental mode.

        I’ve taken to going “oh! I think I have two cents so that I don’t take any of your pennies, filling the change drawers is always such a pain, isn’t it?” type chatter.

        This came to mind because someone accused me of not knowing the math, when I knew the math just fine– I was trying to make sure I didn’t end up wearing the drink I’d just handed over, and remember if I was supposed to count up or count down for the change. (Count up– start at total charge and then count change; count down, “one, two, three, ten, twenty one two three- three twenty three is your change, thank you, have a nice day! I prefer down, personally, but up if I doubt their math… and I may have how they’re called backwards.)

        I’ve also heard that some McDonald’s put in a policy that they can’t accept any change in payment after the amount has been keyed in. Possibly for a time saver, but might be a result of some sort of fraud.

        • Wait, wait, wait! YOU’RE UNDER THIRTY AND YOU KNOW HOW TO COUNT CHANGE???!!!! Quick, someone call the EPA, USFWS, Congress, Greenpeace, and anyone else you can think of. We’ve got a real live specimen of an endangered species on our hands.

          • Had to, I learned cash-counting while laundering beer money!

            .
            .
            .
            Note, the “laundering” involved carefully filling under-thing baggies with bills, putting them through the gentle cycle, and occasionally being allowed to help mom iron them. Yes, she used a little sprayer of starch for the really old bills, or if anyone was watching and she thought they’d be amused.
            My dad’s fire department ran the beer garden at the local fair, and I took to helping mom’s 4-H kids at the county fair food booth out of self defense against boredom. Both of those resulted in some really nasty cash drawers.

        • There’s a very common fraud that involves giving someone a ten and then insisting it was a twenty, or insisting that the change given was not correct, and either bringing a lot of people along to support your claim or going through several different rounds of asking for different change for different bills. The goal is to embarrass the clerk into shorting the drawer, or the manager if the cashier doesn’t embarrass.

      • That was one advantage of the pre-calculator slide-rule days – part of the computation was to do a quick-&-dirty estimation in addition to getting the slide-rule answer, because the estimation was much better at avoiding magnitude (factor of ten) – type errors.

    • Clorinda Madsen

      As we started considering homeschooling, I browsed books and looked through my child’s homework, etc. Then we acquired through a thrift store a basic handbook that walked a child through the basics of American History, grammar, sports, whatever they thought “important”, AND, of course math.

      I started going through it with my oldest – first grader at the time. In 40 pages, it covered math through probably the 5th grade. Because it went step by step, showing you what to do and building on the previous steps in an ordered manner that made sense.

      For some reason, schools thought that if the digits exceeded X in a number, that math operation was too difficult for beginners so was pushed off to another grade. However, once my child discovered carrying and borrowing, it didn’t matter how big either number was, she could add and subtract. Once she got that you multiplied each digit in each number together in the right order and added the extra, carried number, she got multiplication. It didn’t take that long to understand the operation. But try adding 3 digit numbers to 3 digit numbers in Kindergarten and First Grade and “Oh, the kids aren’t ready for that difficulty level.”

      I know some kids take longer to understand things than others, but still.

  8. Rote learning is NOT fun for a lot of people. I get that. Hell, I LIVE that. The fact remains that not everything in life is fun and sometimes we just have to do what we need to do whether it’s fun or not.

    Yes, we’re talking about kids. Yes, it would be nice if we could make everything entertaining for them. No, that is not realistic if we want them to actually LEARN things. Yes, I know that sucks.

    Life sucks sometimes though. I was talking with a friend of mine one day. He’s a computer programmer.Given the fact that he’s been given increasing responsibility I’m going to assume that he’s a good one too. It seems though, that the longer he does it, the less he has to write. Most of his base code is so good that he uses the same code (or at least a large portion of it) for pretty much everything he does. Yup, even in the real world adults have to do things by rote sometimes.

    Now, I’m not saying that everything should be by rote. Rote doesn’t teaching thinking and thinking is an important skill. But it is also necessary to learn how to analyze information in order to use it. Before analyzing information it is necessary to gather it and once it is analyzed it needs to be expressed. Can you see where this is going?

    In order to gather information, one must be able to read. In order to analyze, math is quite frequently (and, no, not always) useful. Expressing information is most often done either by speaking or writing and both skills can be learned and improved by rote. It’s after the three Rs are learned that the rest can be taught. They are the basis for everything else.

    • marycatelli

      Indeed, the exact details of what is learned by rote is less important than mastering the skill of applying yourself to something less than fun.

      Of the generations of children who grew up with these pedagogical methods, it is striking how many of the more intelligent among them sense by their early twenties that something is missing from their lives. They don’t know what it is, and they ask me what it could be. I quote them Francis Bacon: “It is a poore Center of a Mans Actions, Himselfe.” They ask me what I mean, and I reply that they have no interests outside themselves, that their world is as small as the day they entered it, and that their horizons have not expanded in the least.

      “But how do we get interested in something?” they ask.

      This is where the baleful effect of education as mere entertainment makes itself felt. For to develop an interest requires powers of concentration and an ability to tolerate a degree of boredom while the elements of a skill are learned for the sake of a worthwhile end. Few people are attracted naturally by the vagaries of English spelling or by the rules of simple arithmetic, yet they must be mastered if everyday life in an increasingly complex world is to be negotiated successfully.

      More on the horrors of education here:

      http://www.city-journal.org/html/5_1_oh_to_be.html

    • I view rote memorization as the mental equivalent of push-ups. The ability to do a push-up is rarely applied in the practical world, but the upper body strength and balance it develops are frequently handy.

      Knowing the multiplication tables is not in itself especially useful. But the concentration required to (and developed by) that task is important. Memory is a learned skill and the ability to hold the entirety of a complex problem in your mind is facilitated by the concentration developed through rote learning.

      Further, the process of such memorization is handy for developing an understanding of various recurring patterns, such as those relating to multiples of three, of five, of nine and even of ten.

  9. Best and most entertaining way to learn French? Be in the classroom when your Mauritian-French teacher trips on the podium and drops a box of books on her recently-broken and just-healed big toe.

    I learned a lot of new words that day, all spoken at very high speed and in a fluent Mauritian accent. I hadn’t the faintest idea what the words were, or what they meant, but since the class was recording our pronunciation at the time, they were captured on tape in glorious Technicolor (well, they were rather colorful expressions!).

