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Algebra As A Gateway Subject 667

Spock the Baptist writes: "The Washington Post started a two article series Sunday, and Monday August 18 and 19 2002. The articles deal with something that the math, engineering, and physics faculties at colleges, and universities have long known. Algebra is a 'gateway subject' for math, science, and technology, and secondary schools in general are not doing a good job teaching algebra."
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Algebra As A Gateway Subject

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  • by pizza_milkshake ( 580452 ) on Monday August 19, 2002 @10:17PM (#4101547)
    Yup, today your kid is doing algebra, tomorrow he's smoking crack. Just say no.
  • by Inominate ( 412637 ) on Monday August 19, 2002 @10:20PM (#4101563)
    Currently algebra is taught as a "You'll need to know this eventually" kind of a subject. Most of it is forgotten in a few days. Instead of teaching algebra, and then a few years later using it, math classes should be integrated with the science classes in which math skills are usefull.

    A skill without a use is going to be forgotten quickly.
    • by foonf ( 447461 ) on Monday August 19, 2002 @10:45PM (#4101676) Homepage
      Thats rather silly. You're basically implicitly conceding that there is no intrinsic importance to mathematics, and it is only "useful" as a means for solving scientific problems. Of course, as far as most students in middle/high school are concerned, what is being taught in science classes is "useless" also, and simply saying "learning X is important so you can do Y" is not a sound argument in the view of a student who sees no reason to understand either X or Y.

      I would suggest that this attitude is the main problem, and based on my own experience, it is something that the educational system in general seems to promote. After all, instructors are not necessarily encouraged to promote a real appreciation for and understanding of a given subject, but rather meeting various "standards", increasingly codified very strictly in terms of various new state standardized tests. This environment leaves a student no goal but passing these tests, which whether they reject it or accept it does not enhance their long-term understanding.

      Personally, I would rather have seen the intrinsic logic and beauty first, and the "real-world" applications later.

      • Unfortunatly the beauty is something that cannot be taught except to those who already know it. It also does not appeal to the masses...
      • Regardless of education, you'll find that most people don't enjoy doing math for the sake of math, and *no one* likes being told "do this, because you like it". I'm not saying don't try - students who love math would probably produce the most intelligent groups of people you could find. But I can't see it happening anytime soon.

        *However* - nearly everyone has a hobby that involves a fair amount of math. Like cars? Math. Like sports? Statistics. Computer games? Etc, etc. You can't instill a love of math in students - especially at a level of basic algebra. But you can entice them to love math by showing them how they can apply it to things they already *do* enjoy.

        And so that I don't seem overly negative - I agree with the majority of your second paragraph. Everyone seems to agree that the school system needs some help. But can any of us point to a system in use today and say "This is what we need?" This isn't a rhetorical question. If there are any spectacular systems out there that consistently produce well-adjusted students who see learning as a joy rather than a chore, I'd love to hear it.
        • by foonf ( 447461 ) on Tuesday August 20, 2002 @12:39AM (#4102254) Homepage
          I appreciate what you are saying, and I think it is true that there are many people who will never like math, but I also cannot see how any pedagogical system predicated on the assumption that what is being taught is inherently boring and undesirable to know can possibly result in meaningful learning.

          Really, I feel like if a person only likes cars or sports, they should be free to direct their education in that direction, without being forced to study any more math (or anything else) than they want to in order to do what they like. Reciprocally, the only people who would study mathematics would be those people who actually wanted to.

          But a system like this runs into tons of problems, I don't deny that, especially when financial success depends on taking a certain educational path during ones youth. The dynamics of education are totally different when things are made compulsory, and the focus becomes "how can we make people like what we are forcing them to do", rather than allowing people to do what they like. And maybe trying to tie it into things which do make sense to their lives will work better (read: higher test scores, or perhaps more qualified engineers in the future) than working under the mistaken assumption that everyone wants to learn.

          As an aside: Everything I remember of myself and my friends, from before prolonged exposure to education, suggests to me that children in their "natural" state really do enjoy learning. To paraphrase your comment, I think that most students see learning as a chore because learning in the school setting _is_ a chore. I've known many people who ended up dropping out of school or getting through very marginally, who I must say loved to learn, but simply could not work within the framework of school. There are things (drawing comes to mind) that, because they were forced on me at an early age against my will, I don't think I will ever be able to learn to do or even appreciate. And moreover, when I think about those teachers whose classes I really enjoyed, the one thing that they all had in common was a belief in the intrinsic worth of what they were teaching, and a sort of stubborn insistence that really, the students in the class _did_ want to learn, whether that was the apparent case or not.
      • by benzapp ( 464105 ) on Tuesday August 20, 2002 @01:29AM (#4102456)
        For this spectacular collapse of education, we have the renowned professor John Dewey of Columbia to thank. Yes, the same amazing mind behind the Dewey Decimal system also flagrantly defied centuries of knowledge about the way humans learned and decided that in fact, humans do not learn by experience, but learn by rote.

        Men used to learn as apprenctices, learning while doing for years at a time. The educated labored over Socratic dialogues written over two thousand years before, learning that wisdom and knowledge comes only in knowing to ask the right question.
        Many students used to take great pleasure in practicing Socrates' dark art by befuddling others into realizing their own ignorance.

        But then, the powers that be at the great school of Columbia looked at the masses of the great unwashed in the masses of tenaments of the South Bronx and decided that man was in fact a machine, ready to be programmed at any time. One must merely sit, listen, and learn from those more knowledgeable than he.

        And that is when the transformation took place. Instead of teaching children to ask the right questions, it was the teacher who asked the questions and the student who answered them. Critical thinking was no longer a necessary aspect of learning. One could merely develop the inhuman ability to memorize on end without any care as to its purpose. And then succeed. Some can do this, no doubt. Most likely, the abundance of Cocaine in numerous remedies for uncooperative children in the 1890's probably led some to believe humans could practice such tasks better than they otherwise could. Those complaining of stimulant use by children today are sadly ignorant of a tradition going back 120 years.

        But there is a limit, all the stimulant drugs in the world can't teach a child to think critically.

        The human being is different than other creatures in that we solve problems creatively, by using our heads, not our bodies. The dog when attacked, knows it will fight back. It cannnot imagine any other way to do this than by using its teeth. When it is hungry, it cannot imagine any other way to get food unless that food is right in front of it.

        Humans possess the spark of imagination that is wonderous in its abilities to do and create like never before. It is unfortunate when I see anyone creating the false dichotomy of beauty, art, and science, for they are all the same. We must teach children from the beginning to solve problems, to create what has never existed before, and help them along the way. Algreba should not be a subject in and of itself, it is the most basic form of deductive logic that should be a part of a simple logic class. Math in general should not be a stand alone subject, but taught as a tool in the course of study.

        We have followed John Dewey's advice for nearly one hundred years, that a child's brain should be poured full of knowledge. It is false, and destructive. We now have a nation of zombies, unable to question anything or solve any problems. They are hardly human, other than form. is it any wonder they merely stuff their faces with food and vicariously live out there sexual fantasies on television? They know nothing of humanity, they feel only the urges of animals. Eat and fuck, eat and fuck. Is this all life is? Of course, they cannot even ask THAT question...
        • by Zathrus ( 232140 ) on Tuesday August 20, 2002 @09:38AM (#4103898) Homepage
          Ah, so in other words we should go back to the old days of apprenticeship and merely allow the curious to move forward.

          Sure. Go for it. After all, the last 10000 years of human society clearly had a far better education level and standard of living than we do today.

          Or, hell, we don't even have to go back that far. Go look at some of the areas of the world that don't have mandatory schooling. They're top notch. Just last week I was thinking of moving to sub Saharan Africa because they have the best quality of life in the world.

