‘Stuff that you long ago forgot isn’t general public knowledge’

What do Christian fundamentalists have against set theory?” asks Maggie Koerth-Baker at BoingBoing.

She goes on to answer why — basically for the same reason that Christian fundamentalists do everything: Us-vs.-Them tribalism. But don’t let me spoil the ending, go read the whole thing (the kicker is terrific).

What I want to highlight here, though, is her introduction, which I may plagiarize if I ever decide to write my own memoirs because it so closely parallels my own experience:

I’ve mentioned here before that I went to fundamentalist Christian schools from grade 8 through grade 11. I learned high school biology from a Bob Jones University textbook, watched videos of Ken Ham talking about cryptozoology as extra credit assignments, and my mental database of American history probably includes way more information about great revival movements than yours does. In my experience, when the schools I went to followed actual facts, they did a good job in education. Small class sizes, lots of hands-on, lots of writing, and lots of time spent teaching to learn rather than teaching to a standardized test. But when they decided that the facts were ungodly, things went to crazytown pretty damn quick.

All of this is to say that I usually take a fairly blasé attitude towards the “OMG LOOK WHAT THE FUNDIES TEACH KIDS” sort of expose that pops up occasionally on the Internet. It’s hard to be shocked by stuff that you long ago forgot isn’t general public knowledge. You say A Beka and Bob Jones University Press are still freaked about Communism, take big detours into slavery/KKK apologetics, and claim the Depression was mostly just propaganda? Yeah, they’ll do that. Oh, the Life Science textbook says humans and dinosaurs totally hung out and remains weirdly obsessed with bombardier beetles? What else is new?

For me it was grade 3 through grade 12. And neither classroom video nor Ken Ham had yet surfaced, but we did watch those Moody Science movies and read books by Dr. Henry Morris — so I know quite a bit about bombardier beetles, too. We didn’t use the BJU textbook in biology, but one of the textbooks for my Bible class was Hal Lindsey’s The Late Great Planet Earth. (Yes, in high school, I took a final exam on Hal Lindsey. Aced it.)

But I also share Koerth-Baker’s sense that, much of the time, my school “did a good job in education.” The tricky thing, for years afterward, was figuring out the difference between that much of the time and the time we spent galloping off to crazytown.

I also know just what Koerth-Baker means by “it’s hard to be shocked by stuff that you long ago forgot isn’t general public knowledge.” I’ve gotten better at remembering that some of that stuff from fundie-world should be shocking, though. It helps to have a wife who finds it all hilarious. I can usually crack her up just by reciting the Pledge of Allegiance to the Christian Flag, or the Pledge of Allegiance to the Bible, or by singing a few bars of “Bright and keen for Christ our savior. …”

Big-time extra credit to anyone who recognizes that last reference.

(Via Jeremy Yoder’s always cool “science online” roundups at Denim and Tweed.)

  • The_L1985

    The only reason I did even halfway decent in math is because I memorize things quickly and easily.  I was memorizing formulas and rules instead of understanding how everything fits together.

  • Daughter

     I suspect that some of the originators of these anti-set theory beliefs may understand what they’re all about. I remember reading somewhere that one of the founding “moms” of the Quiverful movement had been a computer scientist before her conversion. Some fundie leaders are well-educated; because many of their followers aren’t, they can be easily led.

  • Daughter

     This argument (skill & drill vs. concepts) is similar to the phonics vs. whole language debate of language arts teaching. I think the answer should always be, kids need both. In part that’s because kids learn differently–some grasp better when you move from part to whole, and some grasp better when it’s presented whole to part.  But it’s also because while not understanding concepts limits understanding, not having a strong mastery of basic skills slows you down.

  • Lori

     

    I took AP Calculus in high school, while still being unable to set up the average word problem.  

    I’m simultaneously horrified on your behalf and seriously impressed.

  • The_L1985

     The multiplication table is a chart showing all the multiplication facts from 1×1 to 12×12, all lined up in neat little columns.  In my school, we spent much of 2nd-4th grade memorizing our multiplication tables, so we wouldn’t have to look things up or count on our fingers.

    I know a lot of people who “forgot their times tables,” and thus have to re-learn the basic multiplication facts before they can take any math classes as adults.  Thus, I’m pretty sure that forced memorization of times tables was pretty common.

  • Lori

     

    They made us go to 12×12. 

    Us too. School House Rock came in really handy for both my 11s & my 12s. If I tried really hard I could probably still remember the words to “Hey Little Twelve Toes”.