    When our teacher returned from the school nurse’s office with a heavily bandaged toe, we’d already left for our next class. Someone (naming no names) took the cassette tape with him, copied it that night, and distributed the copies the following morning. We translated her rapid-fire fluency with the help of some sailors on a visiting French warship a week later – we couldn’t find most of the words in the French-English dictionary for some reason. The sailors were so impressed they asked us to introduce them to her. She seemed less impressed when she found out why we were doing so.

    Ah, the joys of youth . . .
    :-)

    • What a *splendid* story! I keep trying to collect Expressions of Extreme Agitation from my various foreign-language colleagues, but they can be tiresomely mealy-mouthed. (I do know how to say something rude in Korean)

  10. If it requires glue, it’s not homework, it’s BS.

  11. Gonna uncork an opinion here that might seem like fightin’ words. So I want to stress the disclaimer that this is JUST an opinion.

    I’ll tell ya what’s wrong with edumication these days. The teachers — er — educators either grew up in the ’60s or were trained by people who did.

    And they’re all a bunch of — as Rachel Lucas puts it — a bunch of whiney titty-babies.

    All during my publick skooling, which lasted from 1960-ish to 1972, I heard kids whine (why do I need to learn THIS?) (applied to any subject matter). And the adults (appears there are none in the modern school system) would say, “Learn it or you’ll regret it Because I said so.”

    Very shortly after I left the publick edumication system (no system and very little edumication), I began to hear the same witterings from soi-disant “educators”. Including arguing against the teaching of history as “Names and dates (to no purpose)” and teaching by rote (all you get from that is a bunch of repetitive parrots)(never mind that a thousand generations prior learned just fine by memorizing times tables and all the begats in the Bible. Have to agree with Glenn Reynolds. Sending your kid to public schools is tantamount to child abuse.

    M

    • The boomers, those born in that period after WWII, or roughly 1945-1960, were the first generation to have ready access to a college education. And for the most part we were strongly encouraged to go for a liberal arts degree first then if we really wanted to we could look into an advanced degree in STEM, though it wasn’t called that at the time. I was the smartest person in my graduating class and all the teachers and counselors knew it, so I was under so much pressure from all sides that upon graduation I took a factory job and didn’t enter college until fifteen years later. BS-ISE, MS-OR thank you very much.
      Anyhow, suddenly you had all those kids usually in their junior or senior year towards a BA in some area of concentration realizing they were actually going to graduate and have to get a real job much too soon. Far too many of them decided the shortest route to a job with decent benefits and a good deal of security was to add those courses required to get teaching credentials. And so we wound up with a crop of teachers with no real desire to teach. Some apparently did not even particularly like kids, but they got to dress well, were paid OK, and the vacation time was very nice. Those that truly disliked the kids or were simply incompetent as teachers quickly migrated into administration where they proceeded to do real damage on a macro rather than micro scale.
      Don’t get me wrong. I know of many fine teachers, but almost invariably they have been successful in spite of the system rather that because of it. And of late most such are being driven out of teaching when things like common core (as implemented rather than the well meaning intent) make it impossible to teach anything of substance.

  12. Yes, and no…

    I was a serious Math whiz when younger (it was all downhill from 13) and self-taught my way thru the entire advanced math curriculum (senior year) by 8th grade, just going thru the textbooks. (My small private school was accommodating and sent me off to college math in high school).

    I agree entirely about rote memorization laying the foundations for many fields (language, history, arithmetic) by providing the basic starter set of tools. But I was also tutoring my classmates in math from an early age, and there’s a point beyond which memorization ceases to be useful. It takes a certain sort of intuition to approach math proofs or to solve algebraic equations or to do a geometry proof. Following along with someone else’s solution is straightforward (like playing a composed piece of music), but creating that solution yourself, attacking the problem in a useful way, is much more like musical composition — you have to have a holistic grasp of the domain to understand how to approach it and a certain amount of creativity. (I remember doing basic geometric proofs by recreating the necessary precursor parts myself, rather than applying them as a memorized list of rules. Ah, those were the days…)

    This was not something I could teach to my 13-year-old classmates, though I understood the problem perfectly well. I could give them a list of approaches to try, in a general sense, but I couldn’t help them understand them as anything other than lists. They have to do that for themselves and not everyone can. It’s like having a tin-ear for music — no way to teach around it.

    • Back when I was interviewing people for technical teams one of my favorite questions was how they felt about math story problems. Always got one of two answers, either love them or hate them. As you so correctly point out taking a real world situation and translating it into an equation is an art and some folks simply lack the ability.

      • I love story problems. Always did.

        • Story problems are awesome, as long as they’re fair. Bad math programs usually feature unfair story problems, or badly written ones which require several layers of decipherment.

        • I don’t know why I have problems with story problems considering I had to have a smattering of algebra and calc to be able to troubleshoot electronics.

        • I loved story problems, although occasionally you would get the really stupid ones where you would go, “why would anybody be stupid enough to do that?” While this answer may be acceptable in R&D, teachers tend to frown on it.

    • There’s a big truth in this. As you (and Sarah) say, there’s a role for rote. An essential role. But there comes a time to move past rote, and at least when I was in school, they weren’t doing it.

      I had massive problems with algebra because they were teaching it as a rote process, and my brain just wasn’t making the necessary connections. I couldn’t click. They predicted I’d do horribly in geometry, and I breezed through (so much so that the teacher sent me to the back of the classroom to work on off the cuff projects so I’d quit disrupting — I was a smartass.) The difference between the two? I could derive the reasoning behind geometry and make the logical connections between the exercises and application. Nobody was interested (or, I suspect, able) to provide such information for the algebra.

      Algebra finally clicked for me in college, during a political analysis course, working with statistics. You know, actually using the equations for a purpose. Oddly, all those kids who were so good at spewing the rote exercises back couldn’t seem to figure out how to assess the variables in the statistical data and plug them into the equations.

      For my own pet theory, all of this derives from two major issues:

      We keep pushing back the age of maturity, and delaying the requirements of adulthood. You tell 14 year olds they’re children and you get children at 14. You tell them they’re adults and they head West and settle the frontier. (I do realize there are multiple developmental realities in the teen years, I’m not advocating kicking everybody out into the real world at 14. I am advocating starting to let them carry some of the responsibilities of adult society.) So we keep feeding them easily digestible soft education and praising them for managing to walk and we keep losing them.

      It’s a subtly disturbing thing to watch a high school student (and his mother, a teacher) gushing and proud of a cut and paste diorama. For history.

