There was a discussion about how whether or not kids should be taught how to write cursive here a little while ago in the comments, and I thought that Kain’s hippie prescriptions for public education — which I strongly agree with — provided a good opportunity to bring up something that I oppose even more than I oppose the teaching of cursive: the teaching of long division. Long division is an utter and complete waste of time, I doubt that more than 2% of adults can still do it, and, moreover, why would you ever do it in a world where there are calculators?
The worst part about long division is that it elbows out a much more important topic, order of magnitude estimation. The ability to estimate orders of magnitude is very valuable and division is a good place to do it. Rather than having kids divide 135 into 5000 with a long-winded mechanical method, why not teach them to estimate that, first off, the answer will be between 10 and 100 (just by counting digits) and then push it down to saying it’s somewhere between 20 and 50 (since 135 is between 100 and 200).
Megan McArdle’s errors along these lines are particularly egregious but not atypical. I wonder what percentage of Americans know how many millions are in a billion and how many billions are in a trillion. Without a feeling for this, it’s almost impossible to understand even the crudest macro-economic arguments.
Cain
I still use long division to divide numbers. Please don’t hate me. I also use the tool “bc” on linux. I am uber.
cain
Steve
I disagree. I can’t abide the thought of a functioning adult unable to divide two numbers unless a calculator is at hand. Surely there are enough hours in the day to teach this very basic skill.
El Cid
I think an increased emphasis on basic statistics and probability would come in handy in boosting scientific understanding.
DougJ is the business and economics editor for Balloon Juice.
@Cain:
Don’t tell me you’re reading this blog with Lynx?
DougJ is the business and economics editor for Balloon Juice.
@Steve:
I am offended by notion that so few adults can write on papyrus, the way humans are supposed to.
Felonious Wench
One of the things I’ve dealt with TOO many times from recent grads (high school and college) is them not understanding the concepts behind what a freaking computer is doing for them. We may be able to cut down on the time we spend on it in the classroom, but kids need to know the concepts.
Joe Beese
Why learn to cook when there’s McDonald’s?
Seriously… We’re already turning out the most poorly educated kids in the industrialized world and you think we should teach them less math?
fasteddie9318
Wouldn’t a simpler solution be to improve our ability to identify special needs students at early ages so that the Megan McArdles of the world can get the special attention they need?
Patrick
Calculators and computers are only useful if you can tell if the result is correct. They are teaching what you propose in math in my school. Drives my wife nuts, who only understands how to do the mechanical math.
There is also some brain training. Eliminating math subjects because they might not be used later would eliminate much of math (when was the last time you took the cosign of an angle?). But I think it trains the brain, much like lifting weights trains the muscles.
LGRooney
Still do longhand division on occasion because when Jebus leaves me behind I have a feeling there won’t be batteries for the calculators and I’ll have to have some way to figure stuff.
Hugin & Munin
Howzabout we strive to do both, rather than pare down expectations to address your pet peeves.
Also, how does forcing people to rely on crutches eliminate innumeracy. Seems to me your are just creating dependency.
Walker
My wife has this really unusual algorithm for multi-digit multiplication that works from the largest digit, much like long-division does. The advantage is that it allows both allows order of magnitude estimation and you can guarantee some degree of accuracy as you work your way to the least significant digits.
She has always multiplied this way, since a kid. However, when she was in grade school, teachers regularly marked her wrong because it was not the “correct” method.
aimai
I disagree on the long division thing. The important thing is to do both and not to descend to rote teaching and drill to accomplish a rote goal. But there’s a happy medium between kids who can recite their times tables and do long division without having the faintest idea what they are doing and kids who can use a calculator.
In fact, the idea that a calculator can substitute for knowing what you are doing is as bad as rote long division practice. You actually have to understand quite a lot to know which functions you want to use on a calculator. Its analagous to the idea that you have to know quite a bit to grasp orders of magnitude, or graphing, or anything else.
There’s been tons of work on teaching math to k-8 that tries to strike that happy medium. Again, one of the biggest issues is class size and teacher quality. The larger the class the more the focus must simply be on herd control and the less time the teacher can allot each student to learn at his/her own pace and to solve problems rather than to fill in worksheets.
aimai
DougJ is the business and economics editor for Balloon Juice.
@Patrick:
Interesting, I’m glad to hear that.
I find myself stunned by how many people I know can’t do basic estimates in their heads and most of the people I know are supposedly well-educated.
QDC
I was thinking back on my math training, and I wonder why I spent so much time learning to do indefinite integrals. In particular, is there some field where people actually do trig substitution? I suppose there is value in seeing how it’s done, but we spent weeks and months learning and being evaluated on fairly specialized techniques,. Good use of time?
DougJ is the business and economics editor for Balloon Juice.
@QDC:
I am with you. Indefinite integrals are also mostly a waste of time.
fasteddie9318
@LGRooney:
Jeebus will have left you behind because you keep doing all that cypherin’ and figurin’ and what not. Probably best to give it a rest at that point.
anonymous
I can’t wait for American Computer Science students to first encounter Euclid’s algorithm in their junior year of college.
Hugin & Munin
And can we not have DougJ’s obsession with the no-longer-interestingly-wrong Megan McArgleBargle be the font of educational policy.
DougJ is the business and economics editor for Balloon Juice.
I think that with indefinite integrals and long division, the same principle is at work: educators and students like the illusion that things are being learned, even if those things are only a step or two above things you can train a dog to do.
Walker
DougJ is advocating with teaching people about a skill that will help people against innumeracy just as much as, if not more than, long-division. Most instances of innumeracy are order-of-magnitude errors; being able to do the exact computation is not as important.
The point that DougJ is making (which any mathematics educator would make if you ask them today) is that we have a limited amount of instruction time and some skills are more important in today’s society than others. If students are not actually learning long division well (which many don’t at that age), why not teach something else that is just as useful if not more?
goldaline
@Cain: I wrote the browser I’m using to read this myself. Uber? Psh.
Kristine
@El Cid:
This, definitely. Cause and effect. The fact that two things happening at the same time aren’t necessarily related.
It would be a good thing.
Walker
I don’t teach Calculus any more, but when I did, I essentially turned it into a numerical methods class where we discussed methods of approximation and determining error.
Students have a lot easier time with series if you drive home that every test for convergence has an associated error bound that goes along with it. Otherwise they forget what the hell partial sums are, because they are always trying to remember the damn tests.
geg6
OT, but I’m in moderation in the religion thread because I had too many links. I know I shouldn’t have, but a pompous narcissist who claims that atheists are never discriminated against needed smacked down.
DougJ is the business and economics editor for Balloon Juice.
@geg6:
I’ll take you out of moderation.
Zifnab
Say whaaaaaa-aaat?
Seriously, as a math major I may sound like a fancy pants number elitist. But I remember how to do long division perfectly well. And although I do tend to estimate and round-off when trying to calculate 17/23 in my head, I would hardly say it’s an unnecessary skill just because calculators exist.
Next you’ll be throwing out times tables and square roots because that’s memorizing and memorizing is hard. :-p
You’ve got 12 years of pre-college classes and you’re honestly suggesting spending a couple months learning the brute force method of number dividing is worse than trying to teach a kid how to fudge off the decimal place?
I strongly disagree.
ornery curmudgeon
To stop teaching long division is probably the stupidest thing I’ve ever heard DougJ say, though my memory isn’t perfect … but I CAN say this is the most foolish idea I’ve heard today.