  • arcseconds

    Some people just object to any method of teaching elementary school
    mathematics that isn’t purely “skill & drill”. I had to explain to
    my aunt

    Yeah, exactly, I’ve encountered that kind of thing myself — forgot to mention that earlier when I was discussing it.   Not from fundamentalists, though (don’t meet too many of them), but I can’t really see why they wouldn’t have a similar reaction.  

    I don’t really know what to say about learning multiplication tables, or mental arithmetic more generally (or even pen-and-paper arithmetic for that matter).  On the one hand it’s boring and tedious, and it’s not really necessary to be able to do mental arithmetic accurately and well in today’s society (I’m not all that good at it).   There are far more important mathematical skills to learn, and I think boring rote learning and mechanical procedures help put people off mathematics,  and having people put off mathematics is a big problem.  

    On the other hand,  it is a useful skill, and it’s good not to be utterly dependent on machines for arithmetic.  For one thing, it’s too easy to make fundamental errors if you really got no idea what’s going on.

    What I would say is that being able to do reasonable estimates is easier and more important than being able to do 4-digit multiplications in your head.   Order of magnitude is useful enough.   Forgetting to carry the ’1′ is one thing, but forgetting where the decimal place is is quite another.

     

  • http://blog.trenchcoatsoft.com Ross

     Yeah. As I understand it, the traditional way of teaching multiplication was not actually to teach the fundamental process of multiplication, but to simpyl drill the 144 squares of the 12×12 multiplication table into the students via rote memorization.

    The “New Math” was not a big thing at the time I was learning math in grade school, but one thing I do remember was my parents’ consternation and “What’s this hippie crap they’re teaching my kids?” reaction when they found out that I was taught how to multiply without having rote memorized a table through drilling with threat of a ruler across the knuckles if we missed one.

  • http://dpolicar.livejournal.com/ Dave

     Yup. This is also true when you get swelling for other reasons.

  • arcseconds

    Yeah, a lot of Camping’s followers were engineers, too. 

    However, I have a lot of difficulty even entertaining the idea that the rejection of New Math on broadly religious grounds originated with people who understand set theory.    I really can’t see how anyone who actually understands it could possibly believe that it’s somehow anti-Christian.  I suppose one could imagine a set theory adept cynically manipulating the ignorant by creating propaganda about New Math, but in this scenario the understanding of set theory is not doing any work.  Someone could develop cynical, manipulative propaganda about New Math without understanding set theory just as well.

    (There would be reason to believe someone had some understanding of set theory if the propaganda showed any signs of understanding it, but I’ve never seen anything that indicates this.  Not that I’ve looked very far, just when it’s come up from time to time, so if anyone knows any better do tell.)

    While there are quite well educated people amongst fundamentalists, and fundamentalists can be easily led given the right circumstances, I don’t think it’s good to assume that it’s the well-educated that are always doing the leading.   The rank and file are quite capable of applying their paranoia of contemporary culture and coming up with craziness all on their own.

    (also, it’s not as if set theory is a sine qua non for being educated, or for that matter getting a computer science degree. )  

  • Turcano

     Useless fact of the day: music was taught as an aspect of math in medieval universities.

  • Mary Kaye

    I was very resistant to memorization as a child–the pain of teaching me to tell time is proverbial in my family, and it took some increasingly frustrating years of cursing (behind their backs) at people who would respond to “What time is it?” by showing me their analog watches to force me to finally learn it.  I was deeply offended, somehow, by the double use of the numbers as themselves and as multiples of five.

    As a result I am still pretty slow at multiplying, and there are parts of the table that I do not have memorized despite using them a lot (I play games that involve a lot of small-number multiplication on the fly).  What I have instead, after many decades of this, is very quick ways to work them out from table entries that I do know.  “Six times four must be two times twelve, twenty-four” goes by so quick I can barely perceive it, but it does go by every time.

    I also have a kind of kinetic formalism, like drawing a little house out of dots, that allows me to add columns of numbers fairly well without being able to intuitively add two one-digit numbers.  But I’m slowly getting better at that.  Maybe by the time I’m 60 I will have it down.

    I work in computational biology and statistics, go figure….I was much happier about math when I realized that it wasn’t mostly arithmetic.

  • http://twitter.com/FearlessSon FearlessSon

    Some fundamentalists do have natural ideological defenses against logic, I’ve seen evidence of that.

    THOUGHT FOR THE DAY:  
    A logical argument must be dismissed with absolute conviction!