      The other issue, for how ever many cycles now education has been an experiment. And it takes decades to get the results, so we run x number of kids through and change some things, and run another x through, and makes some changes… And we just keep working our way through some ed admin major’s pet theories and screwing whole generations.

      I know I went from a student excited about going to school and learning to a frustrated smart ass seeking out my own education and bothering to do exactly as much as necessary to get by. Teachers really hate it when you ignore all their little assignments and ace their tests. They really hate it. That transition started on the first day of kindergarten, when I went in ready to continue working on reading and work with those funny numbers — and they started teaching us to color inside the lines. :\

      Mortally offended in kindergarten, all else follows from there.

      • “And we just keep working our way through some ed admin major’s pet theories and screwing whole generations.”

        ^^^ this and this again until it sticks (see–rote!)

        Every education major, who is progressing in his own education, will eventually have to do some original research. HE WILL DO IT TO YOUR KID. And since he’s been participating in his fellow Ed major’s student projects, it all seems perfectly normal to him to “study” his classroom charges. Teaching them is secondary to advancing his own research and studies. The stories my good friend told me from his adventures in a very rough district near LA are horrifying and eye opening.

        The deck is stacked against the students and I’m dreading my daughter’s entry in the system, after very successful years in a Montessori program.

        I’m gonna try Sarah’s technique, use them for cheap daycare and educate my kids after….

        z

        • My take is that we’ve been teaching basic math skills for roughly 7,000 years, and writing with an alphabet for roughly 5,000 years.
          We’ve had enough trial and error to know what generally works, and what generally doesn’t. Any “ground-breaking” innovation in the field involves digging up the corpse of an idea best left buried.

      • Teachers really hate it when you ignore all their little assignments and ace their tests. They really hate it.

        Which explains the… 8th grade…?… science teacher I had, who insisted that he was going to “teach me a lesson” by giving me a poor grade for reading books in his class and when asked a question, glancing up and answering, then immediately going back to what I was reading. Beg pardon, correctly answering, then going back to my reading. (I wasn’t a smart aleck. I was quiet. And very focused on my reading.)
        The poor unfortunate soul made the mistake of explaining this to my mother when they met in passing in a grocery store parking lot. It’s the closest I’ve ever seen my mother to being in a killing maiming rage that wasn’t directed at myself.

        • Oddly familiar, that.

          I’m not in this class to learn to respect authority. And if you (abstract teacher ‘you’) suddenly decide that instead of science (english/history/sociology…) you want to teach me respect? Gosh, then I guess we’ll have a discussion about respect, from where it is derived, and thus how much I actually have for you in this context.

          Or do you want polite? Because I’m fully capable of polite, and am inclined to it by nature and parental (and grandparental, occasionally uncular, etc.) training.

          I was a smart-alec, but I came by it somewhat honestly. Being the target of teachers who couldn’t deal with the canted brain and especially not the smarts. My patterns of response were set in elementary and I was a bit — sensitive to provocation from there on. Small town, though, so most of the smart teachers figured out how to handle me before I ever ended up in their class (and gained my respect, as a result). The rest? Hm.

          • Yep. I’ll show you some respect as soon as you show me that you deserve some.

            • Or extend some.

              Surprising, the number of teachers who cannot extend basic courtesy to students, much less respect. Insisting upon receiving deference for imparting demonstrably incorrect information, and then treating students as idiots… This does not make for happy schooling.

          • Sounds like what I usually did in my History classes. Read the book in the first week or two of the semester, cover to cover, and then spent the rest of the year reading other stuff. Usually Edward Clinton Ezell’s “Small Arms of the World”, which was my go-to “I’m bored out of my skull…” reading.

            I think what would usually piss off my history teacher the most was that he’d try hitting me with some seriously off-the-wall question about whatever we were studying, and he’d invariably get 15 minutes of elocution addressing his question in nauseating detail. Got to the point where other students were begging him not to call on me, and God help the poor substitute who made the mistake of calling on me. They usually learned not to, after getting one of my patented fire-hose answers.

            Looking back, I’d have been a lot better off if I’d simply canned high school, and gone down to the local community college. Unfortunately, the money wasn’t there for that, sooo… I was a very, very bored young man.

            • Oh, yeah – I remember doing that. To high school history teachers and to a couple of junior college profs as well. Nothing like the fun of making them run for cover when I deliberately asked detailed questions to which they likely didn’t know the answers to.

              • Ah yes, the detailed questions about something the teacher knows no more about than what is on the paper just handed out shtick. :) That was always a good warning to the teacher to, “leave me alone to ignore you in peace, or you are really going regret irritating me.”

                Very occasionally used when I showed up for class without anything interesting to read (or finished what I had, or found whatever book I had less interesting than I thought it would be). Usually I only showed up to class if I had a book I wanted to read, I do recall having a history teacher see me walk through the door with only a pencil in my hand one day however, and asking me if I would like a library pass (this was before class even started. I believe I had that particular teacher well trained :)

  13. About retrieving cats…

    I enlist gravity-assists on my side. I throw the paper wads or other balls up the staircase to a high step, and the cats play them all the way down to my feet. Unlike genius cats, all my ordinary cats get the point of this in a hurry.

  14. marycatelli

    I recently told online the story about a high-school chemistry teacher who found that her students could not memorize. She’d hand them the list of ions to memorize, and they’d have no clue how to do it.

    Someone loftily claimed that chemistry was all logic, that just as a student learns to build words from the alphabet, sentences from words, and paragraphs from sentences, so too all you have to do is look up the atom on the periodic table to know its properties.

    Someone else pointed out that you have to memorize the alphabet too.

  15. I believe most people are under the impression that we have an educational system, when we actually have is just a tax-funded mandatory daycare (where good teachers and learning are possible but not really the goal). I also remain firm in my belief that many of the problems we see would be taken care of if more parents would simply read to their children.

  16. I’ve pointed this out before, but I’ll repeat it, because of the nature of the post:

    Regarding whether rote memorization of the basics works, the vile progs simply don’t care. I bring up again the friend who is totally against rote learning, because when he was learning multiplication, he had troubles with his 3x tables, and had to do them over and over. Even when I asked him, “So, what’s 3 times 8?” and he immediately answered 24, and I pointed out that it had worked, it didn’t matter to him. It was still wrong in his eyes.

    • Washing dishes is wrong too, I don’t like washing dishes, and they need washed over and over again, after every time I eat off them in fact.