The parallel to the benighted quest by the elderly for youngsters to ‘get off my lawn’ may be the desire by younger folks to simply eliminate anything that doesn’t meet their inexperienced standards.
It ain’t about knowing the mechanical procedure, DougJ, it’s the struggle to get the concept that teaches. There’s room for both division AND orders of magnitude in our curriculum. I know, Pollyanna here. Yes We Can!
Ross Hershberger
I strongly disagree on the long division issue. I use it all the time and wouldn’t be without it.
I took community college DP courses in the ’80s. The first requirement was DP Math and Logic. Algebra was the first subject. Anyone who wasn’t able to pass a test in algebra with pencil and paper washed out of the program.
I do a lot of math for technical projects in my head while doing other things. You learn work-around methods for doing math using the limited scratch pad space of a distracted mind. I was so glad the day I worked out an easy cheat for square roots of small numbers.
Catsy
@DougJ is the business and economics editor for Balloon Juice.:
Doug, this has to be one of the dumbest analogies I’ve seen you make, and it’s dumb enough that you have no business being smug and snarky in its delivery.
Papyrus is an obsolete technology. There is no reasonable scenario where a human being in a modern society would find knowing how to make or use papyrus at all essential.
I find it hard to believe that you can’t visualize any scenarios where a modern human might need to perform division but doesn’t have access to a working calculator.
We don’t need to spend years drilling long division and we shouldn’t be banning calculators once kids have demonstrated a solid grasp of how to do it the hard way. But they should know how to do it the hard way.
Michael
You’re talking to a guy who sits around and does story problems from his high schoolers’ Geometry and Algebra II/Trig books for fun while drinking.
I use the initial stages of long division to hit my range estimates. It is more useful as a brain training agent than you think.
KG
There has to be some value to learning the actual process, so you know what the computer/calculator is actually doing. I occasionally do long division when trying to figure something out, back of the envelope style.
There’s a lot of stuff in school that can probably be thought of as a waste of time. I took biology, chemistry, and physics in high school. I took biology again in college, along with astronomy (stupid AP physics credits didn’t cover enough units and didn’t count for a lab). Not entirely sure how knowing that force is mass times acceleration, or what the parts of a cell are, or what a noble gas is actually helps me in day to day life.
It comes down to understanding what you are actually doing (or having the machine do for you). If you don’t understand the process, you’re not really going to understand the result. Which means you didn’t really learn anything.
Felonious Wench
@anonymous:
Exactly. I hire, or don’t hire, those grads. I’m tired of dealing with blank faces when I ask questions that they have to answer without a device of some sort.
MikeJ
@Kristine:
It’s not proof, but it’s a darn good place to start looking. If your car makes a funny noise but only when you turn right you wouldn’t start with changing the presets on the radio.
Ross Hershberger
Don’t underestimate the power of math. If my dog could add and subtract I know who would be the boss around here.
jrg
I used long division just the other day… I was to lazy to tear the house apart to find a calculator, and did not want to waste time booting up my computer.
Clayton
Haven’t taken a math class in a long time, but I seem to remember long division being used in frequently in later high school math classes and college math classes (as well as all sorts of science classes). What I really hate is the move to teach the so called “new math”, which involves ridiculous and obtuse methods for multiplying or dividing, but aren’t compatible with, say, ALGEBRA. The beauty of long division is that it can be used in conjunction with so much else in math.
Bruce (formerly Steve S.)
Most adults don’t crawl on all fours or read Fun With Dick and Jane, either. I think the argument for anything you teach children is that you have to always keep them functioning intellectually at whatever level they’re capable of, the fact that 98% (that’s 98 divided by 100 on your calculator) of it will be of no use in adulthood is irrelevant. On the other hand, maybe America would become a more peaceful and responsible member of the world community if all we taught our children was the feelgood parts of the Bible. I’m open to either argument.
J.A.F. Rusty Shackleford
I don’t no y we bother lerning 2 spell ether. Spell check can due evreething and nobuddy uses it 2 text eneeway.
Hugin & Munin
Again, DougJ’s worst posts are the ones that touch on his area of professional expertise. He suffers the myopia of a specialist: everything else is unimportant other than my priorities.
Thus he concedes that education is going to be shitty and just tries to shoehorn in his hobbyhorse.
Mark S.
Indefinite integrals? Isn’t that Calculus 2 or 3? That’s when I really started hating math, but fortunately, that’s as far as I had to go.
Linda Featheringill
What exactly would be wrong with knowing how to do long division?
Or with being taught how to do these things so that many years in the future you can take a formula and “remind” yourself how to do it?
Speaking of the “left behind” world, maybe we better teach people how to do square roots the long, hard way. Our world is built on geometry and this will continue to be so.
Dave Ruddell
I can’t help but thinking of this classic Isaac Asimov story.
DougJ is the business and economics editor for Balloon Juice.
@Catsy:
I think it is exactly right. Understanding how language works is analogous to understanding how math works. The calculator, the pen and pencil, papyrus are just tools for accomplishing the task. Sometimes the tool of choice changes.
The argument that long division is superior to doing it on a calculator is essentially saying that one black box people don’t understand is superior to another black box they don’t understand.
Steve
@DougJ is the business and economics editor for Balloon Juice.: I have encountered plenty of situations in my adult life where I didn’t have a calculator or computer handy. I have never encountered a situation where the only writing material available was papyrus. That’s sort of the problem with your analogy.
I hope the level of disagreement in this thread has encouraged you to reconsider your snarky response.
beltane
I’m not sure about this. Learning long division is not an end but a means, a way to train the brain into mastering mathematical concepts. It is similar to learning how to cook. Yeah, you can be a passable home cook by winging it with processed ingredients or by following a recipe exactly without understanding it, but if you want to be a chef you have to start with the less glamorous parts of food preparation such as scrubbing pots and pans and eviscerating poultry.
Technology is a wonderful thing, but from what I’m seeing with my kids, it’s like a prosthetic brain that can easily cause real one to atrophy.
Bobby Thomson
Why stop there? Why not stop teaching homonyms, since most people don’t use them properly, anyway? Why not stop teaching spelling, since there’s a program that works on that? Why not stop teaching people how to write sentences and paragraphs, since texting is so much faster? Why not stop teaching about other countries, since America Fuck Yeah! is the bestest one ever and the only one that counts? Why not stop teaching biology and chemistry in high school, since most kids won’t go into science, anyway?
Zifnab
@DougJ is the business and economics editor for Balloon Juice.:
At some point you’ve got to teach a kid how to sit, speak, and fetch. Just because it’s routine for a middle aged person doesn’t mean it’s non-trivial for a child. I mean, are you going to disregard potty training next because even a dog knows how to poop?
I don’t understand how you expect a student to eventually understand primes and irrational numbers if you’ve never even taught them how to divide.
“What’s 2 divided by 9, Timmy?”
“I’m not quite sure, but I think you can round it to a fifth.”
“Hurray! Close enough! Now what’s Pi?”
“Exactly 3!”
/facedesk
ThatLeftTurnInABQ
I imagine it probably isn’t taught this way in the schools, but isn’t long division a fairly simple and straightforward example of solving a complex problem in a serial manner using a recursive algorithm? Isn’t there some value in exposing kids to that idea? Take something too big to solve in one go, break it up into smaller pieces, solve one of them at a time, and then repeat as needed until done. Reductionism as an applied technique doesn’t get much simpler than this.
ondioline
To even pay attention to this flapdoodle is Veal Pen.
Rosalita
I’m innumerate, I admit it. This thread is giving me the same kind of headache that math class used to.
