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  •  Algebra my ass! (28+ / 0-)

    How is it that we let kids out of high school without at least a rudimentary understanding of Calculus?

    Since when did "The homework is to hard!" become a valid excuse?  There are difficult things to learn that are worth knowing.  Hell, most of the things worth having are difficult to acquire, including knowledge!  Talk about knowing the price of everything and the value of nothing.

    So much of what goes on in our society seems like magic to far too many simply because they have no framework for quantitatively understanding the things around them.  That this is so means we have fundamentally failed them.

    Justice deferred is justice denied. -MLK

    by zephron on Mon Apr 19, 2010 at 10:45:46 AM PDT

    •  Exactly. (10+ / 0-)

      Just as important as what we teach is that we are teaching how to think and to learn. A concept that seems lost on so many, and could go a long way toward explaining the Teabaggers.

    •  Calculus isn't even hard (17+ / 0-)

      initially. Once you get the epsilon-delta proof, the rest falls into place easily enough. I think 20% of the problem is that it's not taught in a way that makes it easy or possible for students to see the math in their heads (I finally got e-d when I saw it animated on an old NeXT cube) and the other 80% is that it has this reputation for being really fancy and complex.

      Government is not instituted for the good of the governor, but of the governed; and power is not an advantage, but a burden. -Algernon Sidney

      by James Robinson on Mon Apr 19, 2010 at 11:04:18 AM PDT

      [ Parent ]

    •  The statistics blunder that destroyed a Shuttle (22+ / 0-)

      I think it's sad that we let kids out of high school without a firm understanding of physics.

      Before every Space Shuttle launch, a safety team must first give their go-ahead.  Before the Challenger's fateful launch on January 28th, 1986, the team met to review the launch to give a go or no-go launch decision.  There's always a lot of pressure for it to be a "go", and even moreso than usual, since this launch was to be a big PR event (first teacher in space).  But there was one element from a technical perspective that made this launch different, and which most of the debate focused around: the temperature.

      The launch that morning was to be by far the coldest launch conducted to date, at temperatures below freezing.  And much of the discussion focused on the rubber O-rings.  The Space Shuttle solid rocket boosters, due to their tremendous size causing problems for shipping, can't be built in one piece.  They're built with four segments each.  At each joint there are a pair of two rubber O-rings to stop the combustion gasses from seeping through the joints.  The reason that they use two is so that if one fails, the other can still keep the gasses at bay.  Typical NASA redundancy in action, and all.

      Little did the safety board know that there had already been a study conducted on the O-rings that showed that in cold temperatures, not only are the O-rings likely to fail, but that in such conditions, a failure in one tends to cause a failure in the second.  This launch was extremely likely to cause a disaster, but they didn't have the report.  But they did have something else: data.

      The engineers had data plotting O-ring failures versus temperature. You look at it and immediately think, "Huh -- not many datapoints and not a clear correlation."  One engineer remained staunchly against the launch due to fear of O-ring failure, however; he couldn't put his finger on what he felt was wrong with the data, but he knew something was wrong with it.  Unable to convince anyone else, he bowed to the launch pressure and the team gave its go-ahead.  He went to a bar after the meeting to watch the shuttle lift off on the TV, convinced that it was going to blow up on the pad.  When it lifted off, he walked out, only to turn around and head back in as soon as he heard people in the bar screaming.

      He was right about the data.  The graph indeed showed all failures.  What it didn't show was where there weren't failures.  "Zero failures" is a valid datapoint, too -- they were omitting data.  When you include that data, you get this chart.  All of the sudden, the problem becomes obvious: almost all warm-weather launches went okay, but every single cold-weather launch had problems, some severe.

      Recognizing statistical flaws is incredibly important to society.  And not just in engineering. Way too many people think the plural of anecdote is evidence, for example.

    •  12 Months of School (11+ / 0-)

      High school should have regular Summer sessions that are optional and include a larger athletic programme than the rest of the year. The public pays for the infrastructure year round, teachers need to be paid more money annually, parents can use the "daycare", students need more education.

      Long Summer vacations are a holdover from when America's children were needed to work on farms. Indeed, 6 hour school days are a holdover from when children used to work. Neither of those requirements are typical for any but a small fraction of students.