          The reality is that you're completely wrong. Even as far back as Socrates and Plato the teacher posed questions to the student. Did students ask questions too? Sure. And *gasp* -- they can now too. If you want to bitch about the (US) educational system, bitch about the funding. Teachers work harder than just about any other profession (hrm, an 8 hour day with no breaks plus another 4-8 hours of planning and grading after school hours), pay them relatively little, make them pay for class supplies out of their own budget, and expect them to educate and morally instruct our children at the same time. With little or no parental backup.

          The other minor fact you forgot to mention is the expansion of knowledge in the past 150 years. The concept of a Renaissance Man is dead -- because there is no way for one person to hold the sum of human knowledge now. You can (and should) have a broad base of education, but "jack of all trades, master of none" is becoming increasingly true. Without modern schooling it's impossible to tutor our youth in even a small amount of the knowledge base. Do you know what literacy rates were prior to mandatory education? How many of the illiterate learned basic math, much less algebra?
        • Though your criticisms of modern education are valid, they have nothing to do with John Dewey.
          Let me quote from this page [bgsu.edu]

          Dewey believed that school should teach students how to be problem-solvers by helping students learn how to think rather than simply learning rote lessons about large amounts of information. In Dewey's view, schools should focus on
          judgment rather than knowledge so that school children become adults who can "pass judgments pertinently and discriminatingly on the problems of human living" (Campbell, 1995, p. 215-216). Dewey also believed that schools should help students learn to live and to work cooperatively with others. In School and Society he wrote, "In a complex society, ability to understand and sympathize with the operations and lot of others is a condition of common purpose which only education can procure."

          You can find Dewey's book Democracy and Education at this page [columbia.edu].

          The problem in our system is not that Dewey's arguments prevailed, it's that they did not.

      • You miss the point. (Well, IMO anyway, I can't speak for the original poster.) Making algebra skills required in other classes has a fundamental practical advantage -- it makes it harder to get any good (or even passing) grades if you don't know a fundamental skill.

        Reading is already this way; students that can't read or have trouble are virtually doomed to low grades, as reading skills are relied upon at increasing sophistication almost as soon as they are taught. It is a very obvious red flag that students are missing something very important.

        It is very difficult to impart a genuine appreciation for something before someone understands it at some level.While I agree that this approach needs to be much, much more heavily promoted, I also think you need the negative, "look, just learn it" repercussions of an interdependent curriculum, so society can be guaranteed that children emerging from our schools have a known baseline of educational skills.


    • Hey I agree with you Inominate, but in my opinion, algebra is only useful to people who are in the sciences anyhow. When would a normal person ever use algebra? EVER? I dont really think people should learn algebra unless its for a reason, and if its for a reason it should be for a specific field.

      Currently the schools dont even teach real math they just teach calculation, they give you a million repetitive drills, and make you practice to memorize useless shit, like your multiplication tables, and other various rules.

      This is the problem with how math is taught, the concepts should be taught, put the steps to doing the calculation in a refrence manual end let people look through it when they need to solve a problem.

      Honestly only people who are naturally good at math or who like calculations will remember all the little rules, steps, etc, just like with chemistry, what good is it to make people memorize tables when they still dont really know a damn thing about chemistry?

  • "Stand fast in your refusal to remain conscious during algebra. In real life, I can assure you, there is no such thing as algebra."
  • First it's a little one-plus-two, then they get into algebra. After that, it's a slippery slope into the "hard stuff," like trig, or even the brain-damaging calculus!
  • by NewWazoo ( 2508 ) <bkmatt @ g m a i l.com> on Monday August 19, 2002 @10:25PM (#4101587) Homepage

    I was blessed here in Tallahassee, FL, with some really great math teachers, as well as the option to take a "real" algebra course as "early" as the 7th grade. And we're not talking "algebraic concepts" here - I was required to derive the quadratic formula w/o completing the square, which is TOUGH when you're 12 or 13. :)

    It disappoints me to see schools lowering their standards to raise average test scores. I'm one of the minority who believes that D should be passing, but that a C truly should be an "average" grade (just like it says on the report card). My H.S. has an average GPA of something like 3.4! That's just silly - there's nothing differentiating the truly exceptional from those who could either kiss a lot of arse or slough through it and do all the extra credit.

    I also see a very disturbing trend of schools offering classes that, in essence, "teach the test", be it the SAT, ACT, or the FCAT (in FL's case). Doesn't this skew the results? I'd like to hear some others' opinions on this... :)

    Just my $0.02 worth of incoherent rambling...

    • As far as teaching the test, I totaly agree with you. I've got two kids in school here in Texas and everytime that it gets even close to test time, they go into major "teach the test" mode.

      I've had to sit down and teach my daughter some basic stuff and it is starting to get me more and more upset with the system.

    • That's just silly - there's nothing differentiating the truly exceptional from those who could either kiss a lot of arse or slough through it and do all the extra credit.
      It's even worse at my school--we don't have any weighted grades at all (well, now we do, after I leave).
    • I got my HS education from FL also, (Duval County to be specific), and I can say I got lucky while others suffered. In middle school I had 7th Grade Pre Algebra, then 8th Grade Algebra, both offered under their "honors program". At the time, my middle school was doing down, and was blessed with the only 2 "good" math teachers. The others were incompetent. Moving up to HS I graduated with AP Calculus. I believe the problem is that the minimum for students to get their diploma is Geometry. (it goes Algebra, Geometry, Algebra II, PreCalc/Trig, AP Calc here). From my experience with high school physics and university physics, a lot of the basic things are derived from skills taught in Algebra II and PreCalc. ..and if it's not required, not everyone will take math classes past Geometry unless they intend to go to college.

      now, about the FCAT. Yes, I have taken the test, and last year was on a panel grading a batch of them. I graded the writing/reading tests from an elementary school and the results were TERRIBLE, which goes to show standardized tests do not improve education.
    • I agree about the averaging. I've considered teaching at the local JC (oops. Guess it's a 'real' school these days.) On first day of class:

      "Class, we are going to have a vote. I am more than willing to grade the class on a curve. But only if it works both ways. If the average for an exam is lower than a C, I will add points to the exam for everyone. If the average is higher than a C, everyone gets points deducted."

      Oh my, that would be so fun. And evil. Opens up so many possibilities for the study of game theory.

    • I have no problems with them teaching the SAT, as long as students are required to take it and pass it (pass being being at least say a 1000 combined math/verbal) before graduating Junior High. That's right - not the PSAT, but the SAT. Seriously, there's no math or english on the SAT that any student shouldn't be able to handle and get a decent score on PRIOR to entering High School. There's no trig, no logarithms, the calculator-enabled math is a fucking joke (in my day there WERE NO CALCULATORS ALLOWED.) If you can read an intelligently discuss a book, the english/vocab part should be doable as well.

      That we can't even get HS seniors, with the benefit of a supposed 12 years of education to score decently on the SAT is merely a symptom of how bad the problem is. Seriously, why are we wasting money with remedial education for adults when we should have spent that money when they were still minors?
  • What? Why the heck is algebra being taught in secondary school? Why leave it that late? I mean, they aren't covering linear algebra, are they? They didn't in my high school. Apart from that, I cannot imagine what else they could be teaching about it. The only time I used algebra was in physics class in high school. Everything else, I had learnt by grade 6 (including geometry and trig, though I'll admit that I did not learn about conic sections until high school...)

    So what are they talking about? Linear algebra? I doubt it, I can't see that they have been able to catch up that much. So, errm... what?
  • Home School (Score:3, Insightful)

    by Grumpman ( 64344 ) on Monday August 19, 2002 @10:29PM (#4101601)
    I agree that public schools can't do the job. The teachers are told to crank the kids through as fast as they can with little to no support from the board or, more importantly, the parents. It's not their fault. They are among the lowest paid professionals doing a thankless job.