Linda Featheringill
By the way, Doug, how old are you? Have you recovered from adolescence yet? Do you have children? Do you feel responsibile for preparing this generation to cope with a world that you can’t see?
Or is your life made up of bitching about one goddamn thing after another?
And if you should be taken in the Rapture, would the world miss you?
chopper
dunno. i use LD a lot just calculating stuff out when i don’t want to do it in my head, even when i’m in front of the computer. then again, that’s probably because i did so much of it as a kid.
the problem with the ‘LD is useless’ bit is that there are any manner of similar things you can make that assertion about that kids learn.
Randy P
As somebody who uses integrals and quadratic equations on the job fairly regularly, I’m feeling a little outnumbered. I also do the occasional long division and multiplication.
I don’t tend to hang onto calculators, but when I’m near a computer I do tend to use calculating programs or spreadsheets as a crutch. I’ve also come to rely unfortunately on the Google calculator.
Does everybody know about the Google calculator?
DaddyJ
There’s a math curriculum out there called “Everyday Math” that take a teach-them-multiple-methods approach (like “dot math”) and also does a lot of rule-of-thumb-estimation teaching. Sounds groovy and progressive, right? It isn’t, because they jettison multiplication tables. One teacher branded multiplication tables with a sneer: “drill and kill.” The end result for our daughter was her going into 6th grade not knowing what 7×7 was.
On our own dime we inflicted Kumon on the poor girl for a year (Kumon is a highly regimented Japanese math drill program). She hated it with a passion, but she’s getting A’s in Algebra II now. I’m all for teaching multiple methods of problem solving, but fer crying out loud the basic elements of math require memorization, drill, and a little bit of drudgery!
DBrown
Your repub-a-thug wingnut is showing! Not teach long divison? You really think an esimate is going to cut it? Better hope that pilots that fly you some where don’t use that ‘trick’ to figure fuel for the trip across an ocean or you will be doing a lot of swiming.
Get real, long divison is what makes simple math not just useful but very powerful.
I’m sure the chinese will drop such a useless thing as divison.
MikeJ
@Clayton: People are still complaining about “new math?” I remember reading old Peanuts cartoons from the 60s where it was made fun of.
New math was an issue when I was a kid, but for me it was only because we were told there would be no such nonsense and we’d learn everything the old fashioned way. I never did understand the first thing about math until I got a computer and saw all the neat things you could do if you chained various operations together.
Sadly, the education system is not now, and will probably never be set up to properly teach kids math. The only way to do it is to forget the idea that there’s only one way to do it. Every kid learns differently and the only method of learning math that works for one kid is going to be a bizarre mess to another kid.
This would require treating children as individuals so it will never happen.
Dave Ruddell
In the end, is long division anything but Applied Multiplication?
samson
econ4u.org/blog/2009/05/01/poll-how-many-millions-are-in-a-trillion/
Randy P
@ThatLeftTurnInABQ:
Yes. And I’ve taught computers long division.
I had occasion to want to divide large hexadecimal numbers, bigger than the computer’s processor allowed with built-in instructions. So I thought about long-division a little, worked out the algorithm using the computer’s natural division into chunks (I think I did base-256 instead of base-10) and wrote a little long-division algorithm.
Did the same with long multiplication.
kay
I liked long division.
If they give you enough time and paper, you can always get it right.
mem from somerville
xkcd does numerical magnitude for the media:
xkcd.com/558/
Sentient Puddle
Wow. DougJ just trolled the hell out of most of you.
I tip my hat.
anonymous
@Dave Ruddell:
Brilliant!
MTiffany
Did it even occur to you while you were banging out that half-baked nonsense that the problems this country is facing might in fact stem directly from the fact that “not more than 2% of adults can still do [long division]” ? Maybe if more people put down the fucking calculators and used their fucking brains to do simple math, we might be able to have reasonable discussions about marginal tax rates, deficits, public debt, credit card interest rates, etc. If more people we better at math, then “The gubmint wants to take your hard-earnt money and give it to lazy black people” argument would probably sound like the bullshit it is to a larger percentage of Americans. Hell, if more people were better at math they might figure out that carrying a balance on a credit card means paying more tomorrow for something you could pay less for today.
Hugin & Munin
No, Doug is right. People should just use calcs because math just isn’t that important. There is little functional penalty for being innumerate.
This is, of course, why DougJ gets so worked up about it, but there you are.
Martin
I do long division all the time. My kids were helping me build a fence – more long division. They helped me make a gift for my wife – more long division.
I don’t need to tell you this, but the benefit of lots of long division is that it turns into short division and the ability to estimate better. I’ve got a 43′ long fence divided into 6 sections. What length boards do I need to buy at Lowes? Can I get by with 6′ or do I need 8′?
People do that kind of shit all the time, and having a good ability to manipulate numbers is extremely valuable. Hell, just sitting in a meeting brainstorming, the person who is best able to do that kind of really basic mental math is far more likely to get tapped to lead a project than someone who can’t. That’s what gets you promoted.
Kurzleg
Doug –
You’re assuming that the only test to determine if we should still teach cursive or long division is whether or not one still uses it in adulthood. You’re missing the fact that both of these activities have impact on brain development. Doing either activity stimulates certain areas of the brain and contributes to its development. Maybe there are better ways to accomplish this, but it’s worth keeping in mind that it’s the impact of the activity rather than the activity itself that’s the objective.
And for what it’s worth, I think cursive is a good thing to teach kids. I am continually astonished by the fact that the handwriting of many of my co-workers is just this side of illegible.
If someone has already addressed this issue upthread, I apologize.
Adrienne
@DougJ is the business and economics editor for Balloon Juice.:
Honestly, what annoys me even more is the amount of people I know who can’t do the math that is absolutely useful in everday life — SIMPLE PERCENTAGES. You know, the people who are unable to figure out how much a $29.99 shirt will be if it’s discounted by 30%. If you don’t know that you can shorten [30-(30 x .3)] into (30 x .7) and then into a much simpler (3×7) someone has failed you in your life. Hell, figure out what 10% is go from there.
Or, the people who don’t know how to get a 15 or 20% tip. Drives me fucking crazy everytime someone I know asks me how much the tip should be on a $65 bill. Move the decimal ONE PLACE TO THE LEFT gets you 10%. Double that number = 20%.
They end up thinking I’m some kind of math whiz b/c I can do these things, and I constantly feel like I’m surrounded by idiots b/c they can’t. If I had a dollar for everytime someone asked me a simple percentage question I’d be dealing w/ Bill Gates type money.
/rant over.
djheru
I find it terribly unsurprising that you closet mooslims would support calculations using islamist arabic numbers.
Roger Moore
@DougJ is the business and economics editor for Balloon Juice.:
No. Some fraction of students will actually figure out what’s going on with long division and wind up really knowing how things work. Only students who learn about microprocessors will ever learn how the calculator is doing things. So the correct comparison is between a black box that only some of the students will understand and one that virtually none of them will understand (and those ones will only get it years later). Perhaps more importantly, those order of magnitude estimates can be taught hand in hand with long division, since they’re inherently similar processes, while there’s no direct relationship between order of magnitude estimates and doing things with a calculator.
Belafon (formerly anonevent)
@Walker: Have her write it down. I would be interested in knowing what it is.
Catsy
@DougJ is the business and economics editor for Balloon Juice.:
While generally true, these assertions have nothing to do with why your call to eliminate long division is so wrongheaded and dangerous.