      • The dish problem is easily resolved by only eating food that is chucked out a window at you, wrapped in easily disposable foil-lined paper.

    • As Thomas Sowell has amply demonstrated, the important consideration to the vile prog is not whether a process works, it is whether the process enables the vile prog to declare aesthetic or moral superiority. Requiring a process be effective is so very bourgeois.

  17. A propos of this discussion, see this article on teaching 5-year olds calculus. http://www.theatlantic.com/education/archive/2014/03/5-year-olds-can-learn-calculus/284124/

    Personally, I’d be more impressed with algebra.

    • Clorinda Madsen

      My husband has been “lulling our children to sleep” since the beginning by explaining what quaternions are. What’s a quaternion? Well do you know what a ring is? Blank stare by infant. How about a polynomial? Continues blank stare. He backs up to the very basic math concepts then starts explaining it. He loves math. Every so often, he will still give a mini lecture about a math concept – recently the Pythagorean Theorem. My oldest, who is still working on multiplication and division enjoyed his lesson and followed the theory of it. She was getting it. Kids do have greater capacity to understand than we give them credit for.

      • I taught the Daughtorial Unit how to do exponents by observing that her next birthday (her eighth) would be a “cubed” date. The explanation required less than ten minutes (that being the length of the drive we were undertaking) and extended to discussion of other “significant” birthday anniversaries.

        Mind you, I spent my twenty-seventh birthday proudly announcing to people “I’m three!!!”

  18. “I’m a fairly switched-on person when it comes to figuring things out. Give me a manual, and very little time, and I’ll figure it out, even if I’ve never seen the process, tool, equipment, or technique before.”

    I was directed to an article this morning about teaching five year old kids to learn calculus. The concept was to teach that the goal was/ is an answer in calculus: That caused the child to have to grasp addition, subtraction, multiplication, division in a practical manner in order to reach the goal. At least that was the inference.
    My high school math teacher called me in the eleventh grade and told me that he would pass me in trig if I promised not to take Calculus next year.
    Ten years later, I went to college- military and other employment between- and took the required math class (Dumbell, I think) The instructor said “Math is a completed, correct sentence” and had us doing Algebra verbally while standing beside our desks within a week.
    Rote is good, understanding while learning (which may/should include rote) is not the same as making a group poster where the goal is posters. I need to improve my Spanish and want to learn Japanese. I will start the rote word/sentences practice. Just speaking doesn’t woke well but- writing?
    I have a beginning calculus book plus the Frynman’s tips books and will read when I have time. However, I think I have been using rudimentary calculus all my life, just getting through the day. I wonder why my high school teacher missed the practical applications.

  19. While I’m typing, someone else is saying it. Need speed drills.

  20. I have a question. Has anyone ever used a Venn diagram in practical application? Algebra, calculus, Boolean algebra, sure, but Venn diagrams?

    • Yes – in English Literature– sometimes while setting up a paper.

    • Yes. To explain plots that you’re interested in with plots that make sense to others. Now, mind you, that’s an odd use, so…

      • See now I wouldn’t consider either your or Cyn’s use practical. You are simply using them as an aid to do another theoretical/cerebral task, not to actually do something practical.

        • Making the theory and cerebral task hold still instead of going skittering away while you work the next bit is highly practical.

    • In various pattern analysis applications is useful to illustrate the intersections. Some scale issues can be more readily discerned graphically, particularly relational scales.

      The problem with Venns isn’t Venns, it’s that folks thank “Oh, cool! CHARTS!” and then start throwing them about for the pretty colors…

      • Apparently, the school I went to was odd. From about third grade till somewhere around freshman year of high school, the first two or three weeks of math class was a dead dull review of basic Venn diagrams that everyone had mastered the first time. I guess it has become a pet peeve.

    • Birthday girl

      Yes, but never in a mathematical context. I can see where you might use one in designing a computer program, but I’ve never actually seen that done. Programmers seem to use decision trees instead.

      • QA / Testing of yer output (and debugging to find where root causes were introduced) — and then explaining your process to management that doesn’t / CAN’T “think” in terms of flowcharts or other visualization tools — can be one place the software developer actively needs to use Venn or similar concepts.

    • Conveying information– especially for logic– and organizing information.

      “All cats are mammals, some cats are red, some mammals are not red.” type stuff.

      No, I can’t think of a better example right now, but think like Sir Vimes trying to figure out what his clues mean. It’s very useful if your brain is assuming something without your noticing.

    • Oh, and my math classes never got to Venn diagrams.

      Yes, you may hate me for that.

      • We used Venn diagrams (and didn’t learn what they were called) for basic Set Theory, and nothing else.

      • I had to look them up on Wikipedia to see what they were, yes I have seen them before, but not in a math class that I can recall.

        I can’t recall actually ever making an exact one, but have did rough and dirty/back of the napkin ones to convey information like in your first example.

    • I sort of did that when putting together complicated excel sheets when, for example, doing calculations that include hours that were chargeable as basic pay but could not be included in calculating overtime. It was the IF/THEN function

    • Yes – to demonstrate why I trusted Beloved Spouse and friend to select toppings for a pizza to be shared by the three of us. I demonstrated that the overlap of the set of pizzas acceptable to Beloved Spouse and the set of pizzas deemed edible by friend contained zero pizzas that did not meet my criteria for edible pizza.

      This demonstration was performed shortly before people stopped asking me to share pizza with them.

  21. The human brain has a remarkable capability for recognizing patterns (even if none actually exist!). The problem with many in the anti-rote learning camp is that they don’t acknowledge this and pretend that if they don’t explicity explain everything to little Johnny, he’ll never grasp the underlying concepts on his own. In fact, the opposite is true: once you become so proficient at the basics that you can do them without thinking, then you can focus that energy on the why of how they work. It’s no different than a martial artist who has to learn the basics of how to strike, throw, block, etc through repetition so that he can focus his mind later on the higher concepts of why a technique works.

    • An appreciation for patterns, however, is not enough. I can vividly remember the frustration I felt as a child when I stumbled across the decimal patterns of the reciprocal of primes (*) and had no tools (and still don’t — something to do with modular arithmetic?) to explain the “why”.