      If America's students got 15% more hours of school days and 25% more days, almost 50% more time in school, America would be stronger and better educated.

      "When the going gets weird, the weird turn pro." - HST

      by DocGonzo on Mon Apr 19, 2010 at 11:12:21 AM PDT

      [ Parent ]

      •  The only caveat is (11+ / 0-)

        we must not eliminate the opportunities for children to learn those things that can't be taught in school.

        I was a notoriously bad student, primarily due to the complete lack of interesting challenges.  I learned a great deal outside of school.  Were you to read my CV now, you probably wouldn't believe that.

        Justice deferred is justice denied. -MLK

        by zephron on Mon Apr 19, 2010 at 11:25:13 AM PDT

        [ Parent ]

        •  Extracurriculum (5+ / 0-)

          I'd like to see kids get school credit for what they learn outside of school. It's important adults can claim education when they compete with each other for later education or work, or just their own self esteem. Achievement testing should measure more practical application of skills, not just reporting the words taught to kids able to remember and parrot the teachers.

          I say this as a talented standardized test taker who's taught myself more than most people have, for fun and profit.

          "When the going gets weird, the weird turn pro." - HST

          by DocGonzo on Mon Apr 19, 2010 at 11:37:44 AM PDT

          [ Parent ]

          •  Unfortunately, even the notion of "credit" (4+ / 0-)
            Recommended by:
            Sychotic1, kurt, codairem, Larsstephens

            is complicated.  Not all useful skills are easy to measure.  How does one compare vastly differing backgrounds among job candidates?  What, even, does a given grade mean (diligence, mastery, promise; not all A's are the same, even within a single class)?  But yes, I agree that it might be nice to appreciate the extracurricular experiences more.  Perhaps they would then be encouraged more often.

            Justice deferred is justice denied. -MLK

            by zephron on Mon Apr 19, 2010 at 11:45:16 AM PDT

            [ Parent ]

        •  You also were probably pushed to study something (1+ / 0-)
          Recommended by:
          Larsstephens

          when you weren't ready or had got it and were ready to move on.

          Fear is the Mind Killer

          by boophus on Mon Apr 19, 2010 at 12:48:25 PM PDT

          [ Parent ]

          •  From the very beginning I had (4+ / 0-)
            Recommended by:
            Sychotic1, ER Doc, kurt, Larsstephens

            a visceral dislike for busy work.  The number of teachers I had who did not assign busy work could be counted on one hand.  That's par for the course, of course.  On the other hand, however, I did get to keep some semblance of creativity!  And I did get busy doing very interesting things in college and beyond.  So, things turned out alright in the end.  

            In fact, of particular relevance to this discussion, I have a BS in Mathematics and Physics and a PhD in the latter.  So it is not as if I was turned off of math as a result.

            Justice deferred is justice denied. -MLK

            by zephron on Mon Apr 19, 2010 at 01:06:34 PM PDT

            [ Parent ]

        •  I agree, which is why an optional (1+ / 0-)
          Recommended by:
          Larsstephens

          session is so valuable, and why it should have all kinds of project-based learning and activities that are different from the regular curriculum.

          Fry, don't be a hero! It's not covered by our health plan!

          by elfling on Mon Apr 19, 2010 at 03:05:30 PM PDT

          [ Parent ]

      •  I agree. (1+ / 0-)
        Recommended by:
        Larsstephens

        Fear is the Mind Killer

        by boophus on Mon Apr 19, 2010 at 12:47:26 PM PDT

        [ Parent ]

      •  Even at 45, the thought of studying for those (3+ / 0-)
        Recommended by:
        ER Doc, kurt, Larsstephens

        stupid bleeding NCLB tests and going as slow as the slowest fucking student for 12 months and for 8 hours a day would have made me suicidal, homicidal or both.

        9 times out of 10, school is not a place of learning, it is a place of indoctrination.  My real education began in college and most before that was auto-didactic.