That would be nice if anyone had made that argument. I count two uses of the word “superior” in this thread and both of them are in this single sentence of yours. Nor do I see anyone saying anything to that effect in any similar words.
The point is not that long division is better or worse. It is, as you noted, a tool. The point is that you cannot count on always having a working calculator at hand, whereas you can scratch out long division on the ground with one fingertip if that’s all you have. A woodworker who only knows how to use a nailgun and thinks hammers are archaic is going to run into a wall in their career.
I don’t understand why you’re being this dense. The idea that a person might have to perform math without the use of electronics is so elementary that it borders on insulting your intelligence to even have to explain it. You were wrong. Nut up and own it already, because you’re just embarrassing yourself by standing your ground on this one.
MikeJ
@Roger Moore:
And there will be no overlap between the two groups of people if you look at those employed by Intel.
Martin
@DaddyJ: My daughter forgot a decent bit of her multiplication tables over the summer. I’m sending her back through them with vigor. If you can’t do multiplication and division quickly and accurately, and by quickly I mean ‘instinctively, without thinking’ then forget about a degree or career in the sciences. You’ll simply not finish the exams in time and you’ll get so frustrated over simple arithmetic that you’ll give up on the rest.
Catsy
@Adrienne:
I love you for this.
Punchy
For the SAT, DAT, PCAT, GRE, GMAT, and I think NCLEX. None allow calculators. Thats why.
What an attitude (still cant figgy if you’re snarking). I bet we shouldnt teach kids how to read, right, because of books on tape?
Walker
The problem with everyone here piling on DougJ is that they are having a skills-focused attitude towards a pedagogical issue. The closest anyone has to a legitimate complaint is DaddyJ at 55. He points out that the extreme reaction to “drill and kill” (which is not evil in itself, when used appropriately) can have long-term adverse effects on education. Unless you can make that type of argument to teach long division, your argument is not useful.
Sure, long division is Euclid’s algorithm. But do they need to learn Euclid in elementary school before they do any serious programming? Is there any evidence that instruction in it helps them to learn Euclid later?
You want real damage? Let’s talk about the NTSM guidelines that eliminated two-column proof in this geometry so that most incoming freshman have never seen a proof in their life.
There are quite a few professional mathematicians on this board. We do teach students and assess them. We have a good idea what works and what does not.
RSR
Has anyone seen “Waiting for Superman” yet? The pro-charter (privatization)/anti-union rhetoric has my hackles up.
numbskull
Year after year, students of mine tell me that the best advice I give them in prepping for the GREs or MCATs is to toss the calculator two months before the test and do everything longhand. Why? Why does this result in what the individual student feels is better performance? Who knows. I know it seemed to help me, so it’s what I tell them. Now, maybe it doesn’t help at all, but it sure appears that way to the individual.
Of course, I’m further weird because I pretty much skip using a calculator as much as possible. The more I use it, the dumber I feel.
goatchowder
Interesting. My 4th grade daughter is in fact studying estimation at orders of magnitude right now. It’s a bit of a sharp turn compared to what they have been leading up to all along, so I suspect this is new thinking, new curriculum, in educator-land. It has become important in a world with BILLIONS of people, disk drives with TERABYTES of data, economies in the TRILLIONS, etc.
Also, I graded papers and found that about 40% of the kids could not spell the name of the continent upon which they live– nor the colloquial name of the country in which they live.
Maybe it’s the California vowel shift happening, but I cannot figure out why they think that “North Amarica” is correct.
Lots of red ink on those papers.
Ash Can
You’re full of shit.
Here, however, you start to make sense again. I’m sure it’ll warm your cockles to know that Chicago Public School kids, and kids in any other districts that use the University of Chicago’s “Everyday Mathematics” series, do learn how to estimate, along with a variety of other methods for manipulating numbers — including long division.
mnpundit
I didn’t really get your estimation but off the top of my head, I’d say roughly about 37.
So how’d I figure this?
135*10 = 1350
1350+1350+1350 = >4000
Another one would be too much, but by less than half of the 1350, so less than half of 10. So it’s between 5-10, half of that roughly is 7. Since it’s an estimate, close enough.
Going to my computer calculator I see that if it was 37 it would 4995.
Suck it down DougJ.
Davis X. Machina
I used to do a couple weeks of powers-of-ten estimation exercises in speech & debate, as a form of bullshit inoculation. I think it was inspired by the ridiculously large number of disappearing children that we were told about back in the mid ’90’s….
It was fun to watch kids in debate rounds being able to ballpark something like “Percent of GDP required to provide every unemployed person in the US a 40hr/50wk 2x minimum wage job” in about two minutes… go up against teams that confused millions with billions.
My other party trick was handing an abacus to anyone in study hall who asked to borrow a calculator. Hey, it is a calculator, isn’t it?
I’d like to think U of Chicago’s association with estimation goes back to Enrico Fermi, and his screening questions for lab and grad assistants, like “How many piano tuners are there in Chicago”.
Linda Featheringill
@DaddyJ:
My daughter was in the 5th grade and knew only part of the multiplication tables. So I threw a fit and taught them to her myself and drilled her on them until she knew them up to 12.
And she still knows what 7 x 8 is. Hasn’t hurt her a bit.
Southern Beale
I dunno. I think long division should still be taught, just as you do scales when you are learning piano, you do barre exercises in ballet class, you learn to parse a sentence in English, etc. etc.
I’m a total math dunce. I am simply not wired for math. Math class tormented me in high school. I quite literally cannot function without a calculator. Still, there have been plenty of times when I’ve needed to do a calculation and didn’t have a calculator with me. And I really wished I knew how to do those things.
I think I’m probably the rare person who is mathematically retarded. Just because I couldn’t learn it doesn’t mean other people couldn’t.
The Other Chuck
Aren’t there superior algorithms to long division anyway? Obviously we need to teach division by hand, but I see no need to stick with an obsolete system.
Same attitude applies to cursive. Yes it’s nice to be able to read it, but as far writing it goes, you may as well save it for the art classes.
Adrienne
@Punchy: You actually CAN use a calculator for the SAT. Not a fancy schmancy one, but calculators are allowed and even encouraged.
I found that I didn’t really need my calculator when I took the regular SAT. I should have used it for my Math SATII, but my batteries were low and I winged it. I still scored a 700 or roundabouts though. Me and math were always pretty tight — at least when the math was mostly numbers and letters. Once we got to mostly symbols (Econ and Finance) I was like fuck it. I quit. Can a sistah get excel and a cheat sheet?
catclub
@QDC:
“but we spent weeks and months learning and being evaluated on fairly specialized techniques,. Good use of time? ”
Of course! you just got a blog post out of it.
Educational efficiency and effectiveness, all in one!
Punchy
@numbskull: I specifically teach for all these exams (MCAT, PCAT, GRE, etc), and I am regularly stunned (although by now I shouldn’t be) at just how handicapped students are without their calculator. I had one girl, in tears, tell me she felt it was impossible for her to do the math without one. I didn’t have the heart to tell her she should be applying to law school or a job bartending.
TooManyJens
@Cain: I use “bc” too. I’d use it more if there was a way to set preferences so I don’t always have to set scale=2 every time I use it. Is there a .bcrc or something? man bc is letting me down.
Davis X. Machina
I say, bring back slide rules. Anything with more than three significant digits is just showboating, anyways.
Belafon (formerly anonevent)
Doug, I have to disagree about your arguing against long division. The difference between it and cursive is the same difference between knowing how to cook and knowing how to drive. If I never learned to drive, I can still function because my ability to get around is not eliminated by not driving, only slowed. On the other hand,not being able to cook creates situations where I would not be able to eat.