  • http://twitter.com/FearlessSon FearlessSon

    They weren’t teaching math. They were teaching arithmetic. Not the same thing.

    Quoth my father, “I love math, I hate arithmetic.”  

  • http://twitter.com/FearlessSon FearlessSon

    Mainly, it’s an attempt to reconcile several ideas:  the existence of dinosaur fossils, the YEC idea that dinosaurs and humans must have coexisted, and the fact that so many cultures have dragon legends.

    To be fair, there is some scholarly speculation that dinosaurs had a role in the formation of wide ranging myths about dragons.  But that is not due to living dinosaurs, just due to finding their bones in the ground and making some crude guesswork as to what kind of a beast might have left bones like that.  It is only in the last few hundred years that we have begun to piece together such bones into a more complete picture of what the dinosaurs might actually have been like.  

  • http://twitter.com/FearlessSon FearlessSon

    The only reason I did even halfway decent in math is because I memorize things quickly and easily.  I was memorizing formulas and rules instead of understanding how everything fits together.

    I was good at memorization.  My math and physics professors would joke that they would swear the class notes I took were so precise that they must have come from a computer printer if it were not for the fact that they were written in graphite.  Other students would ask to photocopy my notes because they were that good.  But that did not really help me much.  

    While I might have had the formulas, actually applying them was a different matter.  The teachers observed that I tended to blunt-force my way through every problem, running through each formula I knew, trying to find one that applied and gave me a plausible answer, wasting a lot of time doing it, and not necessarily getting it right anyway.  Other times I would just go with as much calculator-driven arithmetic as possible to get an approximate answer, then retroactively apply the formulas until I got the one that closest resembled the approximate arithmetic answer.  I longed to be able to solve everything with a clearly defined procedure that could be looped through repeatedly until the solution resembled what it was supposed to and it could be looped no further.  But math was not taught that way.  

    Ultimately, the people who studied from the notes that I took did better on the exams than I did.  :(

  • Will Hennessy

    Cheeses!, with the f***ing bombardier beetles! I went to public school and I don’t remember s*** about f***ing fruit flies! Except that we had to deal with masses of the little f***ers in Advanced Bio!

    But then, I am from the Entitlement Generation (I mean, the Millenials!), whose motto is “I showed up to class, teacher, give me an A+.”

    …I’ve said too much…

  • http://www.facebook.com/people/Patrick-McGraw/100001988854074 Patrick McGraw

     Reason begets doubt; Doubt begets heresy.

  • http://www.facebook.com/people/Patrick-McGraw/100001988854074 Patrick McGraw

    Thanks for the info on multiplication tables. That may have been how I was taught, but not how I learned (if you follow me). Perils of being “gifted” and having a non-diagnosed autism spectrum disorder include learning the subject without learning the lesson.

    The idea of “forgetting times tables” seems bizarre to me. I don’t need to memorize the product of 18 and 13 because I can calculate it. That many people with similar educations can’t is one of those things I had great trouble understanding.

  • http://jamoche.dreamwidth.org/ Jamoche

    I did get a “you *could* add X+X+X+X+X+X+X, or you could memorize 7*X” lesson early on.

    My high school physics teacher started the school year out with Uncle Jerry’s Super Easy Rules for Solving Word Problems:

    In any problem there are one or more Givens and a To Find. You can identify them by certain key phrases (there was a list), and other key phrases tell you how to fit them into an equation.

    Simple, right? But not one of the elementary school classes that supposedly taught the things ever broke them down like that. I suspect anyone who found them intuitively obvious (hey, they’re in plain English!) felt the same way about Cobol (ADD X TO Y GIVING Z). But some of us think better in symbols.

  • http://jamoche.dreamwidth.org/ Jamoche

    A logical argument must be dismissed with absolute conviction!

    “We demand rigidly defined areas of doubt and uncertainty!”

  • The_L1985

     Sounds like a very useful fact to me.  If schools did it like that today, we would have a much higher percentage of students doing very well in math.

  • arcseconds

    The idea of “forgetting times tables” seems bizarre to me. I don’t need
    to memorize the product of 18 and 13 because I can calculate it.

    Why is it bizarre?   For most of us, it’s a lot easier to produce a rote-answer than it is to calculate something.

    Do you calculate multiplcation in all cases, even say 5 × 5?  Even if you’ve had the same equation several times in the last hour, would you still calculate it every single time?

    Is it ever faster for you to memorize something than it is to calculate?