      (*) Brief explanation… 1/7 = .142857(repeats infinitely), 2/7 = .285714, 3/7 = .428571, etc. For any prime I was able to show (but not prove, at 12) that 1/prime = .xxxxxx where the cycle of repeating digits was static but started in a different place for each, and the number of digits (N) in the repeating cycle was (prime-1)/N = integer. In other words, all 7ths followed one cycle of 6 digits, all 13ths followed one of two cycles of 6 digits, etc., and the pattern of which 13th followed which cycle was elegantly patterned itself. The number of cycles for each prime was not predictable (by me). (I spent much of my youth playing with Friden machines (mechanical calculators) on weekends in my father’s office running out tables of these patterns.)

      I could very vividly sense a deep fundamental property of numbers and primes, but there was nothing I could do to carry it further with the tools I had, and I couldn’t even find an adult to whom I could explain the insight. By the time I blew off advanced math in college, I hadn’t gotten back to this one, so it remains a mystery to me. I know I wasn’t the first (I’ve run across fragments), but I can’t recreate the tools from scratch to deal with it. Hit my own limits and needed someone else’s shoulders to stand on, and couldn’t find any.

      Spare a thought for the otherwise competent math teachers in 6th and 7th grade trying to deal with this. :)

      • Oh, and BTW, when I say “stumbled” over this, it’s because I was in 6th grade learning decimal fractions for the first time and the fact that there was a pattern for primes became, somehow, immediately obvious to me. This was before the school let me accelerate legitimately thru all the math material in high school, instead of just reading SF paperbacks under my desk, bored stiff by the pace of the class.

      • masgramondou

        I did not know that. Or at least had not observed that before.

        One of the things I’ve found very useful is that 10/7 = sqrt(2) (more or less). Helps a lot when you are trying to do certain trig calcs in your head. And even more when (in the old old days) you are trying to do rough trig calcs on an 8 bit computer with 48k of memory and no floating point in order to rotate a square on the screen.

      • Now, it’s been over 25 years since I studied any of this, so my explanation will be more descriptive, and less proof-ish, but let me see…

        Any fraction that does not end after a finite number of decimals will begin repeating after some number of decimals, because you eventually run through all the possible permutations of divisors and remainders. Once you have gotten back to a remainder which you have already seen, the cycle begins again.

        Take, for an example, 22/7, the poor man’s approximation of Pi:

        22/7 = 3 rm 1 (rm standing for “remainder”)
        1.0/7 = .1 rm .3
        .30/7 = .04 rm .02
        .02/7 = .002 rm .006
        .006/7 = .0008 rm .0004
        .0004/7 = .00005 rm .00005
        .00005/7 = .000007 rm .000001

        Now, we are back to a remainder digit of 1, which puts us back at the second digit, beginning the repeat: 3.142857142857…

        Larger numbers, which can have multi-digit remainders, can take longer to begin repeating.

        • Missing the point, I’m afraid, Wayne. It’s not that there’s a repeating set of digits, it’s that the behavior of prime reciprocals is different and highly patterned. Any non-prime not divisible solely by 2 and/or 5 will generate a repeating decimal portion (hence the application of modular arithmetic to generalize it away from base 10).

          Trivial example: 6 (not prime). 1/6 = .16666666…. That does not behave like 1/7, or all primes greater than 5 in base 10, as described above. (And notice that only part of it repeats, which is not true for prime reciprocals).

          About the time I stopped playing with this, I was trying to see if reciprocals of compound numbers not factorable by 2 and/or 5 (in base 10) had predictable patterns (e.g., 1/(7*13)) and had reached inconclusive results.

          Also, it’s not true that larger primes necessarily have longer patterns in their cycles. The max length of the repeating decimal is (prime-1) & cycle count = 1, but cycle doesn’t have to = 1, so that is not the minimum length — length is unpredictable (part of the underlying sensed number domain pattern). For 1/7, length = 6, cycle = 1. For 1/13, length = 6, cycle = 2. For 1/17, length = 16, cycle = 1. 1/7 and 1/13 have the same length. There is no obvious pattern in primes < 1000 (and I looked). Length is not predictable AND cycle count is not predictable, but length * cycle count = prime – 1.

          I was of the opinion that this was probably a candidate for a prime test: divide suspected prime into 1 and count the digits until it repeats. If suspected prime divided by length = integer, then it's a prime. (Oversimplifying for primes below 7.) I'm sure the devil is in just how you identify a repeat for a very large prime, so maybe it's not a useful test. In any case, I didn't have the tools to research it.

          • From the description, I’m not understanding what you describe as, “cycle count”.

            • Saying it went somthing like, with P= a prime:
              1/P=0.234512345123451 (repeating)
              2/P=0.345123451234512(repeating)
              3/P=0.451234512345123(repeating)
              4/P=0.512345123451234(repeating)
              5/P=0.123451234512345(repeating)

              • Er, or maybe it’d be clearer:
                1/P= .ABC(repeating)
                2/P=.BCA(repeating)
                3/P=.CAB(repeating)
                3/P=.ABC(repeating)

                • Yep, Foxfier — absolutely correct (except you should kill the last line of the example). The cycle is the set of repeating digits in the reciprocal. 1/7 has a 6-digit set; each 7th using the same digits in the same order but starting at a different place = 1 cycle. 1/13 has 2 different 6-digit sets; each 13th using the same digits in the same order of one of the sets but starting at a different place = 2 cycles. I call them cycles because the digital reciprocal extends/repeats infinitely, rolling like a wheel.

                  Predicting the number of cycles for a prime reciprocal was not… predictable or patterned (to me), (Primes are very strange — I read somewhere they’re making progress on twin primes (primes separated by 2, like 17 & 19, 41 & 43). The use of primes in encryption has accelerated the commercial use for research.)

                  When cycle count > 1, predicting which Pth manifested as which cycle was unpredictable (to me), but definitely patterned. The patterns include mirror or mirror inversion symmetry and other effects. For cycle count > 2, symmetry issues are more complicated. Patterns within patterns, wheels within wheels.

                  Example for 2-cycle 13, showing mirror symmetry around the midpoint. Cycle assignment pattern: ABAABB BBAABA
                  1/13 (A) = .076923
                  >>> 2/13 (B) = .153846
                  3/13 (A) = .230769
                  4/13 (A) = .307692
                  >>> 5/13 (B) = .384615
                  >>> 6/13 (B) = .461538
                  >>> 7/13 (B) = .538461
                  >>> 8/13 (B) = .615384
                  9/13 (A) = .692307
                  10/13 (A) = .769230
                  >>> 11/13 (B) = .846153
                  12/13 (A) = .923076

  22. Yep – used a Venn just the other day to help an HR-type finally realize that if she continued to recruit folks who did not possess certain contract-required certifications, that the company would not be able to bid on nearly 80% of the RFPs coming out from one particular customer. As this customer represents 100% of the company’s work, she really was sort of sticking it to herself. Gotta love those visuals.