        Repubs - the people in power are not secretly plotting against you. They don't need to. They already beat you in public. (Bill Maher)

        by Sychotic1 on Mon Apr 19, 2010 at 02:07:44 PM PDT

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      •  Hah! In my small town district, the school board (1+ / 0-)
        Recommended by:
        Larsstephens

        suggested increasing the school day by ten minutes because the district was dangerously close to the state mandated minimum hours of instruction per year. The parents revolted and forced to board to consider other options. So instead the lunch periods, activity period, and class change intervals were all shortened to increase the instructional time.

        "We will restore science to its rightful place." Barack Obama, 1/20/2009

        by Poycer on Mon Apr 19, 2010 at 05:50:45 PM PDT

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    •  "Logic! Why don't they teach Logic... (10+ / 0-)

      ... in these schools", asks the Professor in The Lion, the Witch, and the Wardrobe.

      I think it's far more important for everyone to demonstrate logical reasoning and especially logical fallicies before being allowed to graduate.  I keep telling people the only reason why the Democrats got their majorities back in 2006 was the new popularity of Sudoku.

      Big Joe Helton: "I pay Plenty."
      Chico Marx: "Well, then we're Plenty Tough."

      by Caelian on Mon Apr 19, 2010 at 11:17:13 AM PDT

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    •  Statistics needs to be a core requirement (11+ / 0-)

      for every BA degree across the nation.

      The future: a riddle inside an enigma wrapped in a search engine.

      by Ignacio Magaloni on Mon Apr 19, 2010 at 11:29:40 AM PDT

      [ Parent ]

    •  Calculus (11+ / 0-)

      I had a year of college calculus, but I honestly think it is quite possible to get through life just fine without it.  Algebra is important for everyday life, but I'd disagree with you on calculus.

      Basic statistics, though, and how to understand a study, should be more widely taught in high school.  

      •  It is a powerful tool to help you understand (2+ / 0-)
        Recommended by:
        profh, Larsstephens

        the world. Calculus is a language that allows you to understand and talk about trends in a fraction of the time it would take to do it without calculus.  When someone says "job losses this month were less than last month" you won't start telling others that the recession over, because you realize that though the 2nd derivative is positive, the 1st is still negative.

        Silvio Levy

        •  Sure it is (2+ / 0-)
          Recommended by:
          condorcet, Larsstephens

          Sure, it's a good tool to have.  But critical for graduating from high school?  If you don't let people out of high school without understanding it, a lot of them will never make it out of high school at all.  I don't agree with the idea that only those who can pass calculus should have a high school diploma.

          •  I don't either, but we're at the opposite extreme (1+ / 0-)
            Recommended by:
            Larsstephens

            right now.  It's not that people get a HS diploma without knowing calculus that worries me. It's that it's fairly easy to get a HS diploma without having learned MUCH more elementary stuff than calculus, and not much in other areas either.

            There's nothing wrong with encouraging students, setting expectations and teaching math well.

            Silvio Levy

            •  Agreed (1+ / 0-)
              Recommended by:
              Larsstephens

              Can't disagree with this:

              There's nothing wrong with encouraging students, setting expectations and teaching math well.

              •  Absolutely not. (1+ / 0-)
                Recommended by:
                Larsstephens

                Myself, I was reading fluently at three, and began writing stories around eight.

                But I am dyscalculic. I can understand (though I can't explain the understanding) some of the theories of algebra and of calculus, especially where it intersects with music and shape and I can see and hear it. So first grade pretty much taught me that I cannot do math, and when I do it it is a desperate, painful, horrendous struggle. A lot of any love for math went away when I hit the busywork of cranking out worksheet after worksheet of multiplication and long division problems; since the numbers would shift on me, while I understood the theory I could never be confident that a mistake hadn't happened somewhere along there. Because of course calculators were forbidden.

    •  Personally, I think it's because most people are (5+ / 0-)

      incapable of actually understanding even those portions of calculus that are capable of being taught in the concrete, much less the rigorous, abstract academic concepts that calculus requires. This isn't a failing of anybody or any group.

      Besides, one needn't understand any calculus at all to navigate the rudimentary abstractions involved in 99.99999% of "everyday" living. Would it be helpful? Perhaps occasionally, but more often not in any meaningful, worthwhile sense.

      •  And for that 0.00001%... (5+ / 0-)

        ... we'll increase the drop out rate another 10% by requiring calculus.