    Solution, home school. My wife stays at home and raises our two kids. My 3 year old can count to 20 in English and Spanish (no, I'm not bilingual), do simple sums, and knows her alphabet. I plan on testing her knowledge of the Pythagorean theorem before she hits 10. She will not be rushed, pressured, bullied, or pampered. But we can give her a far better education than some underpaid, overworked teacher afraid to discipline her class for fear of losing her job or his life.
    • Re:Home School (Score:2, Insightful)

      by Cyno01 ( 573917 )
      i'm not going to get into a big debate here, but home schooling lacks a big part of regular schooling, somethign /.rs may be afraid of, *gasp* social interaction, maybe if parents would get off their asses and read to their kids or buy them books instead fo designer clothes our kids wouldnt; be so dumb, i'm currently in highschool and i see astounding levels of idiocy all around me, i attend a public high school, it sucks, i learn next to nothing, and what i do learn isn;t relevant to anything but which bubbles i'll be filling in at the end of the week, instead of just assuming the school was doing its job my parents took me to museums, bought me books and gave me magazine subscriptions for my birthday (popular science is an apropriate subscription for a third grader if you cut out all the doral ads)i dont learn at school, i do whats required of me to get a pice of paper and learn on my own, mostly i go to school to be with my friends, home schooled kids are always super-smart, but i'm sure we all know/remember the weird homeschooled kid who lived around the corner
      • Re:Home School (Score:2, Interesting)

        by andrews ( 12425 )
        I think the social interaction issue is a false argument. How much valid social interaction is there hanging around all day with a bunch of dopey kids your same age? I'd much rather see kids grow up interacting with people of all ages in all walks of life. Public school is an unnatural system created to churn out docile factory workers. Any well adjusted, educated people turned out at the end of twelve years is an accident and failure of the designed system, not a success. Of course the schools are turning out poorly educated people. Thats what they are designed to do.
        • I'm torn on the social interaction issue. On one hand, we have the anecdotes surrounding the 'hellmouth' series by JK. While plenty of it was hyperbolic, I can relate to many of the sentiments. For anyone not in lockstep with his peers, it can be a bitch.

          But it's difficult to get kids to see people from all walks of life. I've seen kids who were home-schooled and/or private schooled who really miss out on the dregs of society. Hell, they even miss out on the averages of society. They interact only with other elitists, be they 5, 15, or 55 years old. They do comport themselves well, but have clear difficulties reacting with children their own age, and those in different economic brackets.

          Then I turn again to the other side of the argument: I attended public school for 10 out of 13 years. I picked up a few friends here and there. But I got most of my friends and social interaction from an after school job, and one after school activity (drama).

          BTW, is there a single kindergarten in the country that isn't a den of socialist dogma?

          I suppose my point is that much of life is dealing with dopey, moronic products of public schools. Better to learn to deal with it early on.
    • I have a 15 month old kid. My biggest concern about home schooling is social interaction. With any luck, there will be a 'critical mass' by the time he is really in the stage where he needs to pick up those skills. What do I mean? There'll be enough kids of varied backgrounds doing various homeschool group things that he'll be able to hang out with real people, not just 'homeschool weirdos'.

  • Flying and Algebra (Score:3, Insightful)

    by HerrGlock ( 141750 ) on Monday August 19, 2002 @10:30PM (#4101603) Homepage
    I thought it was an "I'll never need this or see it again" when I was in HS. Problem is, I became an Instructor Pilot. Algebra was life and used every day.

    I read in the Washington Post that the Maryland schools are putting BS into the standardized tests and calling it "algebra" and then they wonder why Johnny cannot do anything in real life.

    Perhaps we can get back to basic R, R, and R one day and not be as worried about people getting their feelings hurt when they need help in the subjects.

    • (* I thought it was an "I'll never need this or see it again" when I was in HS. Problem is, I became an Instructor Pilot. Algebra was life and used every day. *)

      Yes, people need the basics of algebra, but *most* of the crap they teach in schools is "busy work" (at least in my day).

      Plus, your experience may not be normal. Does it make sense to teach algebra to 100 students if only 3 will use it later?

      It would be more economical to hire a math expert when needed, or those 3 can learn it *when* they need it.

      Math is a lot like law in my mind: there is too much to remember, so you hire/pay experts (like lawyers) when needed rather than learn 1000 facts or algorithms when you are 16 and hope they stay in your head (not) just in case you need it someday.

      Tradition, yes. Logical? Hell no!
  • by Troy ( 3118 ) on Monday August 19, 2002 @10:32PM (#4101617)
    One of my biggest problems teaching algebra is that my students were never given a firm foundation in basics throughout middle school. The philosophy described by the article is accurate as to what I am seeing in middle school math education, but results in a bunch of students who can only solve linear equations in a "trained monkey" kind of way. They have no real cognition as to what their actions mean (ie. When you add to both sides of an equation, you aren't REALLY changing it.) I was halfway through last year (my first year in a new district) before I realized that most of my [otherwise intelligent] students really didn't understand basic concepts like substitution, the difference between an expression and an equation, why you do things to both sides of an equation, etc etc etc.

    Let me tell you how much of a nightmare solving solutions were.

    I also think that algebra is pushed on students before they are cognitively ready. The average middle school student should go as far as evaluating expressions, variable substitutions, (MAYBE) 1 step equations and (MOST importantly) reading an expression (ie. 3x + 4 means three times x plus 4). The rest of their time should be spent brushing up and applying their ARITHMETIC skills, such as working with/reducing fractions. Give me a class of students who know how to substitute and know their arithmetic, and I'll give you a class of all stars.

    In this upcoming year, I'm dedicating the first 2-3 weeks to an intensive review of arithmetic and bare bones algebra. Hopefully that will smooth things over as we go on.

    I really like the suggestion of merging science with math. I would love to see those two subjects team taught over a double period.
    • by Jucius Maximus ( 229128 ) <m4encxb2sw@NOSpaM.snkmail.com> on Monday August 19, 2002 @11:04PM (#4101778) Journal
      "and (MOST importantly) reading an expression (ie. 3x + 4 means three times x plus 4)."

      I agree with you fully on that point. I am a university student (in Ontario, Canada) and sometimes I hear tales from the really enthusiastic professors about some of the madness when they taught grade school level math.

      For example, one kid did something like this:

      Question: 6x + (-5) = 63

      Answer: x = 8

      Question: 3x - (+12) = 15

      Answer: No solution!

      Now really try to think about the thought process which would have lead to these (wrong) answers. Can you figure out what the kid thought? I couldn't until the prof explained it to me:

      The kid thought that the first question read as "sixty-(what) minus five equals sixty-three" ?

      And naturally 68 - 5 = 63

      Thus you can figure out how the kid thought there was no answer in the second one.

      Yes, you are right, and there are too many kid falling through the cracks and with rising class sizes, you can't help them all get the concepts right.

      "The rest of their time should be spent brushing up and applying their ARITHMETIC skills, such as working with/reducing fractions. Give me a class of students who know how to substitute and know their arithmetic, and I'll give you a class of all stars."

      Once again I think that you are right on the money. Too many people are afraid of fractions. Back in the 80s in Canada, fractions were a real subject in grade 6-8 and the students came out of it with a real industrial knowledge of how they work. Most people in my generation in Ontario are scared stiff of the same things. (But if you take a kid from Alberta, they know it cold because they do it all in grade 4-5 there.) Fortunately for me, I was blessed with a really bad teacher (?!?) in grade 5 who was terrible at teaching fractions, so I just ignored him and actually figured out on my own how they worked.

      Even now I see people my age who are half way though a university level engineering program solving laplace transforms and systems of differential equations, and they can't handle fractions within fractions or negative fractional exponents.

      I wish you good SKILL in tuning your students into shape. I believe you have your priorities in the right place and know what the real problems are.

    • I spent this summer tutoring a student who needed "a little math help," according to her mom, in order to score high enough on a standardized test to get into the weakest of our state's universities.