And, for what it’s worth, I am doing integrals all the time. Doing intelligent systems research means I get to do all sorts of fun math without numbers.
Hugin & Munin
The Other Chuck: What’s ‘art class’?
Cat
@anonymous:
Screw that noise, America doesn’t need more Computer Scientists, it needs more Software Engineers.
As long division is to high school students, everything over Calc is to CS majors who plan on working for a living.
Barry
DougJ is SUXXOR the MOST!!!1111!!!
division is one of the basic operations of arithmetic. Without it, we are just apes with thumbs!
(but without the ability to pick fleas off each other and the proclivity to eat them)
West of the Cascades
I also disagree about long division – I don’t carry a phone with a calculator, and it’s a pretty basic tool to be able to do simple daily calculations in your head (“I have 12 dollars and the Cheetos cost $3 each, how many bags of Cheetos can I buy??).
But I agree that teaching other creative methods of estimating basic relationships between two numbers is important – not everyone learns the same way and having more, rather than fewer, tools for basic daily living is better.
Linda Featheringill
@Davis X. Machina:
Ever work with a circular slide rule? Actually quite interesting.
Joel
Maybe if students had more immediate incentive to do well at math (i.e. if you fail you are immediately in the shit, as opposed to sliding by until your innumeracy catches up later), they would be able to learn multiple things at once.
Dave Ruddell
Okay, calculator anecdote time…
Back in grad school, I used to teach freshmen chem lab. One of their experiments had the calculating the purity of an acid (or something). Anyhow, one calculation required them do multiply a mass in grams by 1000, so it was something like:
0.238g x 1000 = ?
And the vast majority of them would reach for their TI-83. After this happened a half dozen times, I’d actually stop them and say “Come on! You can do this in your head, right?”. They all could, they were just scared of being wrong.
catclub
” As somebody who uses integrals and quadratic equations on the job fairly regularly, I’m feeling a little outnumbered.”
A math pun! Lemma tell you another one.
asiangrrlMN
I like long division. I can still do it by hand. Cursive is outmoded and not useful because you can print or type and it does the same thing. I dunno. I am not a math person in general (though I did love calculus), but I would keep long division because it seems more of a tool or a stepping stone rather than an end in and of itself.
Omnes Omnibus
I am guessing everyone has been trolled. DougJ who posts about the Fields Medals is against the teaching of long division? Okay, sure.
Jamie
I doubt that more than 2% of adults can still do it
that is so very depressing.
Ash Can
@DaddyJ: It took me a while, but I finally spotted your comment. My guess is that Everyday Math doesn’t include multiplication tables because teachers cover that on their own, and don’t need the math workbook to do that. That’s what my son’s teachers did, anyway. Are there really teachers out there who would omit the multiplication tables in their curricula?
catclub
@Linda Featheringill:
“Ever work with a circular slide rule? Actually quite interesting. ”
The Lowell observatory had a 64 foot long slide rule.
(It was the observatory from which Pluto was discovered.)
Linda Featheringill
@Omnes Omnibus:
Oh, so the joke may be on us?
Good joke, Doug. Well done. :-)
Hugin & Munin
Omnes Omnibus: I view these DougJ posts as a ‘multiball’ or ‘free play’. It’s an opportunity to let fly and see what sticks.
Very liberating, except for the FYWP that sucks comments into mod hell for no reason!
Now I need a song from WP’s perspective, though.
TJ
So you’re OK with definite integrals?
Brachiator
@DougJ is the business and economics editor for Balloon Juice.:
Megan McAddled’s problem was that she didn’t recognize an order of magnitude problem even though she had entered digits into a calculator. And she’s supposed to be a professional.
I don’t know a good answer to this education problem. I know people who claim that knowing Algebra is worthless, and yet when I go to the supermarket, I use basic Algebra to verify per unit costs for items and do comparison shopping. The store’s breakdowns are sometimes wrong or sometimes stupid (e.g., with toilet paper). I once tried to point out to a shopper that a Jumbo item actually cost more than 2 smaller sized packages of the same product, but the shopper just didn’t get it, in part depending on the store’s misleading advertising claim to “buy bigger” and save.
I’d like to see some combination of conceptual and practical math taught. I still remember a high school geometry class where we went up on the school roof (on a particularly windy day) to practice doing triangulation.
But any way you cut it, the larger problem is that there are too few good math teachers and worse, even some teachers hate or are afraid of math. I was watching one of the local public channels, which has LA Unified School District programs. One featured a bunch of teachers and my heart sank as I watched the instructor bore and mystify future math teachers, who would no doubt soon go out and bore and mystify their students.
Gus
@Sentient Puddle: That’s the only sensible explanation. The post is just too imbecilic otherwise.
Fwiffo
Really, people need to learn how to do more math in their head through simplification, in addition to more emphasis on estimation.
Like, if I need to know 142 x 48, I can say that it’s pretty close to 142 x 50, which is half of 142 x 100. 142 x 100 is 14,200, and half of that is 7100. Take away 142 x 2 (AKA 284), and that’s 7000 – 184, or 6900 – 84, or 6820 – 4 or 6816. OK, it’s more steps than you’d do on paper, but it’s easy to do and check in your head even if don’t have a calculator or paper on hand.
Omnes Omnibus
@Brachiator: My high school math teacher, Patti Hedblom (RIP), began IB Probability and Statistics by teaching us cr@ps and bl@ckj@ck. We saw the practical implications of what we were about to learn and then we done learned it. No one did poorly on the IB Math exams.
Omnes Omnibus
@Fwiffo: Doesn’t everyone just do that?
Adrienne
@Linda Featheringill:
This reminds me of my 6th grade math teacher. Every single day we started the class with a “record test” for either multiplication, division, addition, or subtraction. It was a test on a record with 30 questions each test. First, there was maybe 15 seconds btw each question, as the year went on the time btw questions got smaller and smaller — 12 secs, 10 seconds, 7 seconds, 5 seconds, 3 seconds. I’m now 25 and I can tell you that from these repetitive tests I can STILL rattle off any the product of any two numbers btw 1-12. Scarily fast. We hated those damn tests, but it has proven immensely valuable.
He also tested us on other useful knowledge like how many how many feet/yard, how many feet/mile, how many oz/cup, cups/pint, cups/gallon and any other way you could ask those questions that would make us do some math like how many yards/mile (5,280 ft/3 = 1,760 yards) or how many pints in a gallon (16c in a gallon / 2c in a pt = 8pts in a gallon). He was a crazy, cranky old bastard but he made sure we learned a lot things that are useful in everyday life. I’m grateful to the old coot.
asiangrrlMN
@Omnes Omnibus: Good guess. Especially the order of magnitude estimation bit. Nicely done, DougJ!
Catsy
@Walker:
You have managed to entirely miss the point, and in the process have made an argument that is not german (or useful) to this discussion–except as a rebuttal to an argument most here don’t seem to be making in the first place.
You may want to frame this argument as a pedagogical issue, but Doug’s original post was not limited to that context–it was a categorical, all-out assault on the idea that long division has any value whatsoever as a skill. His argument rests on the bewildering presumption that no one in this day and age will ever find themselves needing to perform division without the use of a calculator, and that’s just flat-out idiotic. Re-read this from Doug’s post:
That’s not an argument about teaching methodology, it’s an argument that performing long division is an obsolete skill that has no value whatsoever in the age of calculators. Of course most of us are attacking it from a skills-focused standpoint–that was the focus of the original post!