    (if for some reason you can calculate all multiplication results where the factors are under 10 just as fast as you can recall them, then maybe it would help to think of another operation, like logarithms, that you can’t perform that quickly)

    or is it the forgetting you think is bizarre?

    I’m not all that great at my ‘times tables’, and I often have to do a bit of calculation even with two numbers under 10, although I’ll normally backtrack to a result I can remember and work it out from there.  e.g. if I can’t remember 6 × 7 I’ll remember back to 6 × 6 and add 6.   I think i did that as a kid, too, which is probably partly why I never memorized them properly in the first place.   My slowness at arithmetic annoys me, and it’d probably be to my advantage to drill multiplication more, but I really can’t be arsed.

  • PJ Evans

     ‘Old math’ was heavy on word problems. It didn’t really teach how to set them up either.

  • PJ Evans

    But some of us think better in symbols.

    Some of us think in sounds and pictures. Doesn’t help in more advanced math.

  • http://www.facebook.com/people/Patrick-McGraw/100001988854074 Patrick McGraw

     

    Why is it bizarre?   For most of us, it’s a lot easier to produce a rote-answer than it is to calculate something.

    This is another one of those areas where I have trouble understanding how neurotypical people think.

    Do you calculate multiplcation in all cases, even say 5 × 5?  Even if
    you’ve had the same equation several times in the last hour, would you
    still calculate it every single time?

    It’s more of an automatic process for me. If I stop to think about it, I do calculate each equation. I think in terms of discrete values rather than “A and B means C.”

    Is it ever faster for you to memorize something than it is to calculate?

    (if for some reason you can calculate all multiplication results
    where the factors are under 10 just as fast as you can recall them, then
    maybe it would help to think of another operation, like logarithms,
    that you can’t perform that quickly)

    Most daily arithmetic takes me less time to calculate than it would to remember a chart or to use a calculator. I’ve never been much good at mathematics outside of arithmetic, basic algebra and probability.

    or is it the forgetting you think is bizarre?

    While I certainly understand people forgetting something they’ve worked to memorize (I remember no calculus or trigonometry), I have trouble understanding how forgetting some specific equation requires sitting down and working it out, as I have seen people do. If you have the basic principles, rote memorization is not needed.

  • lowtechcyclist

    I’ve never understood the point of having a “Christian Flag,” let alone having the hubris to call a flag by that name without the consent of the vast majority of those who consider themselves Christians.

    I mean, we have a cross.  What on earth do we need a flag for?

    I just don’t get it.  Unless we want one “such as all the other nations have”  (1 Samuel 8:5) which seems to be getting the point of that story completely backwards.

    And a Pledge of Allegiance to either the Bible or the ‘Christian Flag’ – maybe Revelation 22:8-9 isn’t in their Bibles.  Our allegiance as Christians is to God, and God only, not to any lesser thing.

  • Daughter

    I think this whole thread shows that people learn differently. What works for one, doesn’t work for another.

    Several have said that they hated arithmetic, times tables and the like. I loved arithmetic so much as a kid that I made up my own math games using it. But when we got to proofs in geometry, I was completely lost. (It didn’t help that my original teacher left early in the year and we had a string of substitutes for the remainder).  I managed to get a 4 on my AP Calculus test in high school, but that took more mental anguish that anything I’d ever done up to that point. When I took my first calculus class in college, I was again lost and totally bombed it, and that was it for higher level math for me. Yet I’ve gone on to teach SAT prep in math to students, because I scored well and basic algebra and geometry continue to be fun for me.

    ~~~~~~~~~~

    I’m not sure how math is taught around the U.S. these days, but I have to say, I’m impressed with how math was taught by my daughter’s first grade teacher. They spent some time on place value and telling time, but most was spent on “number facts” starting with the number 2 and advancing up to 10. So they learned, for example, how many ways can you make five? Can you count to 5? Can you add two numbers together to get 5? How about 3 numbers? How many ways can you add 2 numbers, or 3 numbers, and still get to 5? If you go over 5, how much did you go over? Can you look at that pile of blocks and tell if there are 5 of them? If there aren’t enough blocks in that pile, how many do you need to add to have 5? If there are too many, how many do you need to take away?

    They’d spend several weeks on say, “5 facts,” learning all kinds of different ways you could manipulate objects or numbers in your head and on paper to get 5, and then they’d move on to “6 facts” and do the same thing.

  • lowtechcyclist

     “The idea of “forgetting times tables” seems bizarre to me. I don’t need
    to memorize the product of 18 and 13 because I can calculate it.”