      Well, no. What she needed was to retake math, beginning in about 6th grade. Not that she was dumb, but it is almost impossible to do well on a timed test if you're using your calculator to divide by two. All the basic tools the above post talks about were completely foreign to her, although - to her credit - she could FOIL up a storm. Unfortunately, I don't think she knew what factoring actually meant. Forget deriving formulas by common sense or making intelligent guesses to narrow the range of choices. She was convinced that math was difficult and "other", something to be crammed before tests... but nothing she would ever understand. And understanding should be the goal of instruction in any subject (says a future teacher, with her fingers crossed).

      Personally, I'm in favor of combining math with anything - science, as above, or music (as one of y'all suggested) - that will help students like mine think of algebra as a helpful tool, or even a "fun puzzle" (our local slang for calc), as opposed to some kind of senseless ordeal.

      To be fair, I got an excellent education in public schools (please, Lord, may there be no typos in this boast... err, post), but then, I watch "Square One" and _Donald in Mathmagic Land_ for fun. A good nerdy environment will do wonders.

    • There are a few school districts that are making the attempt. My middle school had a fairly focused Math program which finished with basic Algebra usually taught in high school, if were in the Honors program. They covered basic quadratic equations, substitution, etc... The earlier classes focused a lot on math drills, and the like. In the end every student who took the state end of course exam passed it, even though we weren't 'taught to the test'.

      I think a lot could be gained by just having Math and Science teacher cooperate a bit more. It seemed through my time in High School, that often the math classes and science classes where completely disjointed. Simple things like having one assignment/project crossover into more than one class would definate help. (When I finished HS, they where moving to something like this.)

      The problems for basic math are a lot more prevalent than you might guess. The local community colleges here have to place a lot of people through basic developmental math before they can start with the higher level subjects. (Developmental math covers basic fractions, percentages, multiplication, division, and factoring.) The scary thing is, a lot of the people in devlopmental math have High School Diplomas. Developmental math is then followed by High School Algebra, which is followed by College Algebra.

      I find that a lot of the issue is in the heavy use of calculators. Instead of doing basic operations, and understanding, we have a generation of "use the calculator anyway" students, lacking a firm foundation in math. Punching the buttons to get percentages, etc.. Instead of understanding 3 + 3, they understand the buttons on the calculator.

      Taking multiple post-Calculus classes this semester, I'm very happy that the (public) HS and middle school programs where as good as they where. =)

    • It is not a matter of cognitive development, it is the result of a poor elementary school preparation.

      In elementary school students are taught nothing about mathematics, period. All they are taught is to memorize tables of results of the four major operations. They are taught to apply these operations to larger numbers, but few students will ever grasp why 3x3=9, because they are never taught to understand such concepts, and students who ask are often brushed aside, and frankly this is because few elementary school teachers understand basic mathematics either.

      After learning, or more often failing to learn to perform these operations, students then have the rug pulled out from under them... "Oh, by the way, these fraction things are really unsolved divisions, and and the 'equals' sign doesn't really mean 'do some stuff to these things and write the result over there'..."

      Furthermore, within the teaching of Algebra and onward, the emphasis is on the memorization of equations and specific cases, with little or no attention paid to the underlying cause of these "facts". I am a firm believer in the not-common-enough practice of "open book" tests or allowed "cheat sheets", which in the proper teaching and testing environment would promote actual learning and understanding as the mind is freed from the need to focus on memorization.

      If we actually taught Mathematics from Kindergarten up, rather than teaching counting, then arithmetic, then algebra, we wouldn't have this sudden dramatic drop-off in comprehension at the Algebra level. And if we focused on understanding rather than memorization, we might actually get understanding.
    • by bfields ( 66644 ) on Tuesday August 20, 2002 @01:04AM (#4102352) Homepage

      I also think that algebra is pushed on students before they are cognitively ready. The average middle school student should go as far as evaluating expressions, variable substitutions, (MAYBE) 1 step equations and (MOST importantly) reading an expression (ie. 3x + 4 means three times x plus 4). The rest of their time should be spent brushing up and applying their ARITHMETIC skills, such as working with/reducing fractions. Give me a class of students who know how to substitute and know their arithmetic, and I'll give you a class of all stars.

      No way. This is how we end up with a typical math sequence that goes:

      • 6th grade: we're finishing up arithmetic now, and then we're going to get you ready for algebra with little fill-in-the-blank arithmetic problems and stuff. Next year you'll do real algebra! Won't it be fun.
      • 7th grade: fooled ya! No algebra yet, no, we're doing pre-algebra! Next year you'll do real algebra! Won't it be fun!
      • 8th grade: OK! This year we're going to give you a little algebra. But not too much! You'll learn to solve 2 equations in 2 unknowns, but we don't trust you to actually *understand* something so mind-bending, so we'll just give you a bunch of really mechanical drills on this.
      • 9th grade: wait! We're not sure you got that! Let's go over that algebra stuff again, and maybe do a tiny bit more.
      • 10th grade: you guessed it: more algebra! This time maybe you even get a little trig or very basic analytic geometry or something.
      • 11th grade: pre-calculus, which is, you guess it, more algebra....
      • 12th grade: calculus, whoop-de-do.

      And this is for the super-bright kids. Come on! Even the "slowest" kids want to see something new every now and then!

      I know how frustrating it is trying to teach people something when they don't really have the prerequisites down cold yet, but that's life; they'll pick that stuff up when they have to, and you can't let it keep you from throwing the new stuff at them too....

      --Bruce F.

  • math teachers (Score:4, Insightful)

    by NeoSkandranon ( 515696 ) on Monday August 19, 2002 @10:36PM (#4101629)
    This seemed to be pointed more towards the middle-school level math courses, but I never had algebra that low. I took algebra I, II and precalculus in highschool, and IMHO (this being two years after i graduated) the problem is that algebra classes have to cater to the lowest commmon denominator, since they're almost universally required for graduation. Even in college calc, our teacher had to spend a few minutes refreshing everyone's memory on basic algebra (factoring, synthetic division, etc)because we never really learned it.

    Of course, one approach would be to fail the fuckwits that can't hack it, but apparently teachers catch more flak for failing lazy students than passing smart ones.
    • "...failing lazy students than passing stupid ones."

    • Of course, one approach would be to fail the fuckwits that can't hack it, but apparently teachers catch more flak for failing lazy students than passing smart ones.

      Two reasons:

      First, teacher competency is frequently based on how many students failed. Because obviously, the teacher is the end-all, be-all for education. The students and the parents have nothing to do with it.

      Second, the kids who need to be failed are politicians' kids. After all, how could the jackass that wrote the DMCA and the dumb slut who was ignorant enough to carry his seed possibly mix genes in a manner that would result in a positive IQ? It would throw the theory of entropy right out the window.

  • So what does smoking a gateway drug AND doin' gateway math get you?

    Please, original answers only. Lets get the obvious ones out of the way...

    1) What does it get you? -1=Offtopic, sucka!

    2) pr0n

    • I'll bite.

      So what does smoking a gateway drug AND doin' gateway math get you?

      3) You can see the equations spinning their beautiful graphical representations, but you can't explain them to anyone including your teacher.

      Unless, of course, thats where you got the smoke.

  • I'd have to disagree. I work as a network administrator at a rather large ISP and am fluent in several programming languages. I also am very fluent in computers and fixing them, however math has never been my forte, and quite frankly I couldn't do an advanced algebra problem to save my life. But it's never ONCE hung me up. Math teachers at my Uni told me time and time again that Math is a key component to computers.. but I have yet to see it. Sure binary and hex and all that.. but only if you're working at the lower levels.. and even then you can do it on calculators.. and that's still really only low level math and just knowing how to do it. But algebra you never use unless you're programming a specific program that does something algebraicly in which case you have the formula. And, as a network administrator I have *never* once needed to know algebra.. just lower level math... I disagree and think the whole "math in the comp sci" thing is politics in the schools.
    • Trying actually using a programming language... no matter which one you use, even visual basic, almost everything has to do with algebra. Even if you are writing php scripts for a website you have to deal with alot of algebraic equations. Algebra might not be the fundemental part of using a computer but it IS the fundemental part of programming on one!
      • I agree.