DonBelacquaDelPurgatorio
Eleven. Eleven percent.
Actually I have no idea, I just thought your question deserved an answer.
Okay, so now you have us set up. How many billions ARE there in a million? Wait, what was the question?
And BTW I am a fucking whiz at long division.
trollhattan
@ DougJ (he of the many wonderful McMegan-like tasks)
My 3rd grade daughter’s class is doing just this; in fact, I’ve been proofing homework on estimating, rounding and factors of ten the last couple of weeks. This is in broke, hippie-infested California.
Andrew
I have encountered plenty of situations in my adult life where I didn’t have a calculator or computer handy.
I haven’t.
With calculators in cellphones as a matter of course and a calculator itself costing less than a buck for a basic non-scientific calculator than can handle figures up to 12 digits in length, there’s no good reason not to have a calculator handy anymore.
They’re a standard preparedness item, like having a flashlight in the house for the occasional blackout. I’m sure there are lots of people out there who don’t have one, just like there are lots of people out there who don’t keep a calculator amongst their daily to-carry items, but that’s not because the world is such that having a calculator on your person is an intolerable and expensive bother.
Hugin & Munin
DBDP: 38% of all statistics are made up on the spot.
ronin122
@Martin: This is one of the most bullshit things I heard on here. As a recent science graduate (Electrical Engineering but I have seen material from other engineering and physics), the exams tend to be either of numbers where it’s not efficient to do things mentally (square roots and trig functions galore) or is all symbolic (masses M1 and M2). And that’s just very basic stuff. You spend the bulk of your time understanding the mathematical reasoning of the problem, not doing mental math on 4 times 7.
Catsy
@Omnes Omnibus:
So let’s see. My choices are:
1. DougJ is really foolish enough to think that long division has no value, or;
2. DougJ is intentionally making bad arguments for lulz in order to troll the people who’ve made the mistake of taking him seriously.
Neither of those options really invites much in the way of respect or credibility.
Omnes Omnibus
@Hugin & Munin: 87% of the population knows that.
Chris
@TooManyJens: No, but if you fire up bc with the dash l option (writing this out makes wordpress use strikeout, sorry) it loads the “l” library which sets scale to 20.
Omnes Omnibus
@Catsy: Mad Trolling Skilz don’t exercise themselves. A lad has to stay in practice.
Catsy
@Andrew:
Because smartphones never run out of charge or get unexpectedly bricked.
Gods, how alien a concept is it really that an adult should be able to perform basic, primary-school math without a calculator?
Roger Moore
@Omnes Omnibus:
I tend to do 142*48 = (140+2)*(50-2) = 140*50 + 2*50 – 2*140 – 2*2 = 7000 + 100 – 280 – 4 = 7000 – 184 = 6816.
Chris
@Omnes Omnibus: Yes, it’s important to relate things to something already understood, as it leads to either motivation (leading in turn to understanding) or sometimes directly to understanding.
A friend of mine was trying to teach his brother fractions, and he just could not get reduction … until the friend asked the brother, who was into cars and doing mechanic-type work, “ok, so you grab a socket out of your socket wrench set and it’s 7/16ths but it’s just a hair too small, what’s the next size up” and he says “1/2 of cour.. OHHHHH!”
(Also, btw, re #124, that’s dash ell, not dash eye.)
DonBelacquaDelPurgatorio
We should teach that, right after we teach them how to figure out that the earth is not 6000 years old, and that drilling for oil in the Gulf won’t bring down the price of gasoline.
Sentient Puddle
@Gus: See, now I don’t know about anyone else, but my first thought when reading the post was polynomial long division. I’m sure there’s other concrete things that people can point to in order to justify long division, but that one stuck out in my mind as something you just can’t do with a calculator (or at least you can’t do easily…I don’t know what recent advances in calculator technology look like).
Still, even if we take calculators as a given, there’s the larger point that you just can’t assume that they’re an “I Win” button for math. The last class I ever took in math was probability, and I look back at it as a sort of proof of this point. Beyond the basic conceptual idea of what a probability is, most of the material boiled down to formulas. Those formulas are easy enough to beat to death with a calculator, but the calculator doesn’t do you a damn bit of good in determining the nature of the probability you’re trying to calculate, and to pick the right formula.
Brachiator
@Omnes Omnibus:
Makes sense. Also, a lot of people understand math but don’t realize that they understand math because they don’t connect real world math with what they are presented with in school. Consider any kid who can easily rattle off sports stats about his or her favorite athlete, but who is getting Cs in math at school. It just shouldn’t happen.
A good friend claimed that she absolutely hated math, but I pointed out that she had graduated from fashion design school and was an excellent cook, and used math all the time when she made clothes or cooked meals. Her use of patterns, for example, was pure geometry.
I gave her daughter an introduction to sampling by using the simple example of cooking a sauce. I asked her how she knew the sauce was OK, and what was the smallest portion she could use to determine this. She answered, “a spoonful, of course.” I pointed out that this was the core of sampling, that when you stir the pot well enough you can be certain that the sample you take out with a spoon will be representative of the whole, no matter how small the spoon or how big the pot.
Also, too, it is amazing how we remember some of our teachers, especially the good ones. A tip of the hat to my second grade teacher, Mrs. Grey.
DougJ is the business and economics editor for Balloon Juice.
@Hugin & Munin:
You’ve got the right order of magnitude there. It’s more like 90%, though.
Ailuridae
@Davis X. Machina:
The Fermi Method is still occasionally taught at U of C in the Physical Sciences requirement that the non-mathematically inclined take there affectionately called “Physics for Poets”. People struggle mightily with it to the extent that a lot of advisors send people into the other similar class affectionately dubbed “Rocks for Jocks”
I honestly don’t get the long division issue. There is a process to remember (that any number of people have posted in convenient, easy to follow flow charts) but besides that it is basic arithmetic. Am I missing something here?
One of the bigger reliefs of my life is when I entered seventh grade and was no longer required to write in cursive and no longer have my overall grades brought down by a “handwriting” grade. At that point, like my siblings and father before me I started to write in all caps and have seen been considered to have quite good handwriting.
DougJ is the business and economics editor for Balloon Juice.
@Adrienne:
I agree with you completely. If they know that to take 30% you just multiply by .3, they can do that on a calculator. But if they have no idea what 30% means, they can’t solve it no matter what they do.
Bob the Mediocre
@ronin122: Similar background and I agree. In my experience, even if you do mess up the algebra on an exam, as long as you have the underlying concepts down, you’ll get almost all the points.
And for the record, I use indefinite integrals all the time.
Steve
@Catsy:
You know who else made arguments that are not german? Well, actually, not Hitler.
Ailuridae
@Roger Moore:
Weird. My father taught us this same method when we were young and I have explained it to people over the years with little success. My niece and nephews, though, understand it almost intuitively.
Brachiator
@Roger Moore:
Then there is this, from a NYT article on a school coming up with innovative methods to emphasize literacy, even in math classes (4,100 Students Prove ‘Small Is Better’ Rule Wrong):
Lee
Estimation is a new topic in 5th grade here in Texas. I believe it is new because 3 Years ago when my oldest was in 5th, I do not think it was taught.
They then do the actual long division to check their work.
joe from Lowell
How are you ever going to be able to do division in your head if you don’t learn long division?
joe from LoL
Still no word on whether joey has ever read bin Laden’s declaration of war on the USA.
Why does that question piss you off so much, joe?