    Tru dat, but you are almost certainly ‘calculating’ it from some smaller times-table that you have memorized.  To actually calculate it without a multiplication table would be to compute any products by repeated addition, because that’s what multiplication is.

    Let’s make it just a little more challenging, because it’s plausible that you can certainly get this particular product by (a) going 18+18+18=54 for the 18*3 part, and (b) remembering the rule that you multiply by 10 by tacking a zero on the end, then (c) adding 54+180=234, all without thinking about it much.

    But if we’re talking, say, 37 x 59, then your ability to calculate the answer without the use of a mental times-table that involves at least the products of one-digit numbers is going to be sorely strained.  You’re going to remember 7 x 9, say, not compute it and all the similar pieces via repeated addition.  (I suppose you could add up one stack of five 37′s, and another stack of nine 37′s, put a zero on the first total, and add the results together, but those stacks are where most of our brains gum up, even the brains of those of us who have one of them PhD thingies in math.)

  • Lori

    I don’t know if the story problems I got were part of New or Old Math, but I was definitely taught how to set them up. I really don’t get not being taught that since it’s the entire point of story problems. When the equations are the point you don’t need the “story” part.

  • http://twitter.com/mattmcirvin Matt McIrvin

    This is amusing, because just a couple of days ago, I got into a conversation with my daughter (age 6) which somehow got into set theory. Simple sets, unions, intersections. I described the empty set, and she announced that she didn’t like the empty set, so no more about that.

    We’d already talked about the idea of infinity. So I asked her how many members the set of all counting numbers would have, and she pretty quickly twigged that it would be infinite.

    “Right. So you can have sets with ordinary numbers of elements, and you can have infinite sets.   Like the set of all numbers, the set of all even numbers…”

    And she shouted “The set of all sets!” Into the deep water so soon…

    She seemed a bit put out when I mentioned that mathematicians ran into some paradoxical trouble when they tried to go there, with “the set of all sets that do not contain themselves” and such.

  • http://twitter.com/mattmcirvin Matt McIrvin

    Anyway, I think Eric had it back at the beginning of the thread. The objection to set theory had nothing to do with Cantor and Godel; it was that set theory was part of the New Math, and New Math was one of the educational reforms of the 1960s, which were bitterly opposed by conservatives.

    I went to elementary school in the 1970s, and, sitcom plots notwithstanding, it had pretty much blown over by then, except for some aftereffects: they called carrying/borrowing in addition and subtraction “regrouping”, and explained it in terms of gathering ten objects into a bundle of ten and back again, which I think was a consequence of the New Math-inspired emphasis on conceptual fundamentals.

  • http://twitter.com/mattmcirvin Matt McIrvin

    There are several different models of computation that mathematicians use to study things like the universe of computable functions, and it’s possible to prove that all of the strongest ones we know are equivalent to one another.

    So, for instance, Alan Turing had his Turing machines, in which a device with a finite number of internal states trundles along an infinite tape reading and writing symbols, and Alonzo Church had his lambda calculus, which is a kind of language for defining arbitrarily complex functions without having to give them names.

    It wasn’t immediately obvious that anything you can calculate with a Turing machine you can compute with the lambda calculus and vice versa, but it turns out to be true. So this doesn’t do anything to tell us that arithmetic is “really” the working of some cosmic Turing machine, or some Platonic lambda calculus. But the fact turns out to be useful anyway: the lambda calculus is the basis of functional programming languages, which are used to program computers, which are basically glorified Turing machines.

    So arithmetic isn’t necessarily “really” the working of some logic gates. But that is one of the many equivalent ways you can approach it, and a very useful one.

  • arcseconds

    How strange.  I got an email saying you’d replied to me, but the webpage doesn’t indicate it…  disqus being coy?

    If arithemetic is anything essentially, it’s the Peano axioms.

    There are several different models of computation that mathematicians
    use to study things like the universe of computable functions, and it’s
    possible to prove that all of the strongest ones we know are equivalent
    to one another.

    There’s an entire field called ‘hypercomputation’ dedicated to studying models of computation that are stronger than Turing computation: Zeus machines, oracle machines, analogue neural nets, etc.

    (some dispute that what these machines do is computation. it’s true that it isn’t Turing computation, but that seems a bit question-begging to me.  others complain that the machines aren’t possible, but that’s merely an empirical matter :]  (besides, Turing machines aren’t possible either…) )

  • arcseconds

     Oh, yeah, the other thing that’s interesting about your post is that you talk as if arithmetic is fundamentally a matter of computation.   It could also be seen as being a matter of relations. 