        I started coding when I was six years old, in BASIC. At that point, I was in special ed, and remedial everything. Then. my father got me hooked on programming. I learned to read just so I could read the learning BASIC book that came with the computer. I quickly climbed out of special ed. These days, I'm literally a genius, high IQ and whatnot. I was in the 99th percentile according to the SATs and ACTs.

        I was thinking about it a few days ago, and I owe everything to computers. With algebra as second nature,... I don't know how to finish this, other than, algebra is definitely a gateway to higher learning.

        I'd love to hear similar stories, if anyone has them.
    • Not into higher math eh? Just wait until you have to design and implement more effcient algorithms. Having only a passable calculus background (which I had since forgotten), I had to resort to brute-forcing all of my solutions when I was taking programming in school. For example, instead of notating in polar coordinates, I coded in degrees and converted into X/Y coordinates (this was for a X-windows clock written in LISP.) It worked (ie, it got me the grade), but it was ugly, and ate up a lot of processor cycles. At least take some classes on graphing and number theory. Linear algebra too...
  • by puto ( 533470 ) on Monday August 19, 2002 @10:37PM (#4101643) Homepage
    Well I can't imagine what school's must be teaching these days cause the younger generation I do run into seems to be completely clueless for many things.

    Math, science. But also literature, geography, world events. But no couth is one of the biggest problems.

    I admin from home. Sit in my underwear, drink beer, do not shave. See me in public like that? Hell no. I go on an interview for a possible client and I look like the man from IBM in the 80's. The orginal Men in Black

    I am 32 and not that old(or at least I dont think so). Here is what I know.

    Late 80's schools had gotten so horrid they had to administer tests that had to be taken before graduation. Basic skills tests. You might have passed your exams but still had to take this one. I never took it but I saw one and it was frightfully easy. Along the lines of the ASVAB for the military.

    Schools dropped physics and trig to go to things like Alebgra 1,2 and geometry and that was it in math.

    Anyone have that physics teacher who used the overhead for the notes? And he had written the notes originally back in 63 and over the years had made corrections to them? But sill used them. Probably still teaching.

    TENURE - stay here long enough and we will give you a free cushion for your ass.

    I went to a boarding school for my formative years and while I did recieve a fair amount of ass whuppins I did get some great teachers who really got me into science and math and literature. We built a Heathkit Hero in the dorm and fiddled with ham radios, and even had a unix box in '83. A DEC. And I owned your ass playing miner 2049er and Lode Runner on the Apple //.

    I then switched to a local school and bam. I saw the wonders of a regular high school. Sure I got girls and booze and had quite a bit of fun, but I did not learn near as much or the teachers did nothing to generate my interest in things. Well, methane soap bubble torches were fun.

    Teachers aren't paid enough. Private schools do tend to get the better ones. I graduated in the end from a public school, and had good teachers, but my private school experience was by far superior. And when I choose to lay my eggs I will make the sacrifice and send my little geeks to a private school. For them.

    Teachers also need to be recertified every couple of years, just like people in the tech industry. "I had a TRS-80 back in the day so I don't ever need to take a computer class". Teachers get complacent, light a fire under their asses.

    Bit of a rant here, but we do need to do something about it. Our world ya know.

    And I do not care if you are 18 and can write a script that will control the weather, make Bill Gates give it all to charity, or even make Slashdotters a more level-headed bunch. Education is the the real fucking deal.

    Take the time. I had to do it at 32 and it sucks.

    • "Teachers aren't paid enough. Private schools do tend to get the better ones. I graduated in the end from a public school, and had good teachers, but my private school experience was by far superior."

      I think that HS and Private School teachers are on equal footing in the area of teaching skill.

      The difference is that in Private School, the losers, troublemakers, nitwits, idiots, lamers, etc can be kicked out much, MUCH more easily than in public school. Thus the lowest common denominator in private school is way higher than in public school. Thus private school teachers have way more motivation and there is much more potential for enrichment and teaching more exciting and advanced topics in public school.

      I took public school the whole while and all of the classes that were non-streamed (i.e. there was no separation in General/Advanced/Enriched difficulty levels) were very lame and I usually couldn't stand them - on the other hand the enriched science and math courses were a blast. The teachers loved teaching them because the people there were there because they chose to be there and really were interested in the subject. In those classes, I learned a ton.

      This difference in the lowest common denominator is why private school teachers can do so much 'better' than those in public school on a general basis.

  • by js7a ( 579872 )
    Growing up in Colorado during the '70s, Algebra was optinal in seventh grade and mandatory by ninth. Here in Mountain View, California, in the heart of Silicon Valley, there is a big fuss because the state's new high school exit exam includes algebra, and many high school seniors never took it.

    The way the indignant parents act about this is the worst of all. If it were up to me, a probability and statistics course on top of trig (including spherical trig) and a C programming course (but not calculus) would be mandatory to graduate high school. The way parents get all huffy about their kids homework, taking their own ignorance personally I suspect, it is unlikely to come to pass.

    Are there any other states where it is possible to graduate high school without algebra?

    • Someone please explain to me, after spending one year on learning algebra, they switch to geometry and let you forget everything you learned, after which, they put you into a year of algebra, where you spend half the year re-learning all the algebra you forgot in the year previous?

      Seriously, is there a conspiracy to keep students stupid, or do they just not get it?

      I'd advocate spending Pre-algebra and the first part of algebra the first year of junior high, and follow through in eighth grade with algebra/algebra2/trig and a good dose of AP Chemistry. Ninth grade, you get trig/pre-calc with AP Physics. Tenth grade, you get AP Bio with statistics. Eleventh grade, you do 2 sememsters of college calculus (AP calc is weak, for get it). Twelfth grade, you take shitloads of standardized tests, and optional linear algebra with multivariable calculus.

      Or you could do basic math and continuously flunk, and have to pass remedial math as a senior in order to graduate...

      Don't think I'm neglecting history or english either - the AP Language and AP Literature tests are so similar that you might as well do both and get the extra credits. AP US History, US and comparative government, AP Music Theory, etc. My philosophy is you should be prepared for grad school when you do your undergrad, assuming you've got sufficient maturity to do so. No point spending 4 years of your life taking shit courses (most of them weeders) you should have gotten out of the way when you had the chance as a High School student.

      Seriously, how can you explore different career choices if they have you doing the same remedial crap everyone else is taking?
    • Yeah, it's pretty sad. The California high school I graduated from (in 2000, before exit exams) only required three years of math. Not up to a certain level of math, just three years of math. So some people graduated by taking three years of pre-algebra, or whatever the math class below that was (Basic Math, or something). Hell, I didn't even work very hard, didn't do much homework, and still got to Algebra II. Of course, since I slacked off so much and didn't apply myself, I didn't absorb much of it. But that's my fault. :)
  • My goverment has informed me, a patriotic citizen, that I should be especially aware of anything arabic sounding around me. They like to sneak things in to try and destroy our beautiful country, and this could be one of the very plots that brings about 9-11 the sequel!

    Why, filling our kids heads with islamic math propaganda is the last thing we need right now. Will it help us build bigger bombs? No, I don't think so. Counting to 10 is enough, and if you forget a few numbers in between, that's alright by me. President Bush himself can't count to 10 without his advisors helping, and I bet none of them know al-jebrah either.

    Al jebrah is a tool of the devil! It might help when you're trying to decide how many camels to give away to marry off your daughters, and it might even help to figure out how to build those crazy pointy towered mosque thingies. But as americans, what good does that do us?

    Besides, they come right out and say it. It leads to godless science, teaching us that we're the grandchildren of monkeys. Yes, cousin Cletis kinda looks like a chimp, but by god he's a good 85% human. Keep your godless atheist algebraic satanic brainwashings out of my kids skulls!