        I read things like "calculus isn't so hard!" and just shake my head at the a) ignorance and/or b) intellectual arrogance of that statement.  

        There are a lot of people who simply are not fundamentally willing or able or interested in learning higher mathematics.  And to force them to do so before getting a high school diploma is pushing them to a lifetime earning potential that's about the same as a grade school dropout.

        :: Not so hopeful now ::

        by Rick Aucoin on Mon Apr 19, 2010 at 11:53:04 AM PDT

        [ Parent ]

        •  Agreed. (3+ / 0-)
          Recommended by:
          elfling, Rick Aucoin, Larsstephens

          CA started requiring everybody to take algebra in the 8th grade recently.  I don't agree with that decision.  I think algebra is important (not Algebra II necessarily but first year algebra certainly), but there is no reason why you can't take it in the 9th or even the 10th grade and have a successful life.  Not everybody is going to be an engineer.

          •  eh. (2+ / 0-)
            Recommended by:
            Larsstephens, eaglekid85va

            I don't think it should be required to get a high school diploma at all.  Mastery of arithmetic for the basic high school diploma should be a given, but moving into more advanced math than fractions, percentages, add/subtract/multiply/divide just doesn't make sense on a "Must Pass Or You Get No Diploma" level.

            :: Not so hopeful now ::

            by Rick Aucoin on Mon Apr 19, 2010 at 02:50:32 PM PDT

            [ Parent ]

        •  I taught physics as a grad student (7+ / 0-)
          One of the most valuable lessons I learned is that it is a sort of faux-humility that allows a person to say "oh this isn't hard."

          It damn well is hard for almost everybody just like any other skill, and like any other skill practice will only compensate so much for innate ability. There's no need to punish people for having a different set of skills.

        •  I think the problem is the pass/fail (5+ / 0-)

          system of high school graduation.  Because all it really does is to pigeon-hole you as a loser/not a loser.

          I went to school in the UK, and we did it very differently.  Simplified, you got a separate pass/fail on each of your classes.

          Therefore you do not have to pass something that just doesn't work for you in order to succeed.

          It also gives employers and colleges far more information about your particular strengths than saying you managed to graduate in a one-size-fits-all manner.

        •  No one is talking about higher mathematics. (6+ / 0-)

          Algebra and the fundamentals of calculus are mastered by high-school students in many countries.  Yes, it requires effort, but it makes it much easier to understand the world quantitatively, and it affords a certain immunity against bullshit.  

          No one who understands the exponential function would go for a balloon mortgage, or believe that our society is sustainable, however peaceful your neighboorhood might look.  In fact, a lot of RepubliCrap propaganda is easily disposed of if one understands basic algebra and calculus.

          Silvio Levy

          •  I'm skeptical of your claims (2+ / 0-)
            Recommended by:
            Rick Aucoin, Larsstephens
            The understanding you speak of requires a level of sophistication that our schools don't provide and that I think can't be provided anyway. Few people in America or abroad are willing to invest the effort in making the analysis you suggest even of they are capable of it (which I doubt).
            •  Also... (2+ / 0-)
              Recommended by:
              Larsstephens, eaglekid85va

              ... I honestly don't think most people have the ability.  Not just the knowledge, but the actual ability.  I'm not running down the "average" mentality, but all too often those who are above average seem to forget that they are above average.

              And, sorry, as someone who flunked out of Algebra I twice in high school and therefore ended up dropping out of school completely, I consider algebra to be higher mathematics.  Arithmetic is essential for getting by in the world, just like basic literacy is, but one does not need to clear a bar like Algebra anymore than they need to be able to critically read Chaucer in order to be a good functioning contributor to our society.  

              But denying them a high school diploma for that lack sure does make it less likely they'll be able to contribute in any positive way.

              :: Not so hopeful now ::

              by Rick Aucoin on Mon Apr 19, 2010 at 02:48:24 PM PDT

              [ Parent ]

              •  I don't think you should be denied a high-school (3+ / 0-)
                Recommended by:
                kurt, Rick Aucoin, Larsstephens

                diploma for not being able or willing to learn math, but there is nothing wrong with encouraging students, setting expectations and teaching it right.