    That is to say, you appear to be thinking  that 2 + 3 = 5 means something like ‘once I have applied the addition-operation to 2 and 3, I get 5′, and a further investigation (or modelling) involved detailing what the addition-operation is (a bunch of logic gates, a set of instructions carried out by a universal Turing machine, or whatever).

    But it could also be read as ’2 and 3 stand in the addition-relation to 5′.  And that’s generally how mainstream mathematics has conceived of mathematical entities.  You can see this most strongly with set theory, which is also capable of modelling arithmetic, by treating numbers as sets, and an arithmetic equation would tell you about what relationships pertain amongst sets.

    And set theory was very much in vogue throughout much of the 20th century, so much so that there were those that thought that set theory was mathematics, and therefore 2 is a particular set (either {{}.{{}}} or {{{}}} depending on which school you went to).

  • http://www.facebook.com/people/Patrick-McGraw/100001988854074 Patrick McGraw

    I suppose you could add up one stack of five 37′s, and another stack of nine 37′s, put a zero on the first total, and add the results together, but those stacks are where most of our brains gum up, even the brains of those of us who have one of them PhD thingies in math.

    Taking the time to think about it, that is pretty much what I do. My brain gums up on other things that neurotypical people’s brains perform with ease (such as multi-tasking).

  • Headless Unicorn Guy

    We didn’t use the BJU textbook in biology, but one of the textbooks for my Bible class was Hal Lindsey’s The Late Great Planet Earth.

    Ah, yes.  Back when the Bible was 3 1/2 books — Daniel, Revelation, the “Nuclear War Chapter” of Ezekiel (the 1/2), and Late Great Planet Earth.  Been there, done that, still got the scars to prove it.

  • http://blog.trenchcoatsoft.com Ross

    I knew a guy who was applying for a job at an elementary school a decade or so ago, and he was informed that the math teachers were forbidden from using the phrase “divided by”, as it was considered too math-y and offputting to students who weren’t mathematically inclined. THey were required to replace it with “share”, as in “Eight share four is two”. I believe there were other “friendlier” terms for “plus”, “minus” and “times”.

    A little part of me died when I heard this.

  • http://tobascodagama.com Tobasco da Gama

    No, no, a private Baptist school.

  • Consumer Unit 5012

    I can’t believe we’re this far into a discussion of New Math and nobody’s linked to Tom Lehrer’s song on the subject.

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    I remember the rote multiplication thing m’self. I grew up before computers really took hold, so a lot of my math knowledge is from an era where you were still expected to do stuff without resorting to a calculator right away.

    As a result I learned how multiplication is repeated addition, and division is repeated subtraction. It took a while before I grasped that division is the multiplicative inverse, which is why dividing by a fraction means multiplying by the reciprocal.

    Seeing things as inverse operations to one another helps me understand relationships in mathematics a bit better, I think. It helps that it’s taught similarly in calculus: that differentiation is the exact opposite of integration, and vice versa.

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    I must have been lucky, then, since my teachers tried to cover some of the basic principles in word problem solving (such as identifying the quantities, etc).

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    Yep, I remember the 12s as well. I remember being rather daunted by that part of it.

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    What I would say is that being able to do reasonable estimates is easier
    and more important than being able to do 4-digit multiplications in
    your head.   Order of magnitude is useful enough.   Forgetting to carry
    the ’1′ is one thing, but forgetting where the decimal place is is quite
    another.

    That said, I find in science, multiplication is used a lot more than addition, so I’ve become very practiced at recovering from “off by 10″ type multiplication errors, by just multiplying or dividing by the extra power of 10 I accidentally took.

    On the other hand, forgetting to add or carry a number? Basically I have to scrap the problem and rework it from scratch, because trying to offset the error I’ve made in an addition or subtraction is actually harder.

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

     And set theory was very much in vogue throughout much of the 20th
    century, so much so that there were those that thought that set theory was mathematics, and therefore 2 is a particular set (either {{}.{{}}} or {{{}}} depending on which school you went to).

    As a result, I’ve become allergic to overprecise math professors who insist on postfixing all equations with something like (x e R) or refusing to refer to 3-dimensional space as 3D but instead “as all vectors in R^3″ or the like.

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    You’re joking. That’s the kind of absurdity I would think only someone anti”Politically Correct” would make up, as oppsoed to a real thing which anti-PC people use to beat social liberals over the head with their alleged lack of common sense.


CLOSE | X

HIDE | X