  23. If Auntie Beeb hates you, you are doing something right.

    Recommendation: Read 1984, and then listen to the Goon Show’s parody version of 1984, which is actually more savage about the BBC parody inherent to 1984.

  24. Clark E Myers

    Math is a family of languages – e.g. Rubik’s Cube is a dialect and to solve it requires developing a sort of creole vocabulary for states and moves. The best guide to the process of learning languages I’ve ever seen is How To Learn Any Language: Quickly, Easily, Inexpensively, Enjoyably and on Your Own by Barry Farber Well worth reading as a memoir too. Looking at Amazon reviews some get it and some hate it. Problem solving is a lot like composing including “playing the sedulous ape”.

    The best description of modern education I’ve ever seen is the The Barometer Story reputedly “by Alexander Calandra – an article from Current Science, Teacher’s Edition, 1964.” but I’m sure familiar to many if not all here. Not at all dated

    Some time ago, I received a call from a colleague who asked if I would be the referee on the grading of an examination question. It seemed that he was about to give a student a zero for his answer to a physics question, while the student claimed he should receive a perfect score and would do so if the system were not set up against the student. The instructor and the student agreed to submit this to an impartial arbiter, and I was selected………At this point, I asked the student if he really didn’t know the answer to the problem. He admitted that he did, but that he was so fed up with college instructors trying to teach him how to think and to use critical thinking, instead of showing him the structure of the subject matter, that he decided to take off on what he regarded mostly as a sham.

  25. marycatelli

    “Worse, as I found out, the teachers don’t even remind the kids that homework is supposed to be turned in. “Oh, I told them two weeks ago. They’re supposed to remember.””

    What you should do at that point is get a doctor to certify that your child is disabled (even if it’s called childhood) and can’t do that. Assuming the state issues — I forget what it’s called in mine — orders that teachers have to accommodate disabilities.

  26. Busy work. I absolutely loathe busy work.

  27. I do have to wonder about who, exactly, could possibly think that making schools focus even _more_ on homework could possibly be a good idea, considering how the superabundance of it we already have has already reduced “home” to being “that place where I sleep and eat two thirds of my meals and sometimes see those grown-ups that the TV says are called ‘my parents’”, all to focus on useless, meaningless busywork whose principal effect is to divide the kids into two groups: those who obediently chant along with whatever Authority tells them to do, and those who mindlessly rebel against anything and everything that smells even a little bit like Authority. Neither of which is precisely a healthy attitude. Both of which, in their own ways, serve the interests of the all-consuming Leviathan state. By which every single person who has any kind of role in the promulgation of educational practices is employed…mostly in the sort of career in which one proceeds directly all the way from eating paste to collecting Social Security without ever once spending more than three consecutive months outside a classroom to learn how the productive world operates. Gee…I wonder if that’s a coincidence?

    Why, yes…disputes over homework _were_ the whole reason I almost flunked out of high school despite an IQ repeatedly measured either six or seven sigmas above the mean and the kind of brain that, when ordered to memorize multiplication tables, basically invents algebra instead out of protest, only to be bitterly disappointed a couple of years later to discover that somebody else already invented it first. (But probably not quite as disappointed as my uncle was when, at the age of 8, he discovered that somebody had beaten him to inventing the crossbow. Hey…we’re a weird family.) They also came _dangerously_ close to turning me off of reading as a recreational activity…if I hadn’t been doing it for fun since before I was 3 (and hence _years_ before teachers got their hooks into me), I very much doubt I’d do it at all today, except under duress. (Why, yes…I _do_ fall a lot closer to the “mindlessly rebel” end of the reaction spectrum than the “obediently chant” end. Why do you ask? :) )

  28. “got picked up by the BBC who thought she was “maligning a whole generation.” – I missed it! The Beeb also picked up a ‘not in my name’ anti-Australian government protest about the new boat-people ‘refugees’ policy – which had 250 contributors (comments with selfies) and presented it as representing the dissatisfaction of Australians about the policy. (that’s about 0.001136% of the population). Yes, you can rely on the Beeb. I guess the 99.99886% are unimportant or something.

    • Dave, I would have missed it except for the fact a few folks — most of them readers of this blog or MGC and Toni — either pinged or emailed me about it. And still I don’t have my “I’m evil” membership pin. Sigh ;-)

  29. As much as I can make a case for rote, and can follow the cases AGAINST rote, I find that bridging the gap / scaling the wall beyond what rote can accomplish is where the biggest hurdles lie without regards to what comes before. Learning to think critically — to “really” think — does not happen with rote-learned methods by themselves, and certainly seems to happen even less often with the fun-fun-fun semi-free-associative are-they-really methods in vogue these days. (As others have already noted, one person’s fun is not always mirrored by another individual’s preferences.) Critical thinking can accommodate both foundations, though, and often the “ah-HAH” moments in my own life have happened when I was forced to / needed to straddle the divide between the different types of learning I had previously received.

    Understand for a moment that I was raised in a mostly-rural setting with limited resources. One of those resources I “wasted” many pleasurable hours with was a set of the World Book Encyclopedia. (Yes, I was taunted at one time about reading the encyclopedia for fun. Put on my most puzzled look, stared the commenter square in the face, and said “So?”) Date&place history with enough context thrown in to get a feel for when and where, basic summaries of basic science, and all the rest of human intellectual investigation boiled down and packaged. This was late ’60s, early ’70s, and I had pretty good teachers in school, so no special complaints — that was my academic foundation, and it carried over well enough into college/university.

    The base set of that encyclopedia was published in 1948, so I learned how to use the Yearbooks to build upon a base, and that contributes to my central thoughts here: The most-important piece of root knowledge I received was learning to learn root-concepts FIRST, and develop the ability to reassemble them as needed later.

    A general explanation may be illustrative of what that approach meant as I went forward in life. Never having had a formal speck of classroom French, I still have a demonstrable reading comprehension roughly 40 percent accurate (as long as the reading text isn’t TOO colloquial); same for other “Romance” languages that haven’t drifted too far from the Latin roots or been too reliant upon elements from non-Romance and non-Germanic sources. German, I had two years in high school, so my reading comprehension is maybe 60-plus percent in texts where I can puzzle out the font (less for Fraktur or some of the older very dense typefaces). And the majority of all that comes from studying word roots as part of the vocabulary tests we received weekly.