    (stupid lameness filter won't even let you do a *** seperator bar)
    Dammit. Spent 20 minutes writing one of my best trolls ever, and I can't bring myself to click 'submit'. It wouldn't be a big deal, but I know people like this... ugh. I'm wimping out.
  • Well anyone who's seen the commercial knows the cow can talk, so I bet it's smart enough they can teach it algebra.

    Oh wait...maybe I should read the article...
  • Ann Landers (Score:2, Insightful)

    by jkastner ( 581372 )
    This topic reminds me of a recent Ann Landers letter. The writer mentioned her fear of math, and how the community college she was going to was requiring her to take math she "wouldn't use". She closed by wondering if Ann thought this made sense. Ann agreed that it made no sense to force a person to take "advanced math classes, like Algebra" if they weren't going to use it.

    Since when is Algebra advanced math? That sort of attitude doesn't help this country at all. I was going to write Ann a reply letter, but since she was already dead I didn't bother.

    Disclaimer: I'm currently working on a Ph.D. in applied mathematics

  • Your code without algebra:

    10 print "I never learned algebra"
    20 goto 10

    Your code with algebra:

    for (i=0; i<10; i++) {
    printf("I learned my algebra!!!\n");

  • by jag164 ( 309858 )
    Maybe i'm goofie, but me thinks more people have troubel with basic english than algabra has done. I'll leeve it up to the reeders to decide about it. How many grammatical erreor can you find in the front page comment was on? I'm not trolling b/c I could give too shits about typos here and their, and lots of grammitical errors, and mispellings in /.'s responses in here, however, if you make the 'front page' you should definetly at least double check your work too make sure everything is good and makes sense and their are no run-on sentences are in your article. Yes, geeks have to know how too write to. Very important.
  • So, according to media hype, what exactly are schools teaching well?
  • by MacMasta ( 515853 ) on Monday August 19, 2002 @11:06PM (#4101791)
    Pardon if this is a repeat.

    I remember reading somewhere, and, after much thinking, agreeing with it, that science is currently taught in backward order.

    That is, instead of biology-chemistry-physics, we should teach physics-chemistry-biology.
    The reason for this is that to really get chemistry, you need a strong grounding in why all those little particles do what they do. To really understand biology, you need to have a strong grasp of chem.

    Students today have a very hard time with math - and that's crazy. They shouldn't.

    One way to make math more "real" to students is to apply it to science - perhaps if they aren't math-nuts, they'll be science nerds, and the connection will draw them into both.
    The problem with this, of course, is that physics is classically taught as a calculus-based course, (although it's perfectly possible to do it with trig and algebra - my AP test 5 can vouch for that)

    Chemistry "needs" algebra - at least it works a lot better with it.

    Biology (at least at the high- and middle-school level) needs very little math at all.

    Therefore, we teach them in reverse order.

    As to not teaching algebra, there is no excuse.
    I explained the basic principle behind algebra to a bunch of fifth-graders and had them doing "x+59 = 226" in about fifteen minutes.
    Everything else is derivitive of that - if the textbooks can't get that across, blame them.
    (Note - I would not suggest blaming teachers in the slightest - teaching from books works, even bad books, and teachers, at least in my district, are required to teach from a book - they were good teachers with bad material)

    So damn the torpedoes and shut down Houghton-Mifflin!

    • instead of biology-chemistry-physics, we should teach physics-chemistry-biology.

      While I sort of agree with this, and certainly once people are at the University level, there's a big reason why we don't: familiarity.

      Most any kid can picture his dog (biology). He can maybe think about what happens when the dog eats (chemistry). There's almost no way he can conceive of what the food is made of, on a level so small it has to be described only with mathematics (physics). Even when talking about classical physics, I don't care how much of a science geek you are - balls rolling down planes are NOT exciting. Physics tends to be either highly math focussed (and a lot of memorization), or so abstract that most people don't even grasp the basics (quantum physics, anyone?).

      Biology is an easy course to teach, because it deals with every day occurences. Sure, adding vinegar to baking soda looks cool, but without the biological effects, try explaining to a 10 year old why this should be important to him/her. Why there are so many mosquitoes during rainy years is a lot more relevant, and approachable, to the average student.

      Personally, I think we really need to return to a more traditional "Science" type of course, with less division between the fields. I'll never forget the day in chem lab when it occured to me that everything we talked about in physics and bio were all connected - it was an epiphany I'll never be able to top. Yet all through school, it was never really explained that all of this stuff is not only related, but basically THE SAME THING.

      Same goes for math (esp. algebra). You simply cannot do physics without it, nor chem, nor bio (unless we're talking the ubiquitous worm disection that really teaches nothing). The worst mistake we ever make in school is the old "this isn't english class, so you can't deduct marks for spelling mistakes". I've seen people get away with horrendous mathematical errors (even in University) because "this isn't a math course".

      Abstract concepts like algebra are simply too fundamental for darn near everything, most peope don't even realize they're using it almost every day. Unfortunately, testing understanding of abstracts isn't as easy as checking memorization and regurgitation skills - hence those dozens and hundreds of formulae that almost no one remembers 5 minutes after the final exam.
  • As a teacher (Score:3, Insightful)

    by Quill_28 ( 553921 ) on Monday August 19, 2002 @11:10PM (#4101820) Journal
    I taught math for exactly one year. My biggest problem with teaching was not teaching algebra but fractions!! They were never taught how to add and multiply fractions, except by using a calculator. Some of these kids were quite intelligent and had no problems with
    x^2 +6x +8 =0 but (x+1)/2 = 4 and they were lost. All the blame can't be laid on the jr/sr high some of it also falls before they get there.

  • ... but that they're aiming only for one spot, low or not. Teaching a subject the same way to every student (both those with interests in the subject and those without) isn't going to work no matter what you do; you'll bore the bright ones or lose the not-so. The damage caused by aiming somewhere lower is secondary to the fact that there will almost certainly be damage no matter where we aim.

    Some may point to Special Education and/or Gifted programs as alleviating this, but they are typically under funded, help only the lower/upper 3-10%, and don't have any set way to help, instead focusing on the main weaknesses/strengths of the bottom/top 2-3 individuals.

    Example: my HS gifted program was essentially a quiz bowl team. Why? It wasn't because we learned a lot(we didn't), but because we had 3 people who were really good. Everyone else was perfectly happy, because going to the events meant they could hang out with their friends and usually get free food. For them, it was just a bonus to watch the top 3 do so well sometimes.

    Why hasn't a solution been found and used? Quite simple: parents don't want their kids labeled negatively, and quite often kids don't want to be labeled positively by teachers because it leads to more negative labels from their peers. Having multiple classes, each for a certain level of performer, and you will have complaints, and lots of them.

    In other words, don't necessarily blame the teachers or the buereaucrats for the problems of the system--blame our culture for being too Politically Correct.

  • All Messed Up (Score:3, Interesting)

    by danheskett ( 178529 ) <danheskettNO@SPAMgmail.com> on Monday August 19, 2002 @11:18PM (#4101852)
    This is a very good topic, and point. Teaching and education is all messed up.

    The problem I always had growing up and learning from teachers was inconsistency. I hated it then, and I hate it now.

    Most of my teachers had coursework hobbled together from various text-books, teacher resources, etc. It was really lame. They usually didnt fit well together. One series choose one set of themes, another choose another rather incompatible set of themes. Things were out of order, we skipped around, and generally made a mess of things. Most teachers have absolutely no course plan whatsoever. They go from page 1 and continue till they run out of time (how many times did you get to the back of the book!).

    But what also made me the most mad, the most insanely unable to pay attention were the pure lies come teachers mouths in a vain attempt to motivate us. "Dan, you'll never be a programmer unless you can do this stuff!" Okay. Well thats funny. I talk to many of my successful adult uber-programmer friends and 4/5 of them couldnt do that. Odd. "Dan, you'll never get into a decent college unless you learn this stuff!". Odd. Sibling got into good colleges, and they were dumbasses.