Cermet
The issue between cursive and non-cursive has no bearing on the issue of long division. If you do not know, or even understand cursive, you can still write and type and is no big deal. If you can’t do long division, then all higher math and science is beyond you and you are f’ed.
That aside, besides language, no greater invention has ever been created then math. And in math, the Indo-Arabic number system with zero, place value system and decimals is beyond doubt, our greatest leap in knowledge as a species (writing follows organically from the spoken language but that too, is an amazing invention.)
To make a short comment very long, as a result of these thousands of years of development (most done the last thousand years), long division is the most beautiful and amazing process. It takes a complex and somewhat abstract concept that is almost impossible to do in your head for large, prime numbers and makes it a simple, straight forward process that even a child can learn to do – even a third grader (ok, in the advanced classes.)
For an Engineer or any scientist to not value long division is a display of tremendous ignorance – sorry, but no way you will handle more advanced math if division is beyond your understanding and it is crucial to learning more advance concepts.
I too use integral calculus and partial differential equations in my work but just because I rarely use simple numbers does not in any way reduce the importance of simple arithmetic operations and their importance – in fact, some of the deepest ideas in mathematics is number theory which uses these operations to really understand mathematics – it is numbers (esp. integers) that are rather useless.
But of course, we should all just sit back and let the the Chinese do all the real intellectual work and supply us with endless games, planes, rockets, advanced electronics and all on credit – our children should just learn how to play electric games, not math.
Andrew
@Catsy:
Again, planning against the eventually of your smartphone dying and leaving you without a calculator is like planning against the eventuality of a blackout, leaving you without overhead lights.
Get a flashlight, buy a dollar calculator at a store.
Yes, you can hypothetically come up with a scenario (what if you’re lost in the woods, have no batter yon your cell phone and a bear is threatening to eat you unless you come up with the root of 37 within five minutes?!), but the number of scenarios that are actually plausible that aren’t 100% solved by “buy a dollar calculator and stash in in your purse/glovebox” are few and far between. If you can envision a situation where you own exactly one calculator and that calculator is in danger of losing its charge, then you are capable of envisioning how to get around that fact. Calculators are not large, expensive, bulky, inconvenient to acquire or anything that could possibly prevent you from always having a calculator handy – and this is speaking as someone who doesn’t regularly carry a purse, or a bag of any sort.
It’s not a wild idea to think adults ought to be numerate. But hinging your definition of numerate on “able to perform mechanical calculation” is not really convincing. Numeracy is much larger than being able to do long division by hand on a napkin when it comes time to figure out the tip.
Earl Butz
Magnitude:
Take 1 dollar bill out of your wallet every second and throw it on the ground.
Time to get to one million dollars: 11.6 days
Time to get to one billion dollars: 31.7 years
Time to get to one trillion dollars: 31,709 years, 9 months
Magnitude matters. And the media doesn’t get it at all.
Adrienne
@Catsy: I’m glad I’m not the only one! I mean really, how mentally lazy do ppl have to be in order to be unable to move a decimal point around or to figure out how to go back and forth btw decimals, percentages, and fractions?
I’m amazed by how many ppl really don’t fully grasp these concepts. I learned that (N x 1/3) is the same as (N/3) is the same as (N x .33333) in the third damn grade and have used some variation of that knowledge almost everyday since whether in school, at the grocery store, at the mall, whatever. How ppl go through life so clueless about numbers, and money bc that’s really what it should be related to, is just beyond my level of comprehension.
Michael Finn
Trust me, knowing how to multiply and divide without the use of a calculator is kind of important.
If a doctor/nurse cannot multiply or divide while putting in a correct dose and has no access to a calculator then the patient is fucked. Checking their flow rate is kind of important as well. If you are stocking a shelve and you want to put the correct amount of crap in there and you need to call in some from the storage, knowing how to multiply can save you tons of time.
One question that I do have though is why are we always trying to do math the difficult way? Right to left instead of left to right.
For instance, take this..
31 * 24 = 31*20 + 31*4 = 620 + 124 = 744
That’s a heck of a lot easier than…
31 * 24 = 4*31 = 124 + (62*10) = 124+620 = 744
Steeplejack
@Davis X. Machina:
Win. I wish I still had my slide rule. Can you even buy one now? (Maybe at the Smithsonian gift shop?)
RareSanity
DougJ,
For the first time in the years I have commented on this blog, I’m going to have to disagree with you.
This shows a lack of understanding of the purpose of mathematics (and science for that matter), beyond actually being able to calculate an answer.
Studying math and the sciences teaches kids how to solve problems, by using a methodical process, to break those problems into smaller pieces and solve them. It teaches logical thinking, organization of thought and, applying a generic, problem solving procedure, to specific and differing situations (the actual problems).
Here is the reason why this is not more readily understood:
@Brachiator:
That is being transferred to the students, which propagates the problem.
artem1s
@Brachiator:
that’s just brilliant. I have that argument with my quantitative analysis professor all the time. he is a fabulous teacher in many respects but just absolutely falls short on presenting some of the concepts in a way that lay people will grasp (it was a intro course for non majors). he was constantly falling back on using jargon and technical terms that one might use every day in the social science world but would never hear in everyday usage.
Agoraphobic Kleptomaniac
xkcd.com/759/
This seems appropriate.
Adrienne
@DougJ is the business and economics editor for Balloon Juice.:
But that’s exactly my point. If they don’t know that 30% = .3 then someone has failed them. If they don’t know that all percentages translate into decimals they should be entitled to a refund at every educational institution they attended beyond the (being generous) 4th grade.
Further, standing in a Macy’s there is NO reason why an adult should NEED to stop, dig through his/her bag to find their phone or calculator, and punch in some digits in order to figure out what 30% off is. Period. Multiply by 3 and move the decimal. It’s not thermonuclear physics. It’s 3rd grade arithmetic.
Agoraphobic Kleptomaniac
One more thing:
Cursive is a font and that’s all it’s ever been. Even the 8 year old me knew it was neutral to my knowledge of the world. Same goes for roman numerals.
Long Division, on the other hand, is a skill. Knowing long division gives you knowledge outside of Long Division itself, unlike cursive and roman numerals (which only give you knowledge of cursive and roman numerals).
Anytime you can teach kids a skill to arrive at new answers is a good thing. Time spent converting arabic numerals to roman numerals is a trivia point, with only limited application.
One more thing: the more you can teach kids about long division and the more it makes sense, the better off they’ll be with fractions. Fractions are when most kids are old enough and stubborn enough to give up on math, because fractions are a major hurdle for most kids.
PeakVT
Somebody probably has pointed this out before (no time to read every comment today) but I think the two topics aren’t substitutes. There definitely needs to be more time spent teaching how to quickly understand large numbers, especially those that are involved in the modern economy. But that skill shouldn’t be taught until the teenage years because it isn’t really possible until kids have an understanding of larger things in general. I think most people don’t really grok the difference between big, huge, humongous, etc., until their early teens. OTOH, long division is a basic math skill that should be taught starting in the 2nd or 3rd grade.
Bill Arnold
@Agoraphobic Kleptomaniac:
LOL.
You did read the hover comment for that comic right?
I recall learning a square root procedure in elementary school (and promptly forgetting it), and IMO the time would have been much better spent learning a basic bag of number facts and in-head estimation tricks.
Beyond multiplication and division tables, my basics accreted over the years (mostly not taught in school), include squares up to 25, doubling/division by two for all 2 digit numbers, intuitive familiarity with powers of 10, basic estimating, 2-decimal-point-in-the-head computations, and knowing if an integer (in decimal) is evenly divisible by 2, by 3, by 4, by 5. These (or a less haphazard set) could mostly could be taught in a week or three.