    Not spelling tests. VOCABULARY tests, and the underlying instruction / study time devoted to building vocabulary.

    BLESSINGS UPON YOU NOW AND FOR A LONG-TIME TO COME, Pauline Wilson, Bonnie Dage, and Frau Teders . (And those who came before you, and made me WANT to learn how to express myself intelligently.)

  30. “but which ends up imprinting the idea that obeying pointless instructions is good.” I think you hit the nail on the head at this point to be honest. Compliant little drones cause the powers that be less trouble, to their limited thinking. Great blog btw, followed a link trail from Vox’s blog and spent a good long while reading.

  31. “… kids are taught is that they must perform senseless tasks they don’t want to do, which accomplish nothing…”

    That’s the formula for creating a bureaucrat.

    • No, bureaucrats perform senseless tasks they want to do, while not performing any tasks that either a) they don’t want to do, or b) accomplish anything.

      • …that cause them to actually work, that they might get blamed for in the future for doing, or they will get notices for not doing.

  32. Actually, Sarah, I don’t think kids need more homework as much as they need homework that actually helps them learn the subject. My objection comes when school districts say a teacher isn’t to assign homework period or, if they do, they can’t grade the homework. My issue is with the tendency of schools to teach our kids they can do what they want, when they want and there will be no consequences. It goes hand in hand with the everyone is special and not keeping score on the playground. We’re raising a whole generation of kids who will get out into the real world and not know how to cope — so they turn into GHHers and their ilk.

    As for the rest of it, you and I are in total agreement.

    • As I said, I figured we’d just encountered different slants of teh stupid.

    • My sixth grade teacher asked us if we thought we should have homework. I said no. My parents also felt that 8 hours was enough and that more work at home was counter productive and ought not be necessary. After she verbally harangued me for having an unacceptable answer to her question of opinion (she actually was emotionally abusive, but that’s another story) I realized that by “homework” she meant “assignments done either in class or at home” and so she yelled at me for saying she should never give us *any* work to do. Which wasn’t my opinion at all.

      Considering that some kids work much faster than others… enough “homework” to make it so that the fast kids have to do it at home at night means that the slower students are just entirely screwed.

      • That’s something I had never seen or heard of before: in-class work that could turn into homework. We had class, were given the homework assignment at the end of class, and that was it. There was no time to do the work in class.

        • See, I graduated high school without once having ever brought work home. They had eight hours of my day, and that was all they were getting, if they wanted to waste most of it standing at the front of the class blathering on, well that was fine by me, but I certainly wasn’t wasting any of the rest of my time out of school to do school work. It either got done in class, between classes, or it didn’t get done. The fact that I could walk into class during the five minute passing period between classes, sit down and scratch out a complete essay and turn it in before the bell rang used to drive some teachers nuts.* I had one of those attempt to refuse to take them because they weren’t typed. That row went clear to the principal, and involved my mother calling the school and explaining in, as she said, “very small words, so you can understand” (and rather high volume) that we didn’t have a computer, we lived twenty miles out of town, and I had to ride the bus to and from school so I couldn’t stay after school to use their computers, so either they could provide time during class for me to use a computer (this was back when there was a computer lab with all the computers in the school in one room, teachers didn’t even have their own computer in the classroom) or they could accept handwritten work.

          *This is also why in classes where the teacher went around and collected the papers, instead of having a box for you to drop them in, I tended to sit as far from the teacher as possible, because it gave me an extra minute or two to finish work.

          • Hah! My process exactly…

            • And mine. I finished all my assignments in the class where they were assigned or, at worst, in the next class hour following the same day. It was a very rare homework assignment that ever needed to come home with me. Of course, I predated computers pre-college (unless you count the BASIC we learned to code over teletype machines to some bank’s mainframe, as a special treat), so typing didn’t come up. And I had horrible handwriting. :)

              My big teacher contests were over things like refusing to use pencils (I hate the scritchy feel). When I demonstrated that I had no difficulty doing math in ink, it… died away.

              Things got a lot better when we reached a modus vivendi in 6th grade. I wouldn’t disrupt classes out of sheer boredom, and they’d let me read under my desk and turn in homework “live” without comment. That was the foundation of their tacit permission for me to rocket through the remainder of the school’s math courses and on into college ones a couple of years later. (Strangely, my parents were never involved in these discussions, far as I know, beyond the “yeah, sure” stage.)

              • That and my first grade teacher who was a grade A … um, yeah… were the only times I recall my parents being involved in conversations with the school other than parent teacher conferences in grade school.

        • Doing work in class is really important because the student can ask for help if they don’t understand part of it. Once you get home, if your parents don’t get the “new math” or can’t make sense of your assignment, you have no recourse.

          Some of the new computer aided instruction structures turn the old way entirely on it’s head and assign instruction and lectures to be done at home (on computers) while all “homework” is done in the classroom while the teacher is there to answer questions.

          • Of course this presupposes a teacher who actually knows the subject, rather than just having an answer sheet to grade off of.

      • I can only account for grades K-7. I either did my homework in school or I did it on the bus (45 minutes morning and afternoon). If I didn’t get it done on the bus, I didn’t get it done because when I was home I was cooking, cleaning, and chores. (feeding animals, weeding, etc)

  33. My favorite math teacher was Ms. Cavagnaro in High school. Took two years of calculus from her. At the beginning of the semester, she explained to us that her job was to teach calculus, and ours was to learn calculus. If we passed the College Board test at the end of the year, we had obviously learned calculus, and would thus earn an A for both semesters – prior grades notwithstanding.

    Didn’t do one damn page of homework for that class. Earned an A for all four semesters.

  34. Oh, recent happy discovery– at some point, I think it was here, someone mentioned how much they loved Armageddon Girl, a “sort of” urban fantasy. I shuddered and mentioned I’d utterly hated it, couldn’t get more than a bit in.

    I’m now able to say that I highly enjoyed Armageddon Girl…if we’re talking the one from the New Olympus Saga, by C.J. Carella. :D

    No wonder the person’s praise sounded so incredibly strange– they weren’t talking about the “girl from some sort of Van Helsing family meets Strangely Hot Guy she’s supposed to be opposed to and is trying to get in his pants, while thinking about nothing but sex and backstory, for the entire first chapter” one I unfortunately donated so I can’t find the author’s name.