    I finally got through school by deciding to tune out the teachers entirely, buying my own text-books (after online research), and doing all my homework and papers in class while the teacher was lecturing.

    After I figured this out I had a great grade point average, never any after school homework, and great fun pissing off teachers who couldnt understand how I was acing classes without paying any attention to them at all.

    In the end, the final analysis, it all comes down to personal motivation. Why bother to get motivated about math if you have no interest in it? Why bother getting ready for high-education if its out of your financial grasp? Why bother getting ready for a decent job when you know that your area has nothing but minimum wage jobs to offer you for the next 40 years?

    • This is a very good topic, and point. Teaching and education is all messed up.

      Why does the blame immediately fall there? Here's a clue for all the parents or wanna-be moms and dads out there: Your Johnny many not turn out to be all that bright a boy! In fact, nearly 50% of the population is going to have below average intelligence. While you'd like to assume it'll be the Smiths next door that raise the moron, you'll do your own kid a bigger favor if you assume the coin flip is not in your favor and thus actively participate in their education.

      The problem I always had growing up and learning from teachers was inconsistency. I hated it then, and I hate it now.

      Clue time for the young student now: teachers aren't high holy men (and women) with any ultimate truth to offer up. At best, they're just guides along the path and you need to get up off your ass and do the walking yourself. Socrates gave perhaps the best phrase regarding education I can think of: "I cannot teach anybody anything, I can only make them think."

      I finally got through school by deciding to tune out the teachers entirely, buying my own text-books (after online research), and doing all my homework and papers in class while the teacher was lecturing.

      Now that is a worthy solution. Keep it up and you'll end up doing well in life. But don't go expecting everyone in your class to be so motivated, and then don't go blaming the teacher because some who coasted through their first 18 years ends up hating the rest of their life. You learned the lessons of learning early; some never learn to learn. Sucks to be them!

  • by matroid ( 120029 ) on Monday August 19, 2002 @11:25PM (#4101900) Homepage

    In an effort to overcome our country's mathematics woes, the National Council of Teachers of Mathematics (NCTM) [nctm.org] put together a monumental group of standards and principles [nctm.org] revolutionizing the way that Mathematics is taught at the High School level.

    The NCTM-based curriculum [mathematicallysane.com] is different. Some teachers and college professors [mathematic...orrect.com] believe it to be weak on mathematics because it doesn't look like the curriculum they grew up with. Traditional curriculum (teacher does a couple examples, students practice solving 30+ problems similar) has not been good enough though.

    The new curriculum, based on psychology and education research from the latter half of this century, focuses on understanding in addition to the traditional acquisition of skills. It is mathematics rich with connections to other areas, and deep in content. Students start in 6th grade learning basic algebraic concepts, number theory, geometry, probability, etc. Obviously mastery of all these concepts does not happen in a single year. In fact, the curriculum spirals around the same concepts, building new understanding and making new connections with each pass so that, ideally, when students graduate their skills AND understanding will be better than that of previous generations.

    Sometimes this math is called "Fuzzy Math" or the "New 'New Math'". Some educators, professionals, parents, and children feel the curriculum is weak on "real math." My concerns were similar before I started teaching the Interactive Mathematics Program (IMP) [mathimp.org].

    Between 9th and 10th grade, students master basic algebra, learn the basics of the trig functions, work with standard deviation and the chi-squared measure, build and solve and maximum profit linear programming (something most math majors don't do until grad school), derive and prove the pythagorean theorem, work with exponential and logarithmic functions, do all sorts of number-theory related problems, and so much more. Still IMP and other standards-based curricula have their problems. In my opinion, although there's plenty of problem-solving and understanding-based activities, there needs to be more traditional skill work. I supplement my lessons with such work where appropriate. Any teacher worth their stuff would do the same. Additionally, the curricula is very wordy, which is fine for middle-class suburbanites, but when you're teaching in a city where 25% of the students don't speak english as their first language, and 75% are in poverty (typically correlated with smaller vocab and weaker reading/writing skills), a wordy curriculum is just one more thing making it tough to teach/learn math. In sum, there's a lot of hostility from the non-math-teacher world toward this new curriculum because it's so different. But, with the abismal performance of American mathematics when compared internationally, it can't be business as usual. The curriculum is already working well in the classes I've seen. And the research points to positive improvements after curriculum implementation (no large study has been completed as far as I'm aware). NCTM-based curricula is no panacea, but it's a definite improvement over the more archaic traditional curricula.

  • That America's education system took a turn for the worst when it became a public, government subsidised education system? Algebra isn't the only thing that they're falling down on, gateway or no.
    • Before it was public, government subsidized, American education was non-compulsory and only the wealthy were educated. Both Thomas Jefferson and Horace Mann felt that public, free education would be the "great equalizer" in society.
  • by edrugtrader ( 442064 ) on Monday August 19, 2002 @11:31PM (#4101921) Homepage
    all through middle school and high school i had a ~40% homework average in algebra through calc 2. i also had a ~97% test average to make my B- or C+... i got the whole "you aren't applying yourself speil" but i DID know the material. i was just a lazy fuck and didn't do homework. then i go on to college... homework isn't graded and suddenly i have straight A's.

    can not grading homework WORK for a middle school student? or will they all just not do homework and fail?

    i have always hated the learning process in math for that very reason...
  • By sixth grade some of us were helping the teacher with our math. An elemenary ed teacher can teach 6th grade math (at least in Pennsylvania) with no special background in the subject because 6th is "elementary". This is very, very wrong, and must be changed ASAP.

    Fortunately I had good 7th -9th math instruction. 7th = "Algebra 1/2", 8th = Algebra 1, 9th = Advanced Algebra 2.

    Advanced Alg 2 was probably the hardest math class at my high school (considering that only 9th graders took it). In pre-Calc you could immediately tell the difference between the normal Alg2 and the Advanced class. Basically, Precalc was redundant for us, but it was pre-req to take Calc.

  • When I was growing up, I did exceedingly well in every single subject tought in the schools I went to. Except Math, but at the time, it was no big deal.

    However, by the time I reached the second half of Middle School, it was painfully obvious I needed some extra help. I simply couldn't do most of the Math course work.

    Nobody really seemed to care. They only funded Special Ed classes for the violent kids in my school, and the teacher was highly disinterested in helping me out. She was too damn busy teaching almost the entire school single-handedly.

    I arrived in High School with a serious math deficiency. By that point, most people had blown past me. But I was still a whiz at all the other subjects....right?


    Other than English, History and Art courses I found myself falling further and further behind. As you progress in school, Math becomes such an intregal part of most courses, that a deficency in it can be catastrophic.

    And that is exactly what happened.

    Falling behind early on was like a ticking time bomb. It left me helpless in later years, and tore to shreds my dreams of becoming an Architect.

    There needs to be an intense focus on Math in schools from the earliest years, but not just for the kids who do well at it (as was the case in my school system). Throwing advanced class after advanced class at those who have no problem with it, while ignoring those who do poorly creates a situation that will seriously affect the lives of students for the rest of their lives.

  • So who wants to karma whore and post a link to the first article?
  • There are many things wrong with education systems, but the basic problem is: Kids are not all the same.

    Here's a short version of the usual education process:
    Take 30 kids, and force them to listen to a series of variably competent teachers, then give them tests and assignments to grade them and then leave the kids to completely forget about what they learned.

    Sometimes it works, sometimes it doesn't.
    The problem is: sometimes it doesn't, and its a sometimes that comes around much too often.

    I personally think that kids should have more controll over their own education. Grownups are the ones that know what the kids need to know, but the individual kids know what they actually learned and what they need to get explained to them again.