Sad_Dem
Former teacher here, and I agree that cursive is dead, but disagree about not teaching the mechanics of math. The idiots who occupy departments of education almost universally disparage rote learning, I think because it works.
Binzinerator
I thought this ‘ditch long division’ thing was snark. Then I realized you were serious. Then I realized this is good point.
I learned long division in school, and it works for me. But I see that having people literate (as it were) in number sense would mean they wouldn’t be so damn easily fooled when big numbers get bandied about. (Or make fools of themselves like McArgle-Bargle does.) We’d have a lot fewer teabaggers (at least a few orders of magnitude) because damn few would believe a 2 trillion dollar deficit can be solved by cutting programs worth 20 billion.
I am reminded of some of the work my kids did in their Montessori school. They do activities intended to develop a sense of numbers relative to other numbers. For example I once was asked to send them to school with ten baggies of a hundred of some simple common item in each bag (parents used pennies, paper clips, candy corns, etc). They got to touch and see what a stack of ’10’ of something is next to a stack of ‘100’ and ‘1,000’. Orders of magnitude made visible.
Somewhat related, as far as our innumeracy with orders of magnitude beyond our our fingers and toes: I recall seeing an exhibit years ago that vividly demonstrated just how many the world’s arsenal of 60,000 nuclear warheads was. The exhibit consisted of 60,000 of smaller versions (made of ceramic I think?) of the actual cone-shaped warheads used in ICBMs filled the huge room. Each facsimile warhead was large enough to have a presence of its own and be perceived as an independent unit, but small enough so that the 60,000 of them could be perceived as a collection (unlike, say, trees in a forest). It was a genius use of scale to demonstrate a very big number. People easily ‘get’ 10, and maybe 100. But 60,000? No way. Not as a number by itself.
Bill Arnold
@Binzinerator:
Three dimensions help. Soup cans for instance – 1000000 is 100 wide by 100 deep by 100 high soup cans.
(They might need to be especially strong soup cans.)
TooManyJens
@Chris: Awesome, thanks!
Nylund
I teach undergrads. They cannot add, subtract, multiply or divide anymore. Fractions? Heck, most couldn’t even tell you that 1/4 = 0.25, much less what 1/3 + 1/4 is (and I teach at a “top tier” school). I too wish they could understand orders of magnitude so that they could at least realize that something is probably wrong when they calculate a price of an orange as $4,384 on a test.
That being said, I don’t see why they can’t be taught orders of magnitude AND how to do calculations by hand.
My main issue with calculators is that many problems can be simplified by factoring out common roots, but they just type away, writing down some weird decimal, then using that decimal in another equation, compounding rounding errors until you get students writing down 14.9837218 as an answer when, if you did it by hand, you’d quickly realize half the numbers cancel out and, in the end, you’re left with simply 30 divided by 2.
Davis X. Machina
@Steeplejack: THinkgeek.com had them recently
frosty
Order of magnitude estimation died with slide rules. They gave you three digits, you had to come up with the decimal in your head.
And another thing. I’m tired of these kids giving me printouts from spreadsheets with 6 decimals. Are you kidding me? Your input data was that good?? Get off my lawn!
frosty
@Walker: So that’s why my 10th grader’s geometry book has no proofs? It floored me. That was my favoritest class until Abstract Algebra (rings, groups, etc).
frosty
@Steeplejack: Loads of ’em on eBay. K&E, Post, Pickett, Dietzgen, circular, straight, you name it. USAAF D-4 flight computers. That’s where I replaced the Log Log Duplex Decitrig I lost years ago.
Danil
2% huh… 1 in 50.
statemaster.com/graph/edu_bac_deg_or_hig_by_per-bachelor-s-degree-higher-percentage
Assuming I’ve pulled a reasonable census here, and I’m doing the math correctly, 2% means 1 in 10 college graduates and nobody else.
I realize my life is not a statistically significant sample, but does that even pass the smell test?
Steeplejack
@Davis X. Machina:
Thanks for the tip.
@frosty:
I forgot–everything is on eBay.
LiberalTarian
I use long division all the time … easier than whipping out the calculator. But, my advisor taught me you only need to be in the ball park, not have the exact number, all the time. Why go for 4.95732 when 5 will do?
Original Lee
@Dave Ruddell: You got there first, darn it.
Frank
There’s an old story, from before the days of the NFL draft and from before the NCAA became the farm system for the NFL, about some football players sitting around discussing why they turned pro.
One says, “Man, it was differential calculus. I just could not understand it.”
The next one says, “Quadratic equations. I managed to fake my way through them in high school, but not in college.”
The third one hangs his head. After a long silence, he looks up and asks, “Did you fellows ever hear of something called ‘long division’?”
Dammit, I went to school in a very poor rural school district a long time ago. But, when I graduated, I sure as hell knew how to read, rite, and cipher.
Give me a break.
mnpundit
I saw something a while back which said that learning cursive actually makes you a better writer so I stopped dumping on cursive a few months ago if anyone here noticed.
DaddyJ
@Ash Can: Well, the switch to “Everyday Mathematics” came between, I think, my daughter’s 2nd and 3rd grade; perhaps the 2nd grade book had some memorization drills. Dunno.
I do know that many of the teachers at her school had a reflexive hatred of anything resembling rote work. We would argue that she couldn’t do the estimatin’ tricks without the basic underlying knowledge. We were told that if we insisted on drilling her, they wouldn’t support it. “Do it in the car when you pick her up,” we were told. Well, we didn’t do it in the car, but did do it ourselves: Flash cards, a “math picture book” from the 60s in which “four times eight were swinging on a gate,” a string toy called the “Wrapper” and eventually Kumon.
We were also told that kids didn’t need to learn how to type because they learned everything they needed to know about keyboarding by texting on their phones.
At this particular school, there did indeed seem to be a reluctance to do anything in a classroom that kids wouldn’t consider fun.
Sir Paul McCartney
Reasons to learn long division:
First, if you only learn things forwards, it’s harder to use them sideways or backwards. For example, recite the months of the year – in alphabetical order. Division is multiplication backwards (mathematicians use the fancy word “inverse”). To estimate a lot of things, you need to do inverse multiplication, which you need to learn and practice to be any good at.
Second, if you favor being able to estimate, long division is the first place you learn to do it. The formal method for long division actually gives you permission to guess an answer, and then requires you to check it. Checking being equally important.
Third, along with estimation, it gives you your first opportunity in math to actually make use of inequalities like greater than or less than. Speaking from teaching experience, even a lot of nerdy engineering students have trouble when you change = to or some other variation, and it’s important to be able to do that.
Fourth, people can’t do percentages because they have trouble with fractions. Science and engineering are all about fractions, a lot more complicated than the simple fractions involving numbers that you do in school. Being able to divide and practicing it teaches you to recognize relationships like 1/2 = .5 or 50%, 1/3 = .33333 etc. Long division is necessary to work with numerical fractions, and using a calculator doesn’t teach you how to do it.
As far as “order of magnitude” – I can guarantee fewer people can understand or use that than know or mastered long division. I once won an argument with one of the most brilliant computer scientists ever, because his “obvious” calculation was off by three orders of magnitude. And his mantra was “Do the math”.
If people understood orders of magnitude, there would’ve been a Marxist revolution in this country sometime after the Nixon era, when income inequality began growing rapidly. For that reason alone, schools will never teach it to most kids.