    • That was probably me. I’m on a mailing list with Carella, so I’ve been plugging Armageddon Girl wherever I could. Didn’t realize that there was another book by that name. Glad to hear that you enjoyed AG. The next book should be coming out sometime this year.

    • Heh, that reminds me of when Amazon.com first came along, I thought it was something else entirely. In the early 1970s, there was a bookstore in Minneapolis called Amazon that was run by radical feminists. So when Amazon.com came along, I ignored it for awhile because I thought it was just the online outlet for that store. Eventually, I realized that it had to be something different because too many people were praising it who did not like radical feminists. As for the original store, I think they had to change their name because the idiots hadn’t bothered to get the rights to that name.

  35. Repetition is very important, and why I got weeded out of the engineering weed-out courses in college. Once we started getting into the advanced calculus and linear algebra, I was thinking “Oh, I understand this.” and didn’t do enough of the homework, and when test time game, I’d end up with exams that were half right because they were half done. I wasn’t fast enough at solving the problems, even though I COULD. (On the other hand, I still don’t know what the heck they were talking about with “Black body radiation” in Physics 4. But damn, I wish I’d kept that textbook).

    I’m appalled at the current state of education. I’m even appalled at the state of it 20 years ago. I was having a conversation with a friend of mine back then that centered around WWII. His 19 year old housemate at the time, interrupted us, and in all bright-eyed innocence asked “Who’s Auschwitz?” We educated him, and he’s much better now.

    But more recently, I was at my neighbor’s and his daughter was explaining what they had learned in Math class. Something she called the “Numerical root”. It seemed to me to be something that came out of numerology, rather than math, since it involved adding up all the digits in a number (and repeating the process) until you had a single digit number – the so-called “Numerical Root.” When I asked what the heck it was good for, she had no answer.

  36. Ok, I plead guilty. I graduated from high school in the late 1960s and felt my schooling had been a waste. I hated rote memorization and I thought learning should be fun. Apparently, a lot of my generation felt the same way, except that two or three decades ago I realized it was all wrong while they continue to believe what they believed back then.

    The only problem I now have with rote memorization concerns the way they teach it in foreign languages since foreign-language teachers have the strangest ideas on what should be included in beginning vocabulary. When I took Arabic a few years ago, we learned the Arabic word for “United Nations” very early on, and since it was eight syllables long and was never used again after that lesson, we all had forgotten it by the end of the year. (Plus, there were group projects and we all had to choose an Arabic-speaking country and make a poster and do a presentation about it. We even had to do some kind of circle dance. But at least there was no propaganda, even though the instructor was Palestinian.)

    Here’s what I’d like to see in a beginning foreign-language class. I’d like to learn some basic verbs (to want, to be, to have, to know, and a few others) and to learn them in all their forms before getting any new verbs. Instead, one learns a bunch of verbs in the present tense, and then many, many weeks later one learns the past tense. At some point, they deign to give you the imperative. This doesn’t make any sense to me.

    On the other hand, I was wrong before, and maybe I’m wrong about this. Anyone?

    • When I taught, I spent the first two years on verbs you find in every day life, and for things like have and be I gave all forms. I also gave all the vocabulary that would cover normal situations. HOWEVER be aware that you can not cover every situation from the classroom. When I came to the US, I was fluent in English and had studied it for four years. I’d never learned the word for faucet. This meant I stood in my host family’s kitchen going “thing water comes out of, what is the word?” Also, from translating from Portuguese, because I didn’t know the word, I called pot holders pan handlers and pilot lights “guiding lights” My host family was amused.

      • I can see why “pan handlers” would be amusing.

        And I can also imagine the frustration of standing in front of the sink, thinking, “OK, just exactly what the hell IS that thing?” :-)

      • Pan handlers, that’s cute. And logical, too.

        I was trying to learn Swedish from older relatives and, when writing one of them a letter, made the mistake of using a word in the greeting (dyr) that meant “expensive” rather than “dear” (which was kara). They thought it was pretty funny. I also think my dictionary was produced by a Brit because they are more likely to think that “dear” can mean expensive than an American would.

  37. I have mixed feelings about rote memorization. On the one hand, I hate it, and I avoid it when possible. I find the example of memorizing addition and multiplication funny, because when I was taking my AP Calculus AB test, I was using my fingers to help me add. And I still got a 5 on the test.

    On the other hand, I took my topology prelims two or three times, and the only reason I passed it the last time was because I studied for three weeks over Christmas break, memorizing by rote theorems and proofs…and working on dozens of topological problems, and working out proofs as well. In the end, I had topology coming out of my ears /and/ my eyeballs.

    Sometimes you /have/ to sit down to memorize things…but I couldn’t do geography very well (ironically, in school, I intellectually thought that memorizing capitals and countries was important…today, I’m convinced that the most important places in any region are almost certainly not the capitals of that region, but you have to understand the culture of those places to fully appreciate them), and 10th grade English was the worst: when I finally decided to take vocabulary seriously, it was too late for me, because my teacher tested us cumulatively.

    I have found, however, that if I’m given /good/ assignments, I can do well on the vocabulary tests, and even mathematics tests (prelims being the exception, but they are designed to be especially hard). I think, however, that if I were to try to learn French the way Sarah described her sons being required to learn French, I’d be driven mad.

    And I’d suspect that “good” assignments would be considered pedagogically incorrect nowadays, though, because they would borderline on rote learning anyway. Practice makes perfect, and all that…

    (Which reminds me of the story of a girl who was taught by Jaime Escalante, who was asked if he was a good teacher. Her answer, effectively, was “No, not really. I had this problem in Algebra, and all he did to help me was have me do problems over and over again. In the end, I got it, but he didn’t really teach me anything.”)

    (Having said all that, and having attempted to study French myself, I have concluded that what I /really/ need to do to familiarize myself with a language, is gather together about 100 to 1000 words in a target language, memorize them, and then use those words to memorize the grammatical rules of the language…and then use that as a basis to become fluent from there. I once tried to gather 100 English words, with the plan to translate them into Russian, but I haven’t pursued this linguistic experiment to the degree that I would like…)

  38. This is what home educators generally lump under the grammar phase of The Trivium method, as described here: http://www.gbt.org/text/sayers.html by Dorothy Sayers, if folks are interested in further reading.