                And the Algebra=Chaucer equation is way off base.  Chaucer is but one author, and he wrote in what is for all intents and purposes a different language that is no longer useful in our world.  One leans Middle English and reads Chaucer to broaden one's horizons.

                But algebra is everyone.

                Silvio Levy

                •  Not academic algebra. (2+ / 0-)
                  Recommended by:
                  Rick Aucoin, Larsstephens
                  I think a concrete, applied algebra is appropriate to describe as being for everyone. Few people ever have the need to have a genuine understanding of something even as basic as the empty set (for example) much less the concept of number base, various polynomial theorems, graphing things other than very basic linear equations, and so forth.

                  The concept of limit, basic dericatives, and even useful application of say Newton's Method (e.g. for approxinting square roots), and so forth is even further removed from necessity. May as well tell them they should read up on Tangent Bundles and Killing Fields or the fun of S(2) groups while we are at it: it's about as useful and comprehendable.

                •  But, that's not what happens in American schools. (0+ / 0-)

                  In our schools you aren't encouraged to learn Algebra, you are forced into it and if you can't do it you pretty much get to live your life at the earning potential of a GRADE SCHOOL dropout.

                  Algebra as an option, Arithmetic as a requirement.  Not everyone is going to grow up and be an engineer, they really aren't.  We NEED good plumbers, carpenters, we need good Grocery Store managers.  It's OK.  It's honest work.  

                  :: Not so hopeful now ::

                  by Rick Aucoin on Mon Apr 19, 2010 at 10:19:18 PM PDT

                  [ Parent ]

                •  Spoken like a mathmetician. (0+ / 0-)

                  I also know a English Literature Prof who would agree that the comparison is way off base, but for the opposite of your reason.

                  Since I don't really have a dog in that race, I don't understand Algebra or Chaucer, I'll settle for "Both Are Superfluous To Most People's Lives".

                  :: Not so hopeful now ::

                  by Rick Aucoin on Mon Apr 19, 2010 at 10:25:55 PM PDT

                  [ Parent ]

                  •  By all means let's hear your English Lit (0+ / 0-)

                    prof's reasoning.  I'm not hard to persuade with lucid argumentation.

                    Is your friend a Kossack?  Invite him to explain why he/she thinks learning Middle English is important for everyone and learning algebra is not.

          •  There is no country in the world (1+ / 0-)
            Recommended by:
            Larsstephens

            that expects EVERY student to master calculus in high school.

            Their elites, sure.

            And it may shock you to know that I know some very conservative Republicans who are quite good at math and physics. (Plenty of liberals who do too.)

            Fry, don't be a hero! It's not covered by our health plan!

            by elfling on Mon Apr 19, 2010 at 03:09:19 PM PDT

            [ Parent ]

    •  lots to learn (10+ / 0-)

      I teach engineering. Most of my students, not all, but most, come in with some exposure to calculus before college. Believe, me, I understand the need for calculus as well as anyone.

      That said, I don't think everyone needs to learn everything. You for example, spelled a word wrong. (too <> to) Not a big deal, but it points out that you don't need to be an expert to be productive.

      Most important, more than calculus, more than spelling, is the ability to think critically. The ability to observe, evaluate, and act. The ability to listen critically to people you admire.

      That's what we need to teach our kids.

      •  This happens when I type faster than I read! (2+ / 0-)
        Recommended by:
        kurt, Larsstephens

        The problem with teaching critical thinking skills is that there are few examples in the standard curriculum where these are stressed as heavily as in math courses.  Unfortunately, that is only true when we get to proof-based courses (turn-the-crank formula based courses, not so much!).  For many, Calculus is the first example of that, which explains the culture shock that arises when students first encounter it.

        Justice deferred is justice denied. -MLK

        by zephron on Mon Apr 19, 2010 at 11:56:38 AM PDT

        [ Parent ]

    •  So how many high school seniors (2+ / 0-)
      Recommended by:
      ER Doc, Larsstephens

      do you think could figure out how many square yards of carpet to buy for a non-square living room?

      Without geometry, life is pointless. And blues harmonica players suck.

      by blindcynic on Mon Apr 19, 2010 at 12:42:16 PM PDT

      [ Parent ]

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