    I was forced to sit through endless hours of incredibly boring explanations of things I already knew or understood, and was then not given the time I needed to understand or learn the bits I missed when I was snoozing (from all the previous boredom...teachers go from mind-numbing crap to important stuff without any warning, the sneaky bastards). Once I had a physics teacher that actually let me do my homework in the class while he explained "f=ma" over and over and over to that slow witted girl. Guess what, that was the class where I got the best grade I ever had in science, simply because the teacher decided to let me learn on my own.

    There are teachers that want the kids to listen to their every word as if they were our god for 50 minutes 3 times a week (or whatever schedule they have), I had terrible grades in those classes. I've had one of those teachers claim that an experiment we were gonna do HAD to be done in teams of 2 or 3 because it was physically impossible to do it alone, even AFTER I had shown her that I could do it by myself. Now, seriously, you expect rebelious teenagers to listen piously to someone who makes grossly false claims like that?
    Granted, she was a skinny bitch, so she wasn't strong enough to do it alone, but I was, and I did not appreciate being lied to about what is physically impossible by a science teacher.

    I have been to "alternative" schools and to a good ol' catholic school, and they both had their good and bad sides. But I think that the one thing that made a difference was the teachers. I've had terrible teachers and great ones in either systems, and I wish I could have been taken seriously when I told my parents or my principal thart my teacher was insane and I was suddently getting bad grades because the problem was him, not me. (How many doors must he break before they believe a kid when he says the teach is nuts? The guy threw chairs and desks for crying out loud!) /rant
  • by chaih ( 170120 )
    As an intructor in an undergrad EE course, I have found that students can't survive without a fancier-than-computer calculator. They just whim and complain when I am giving out quizzes that involve additions of simple fractions(eg. calculating equivalent resistance of resistors in parallel). A guy complained he couldn't figure out the answer of 0.25 when he kept getting 1/4. duh!!!
  • ...as opposed to "memorization"
    or studying for tests - read
    this article [guardian.co.uk].

    Fire hordes of unionized teachers, find and hire
    people like these for six-digit salaries!
  • by Ride-My-Rocket ( 96935 ) on Tuesday August 20, 2002 @12:10AM (#4102092) Homepage
    I was fortunate enough to be sent to private school for my entire run through school -- K - 12 and then college. It was great -- I had a lot of excellent teachers, and I was encouraged to learn by an environment that was kinder than others probably would have been to a skinny, shy, geeky kid with a fetish for comics, computer games and programming.

    However, the prospects of me being able to give my children (if / when I get married / have kids) is virtually non-existant: at $25k - $30k a year, I was utterly privileged to have had such an education. And while some public schools are actually quite good, most stories I hear aren't encouraging, either in terms of the curriculum or the student environment. As such, I'm actually quite afraid of what the future holds for the coming generations.......... is a proper education doomed to be the demesne of the affluent?
  • by call -151 ( 230520 ) on Tuesday August 20, 2002 @12:24AM (#4102183) Homepage
    Moreso than any other subject, mathematics has more of a linear structure- meaning dependence upon previous material.

    If you have a bad teacher for 7th grade English, you may never quite be the greatest at diagramming sentence grammar, but the chances are high that you can overcome that shortcoming and still learn to compose good essays, read literature for more than just content, and so on. Other subjects also have the potential to recover from a bad teacher or missed material.

    But mathematics has much more of a reliance on prerequisite material. If you have a bad instructor and don't develop good algebra skills, you will struggle and have a great deal of difficulty in algebra 2, trig, etc. When people find out that I do research in mathematics, (a casual conversation-killer if there ever was one) they often have a story, something like "I was always good at math until Mrs. Crabapple in 10th grade" or something like that. One bad experience leads to poor understanding in that subject, and, unfortunately, is rarely overcome and years of struggle result.

    I've seen people get derailed at all levels and it really is a problem that needs addressing. At the undergraduate level, sometimes it is particularly painful to witness when a student passes a class (such as first-semester calculus) without learning the material. This can put them into a hopeless limbo- they have no chance of passing the next class, and will probably fail it a few times, but they cannot take the preceding class since they already passed it (sometimes even with a reasonable grade.)

    There is a unfortunate stigma to taking something a second time, and that stigma undermines healthy mathematical learning. Sometimes it takes seeing things more than once, or from more than one teacher, before it makes sense. Passing students who just barely have a grasp of the material does them little good and may doom them to years of floundering.

    Until there is more recognition of this fundamental aspect of mathematical learning, there will be way too many people who grow up dreading "story problems" and "meaningless algebra"

  • by call -151 ( 230520 ) on Tuesday August 20, 2002 @12:41AM (#4102266) Homepage
    One of the things that seriously separates humans from other animals is our ability to think, and to think abstractly. Too often the comments are made about algebra- "I'll never use this..." "What is this good for?"

    Even if algebra problems per se never occur in whatever "real life" people end up having, the ability to think quantitatively is essential for an reasonable person. Thinking more abstractly about problems of many kinds is essential- for developing efficient code, for having a reasonable business plan, for managing one's person finances, for voting in a responsible way, and basically for being a productive member of society. The evidence for poor critical/mathematical thinking is everywhere- people falling for Ponzi schemes, short-sided economic policy, unwise credit-card debt, bad laws, ridiculous jury decisions, and the list goes on. The proper perspective about mathematical reasoning is that it is fundamental for most productive people, and essential for all citizens.

    Unfortunately, this perspective is usually not instilled by our current generation of underpaid, frequently under-qualified (more than half of the math and science teachers in CA have "emergency certification", which can be extended indefinitely since there is no adequate supply of properly trained and willing math and science teachers.) Instead, students are often exposed to math teachers, who, to be honest, don't actually like math or understand its central role as a foundation for science and modern reasoning. Kids are smart- if a teacher doesn't like math and is just going through the motions, they pick up on that. And given the sympathy that students get from parents, teachers, etc for the horror of "word problems" it isn't a surprise that mathematical reasoning skills are a consistent weak point of students at all levels in the US.

    Everyone agrees that more resources should be directed at education, but people have been agreeing on that for at least 30 years with much of the same problems enduring. Good education is more expensive an investment than many decision-making bodies are willing to undertake, and that shows in the wide disparity in education between the "haves" and the "have nots". Until there is a significant change in how much energy and money people are willing to invest in education, it seems that these phenomena will continue.
  • Algebra Teaching (Score:3, Insightful)

    by Artagel ( 114272 ) on Tuesday August 20, 2002 @12:56PM (#4105710) Homepage
    First of all, teachers can't serve as the sole source of motivation for students. Parents and communities have to do that too. The transition for fractions to algebra is one of the hardest on young people. As noted above, one problem is that students that did not have a good grasp of fractions just become more lost in algebra. A second problem is the motivation to learn this new, hard subject.

    Students need to understand that "the future is now." This is part of a runup to calculus in college (if not sooner), and that what you can or cannot do in math can and will shape your future. If you do not know algebra II and trigonometry, you are going nowhere in Physics I. No Physics I, no engineering, no chemistry, likely no computer science, etc.

    Second, we have to face the fact that many students in math want to get through the class with a decent grade, but have no ambitions to actual understanding. They WANT to be trained monkeys. Their parents often have uncritical aspirations too, and will be happy with trained monkeys.

    Thus, they do not want to understand the associative and distributive properties. A trained monkey type of student can solve problems while not fully grasping the properties. A student who understands these properties will have an important intellectual tool available. The idea that certain types things can or can't be related in certain well-defined ways is an important idea.

    To those who want to teach math only in the context of solving science problems I say: foo. Mathematical training needs to be broader than the known scientific problems to be solved or you encourage inside-the-box thinking. Where in a physic experiment does someone like Godel become relevant? What about Fermat's last theorem?

    Gear the teaching to allow the best to be the best. The crank-churners who don't want to excel will find a way to get a B or C on the test. That's why they call average grades "mediocre." The system has to tolerate the mediocre accepting their lot, but it doesn't have to discourage virtuosity in doing so.

Each honest calling, each walk of life, has its own elite, its own aristocracy based on excellence of performance. -- James Bryant Conant