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Have Mathematics Exams Become Easier? 853

Posted by timothy
from the not-to-me-they-haven't dept.
Coryoth writes "The BBC is reporting on a recent study in the UK that found that the difficulty of high school level math exams has declined. The study looked at mathematics from 1951 through to the present and found that, after remaining roughly constant through the 1970s and 1980s, the difficulty of high school math exams dropped precipitously starting in the early 1990s. A comparison of exams is provided in the appendix of the study. Are other countries, such as the US, noticing a similar decline in mathematics standards?" Readers with kids in school right now may have the best perspective on changes in both teaching and testing methods -- what have you noticed?
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Have Mathematics Exams Become Easier?

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  • Pay teachers more (Score:5, Insightful)

    by kramulous (977841) * on Wednesday June 04, 2008 @05:09PM (#23659045)
    Clearly this is happening ... in the western world anyway. It's the only way that schools can keep up with the shear numbers of parent classified geniuses.

    We've noticed this 'dumbing down' (thanks Idiocracy) for a while now at Uni. The newer mathematics students enrolling in first year are lacking some of the basic skills. Example: a couple of years ago, trigonometric functions and identities were completely removed from the high school syllabus. It goes back all the way to year one at school.

    I don't think teachers are being paid enough and they are certainly not valued enough by the community. Once upon a time, the best and brightest minds went into the teaching profession; it had respect and was highly valued. Now, it's whoever wants to become one, winner by default. The best and brightest need to be attracted back. Why would somebody who has the ability to earn more than four times the national average wage go into a job that earns less than the average wage?
    • by NewbieProgrammerMan (558327) on Wednesday June 04, 2008 @05:20PM (#23659225)

      Why would somebody who has the ability to earn more than four times the national average wage go into a job that earns less than the average wage?
      Yep, that's damn sure one of the big reasons I'm not interested in being a teacher once I finish my graduate degree. If I wanted to deal with children telling me what to do and get paid peanuts for it I'd go back to software development. ;)
      • Re:Pay teachers more (Score:5, Interesting)

        by Itninja (937614) on Wednesday June 04, 2008 @05:47PM (#23659689) Homepage
        Teaching the masses in free public schools has never historically been a profession ones chooses if they want to do well financially. And it's not just teachers either. I work in the education sector as a IT engineer and get paid significantly less than I could get in the private sector doing the same job. I took this job, not for the money, but because I wanted to contribute something to the community and still be able to make a modest living. Also (just like teachers) I get PTO on par with Europe (about 45 days off per year).
        • Re:Pay teachers more (Score:5, Interesting)

          by Original Replica (908688) on Wednesday June 04, 2008 @08:07PM (#23661555) Journal
          Teaching the masses in free public schools has never historically been a profession ones chooses if they want to do well financially.

          The caveat is that you frequently have to go to grad school to be qualified to teach, and grad school prices are rising much faster than public school salaries. Of course housing prices and food prices are also rising faster than salaries. Every career that used to be "just enough to get by" is in danger of falling out of the bottom of the middle class. When you have something like modern public school teaching, where most of the potential creativity and chance to influence young intellects has been replaced with neck deep bureaucracy and a focus on preparing for the next evaluation test, there isn't even a "contribute to the community" sliver lining any more. Public schools in America are broken.
          • by RockModeNick (617483) on Wednesday June 04, 2008 @10:35PM (#23663027)
            While I agree with the sentiment, I don't like the word broken. Broken implies they aren't doing what they're intended to, but I don't think thats the case. They're generating the needed numbers of Walmart clerks and other low wage workers, which is success if preparing students for their most likely future occupations is the goal.
        • by billcopc (196330) <vrillco@yahoo.com> on Wednesday June 04, 2008 @09:28PM (#23662443) Homepage
          I used to think that way, I briefly experimented with teaching, early in my career. What I realized is there's no amount of wisdom that's going to un-fuck the educational system. The pay sucks, the students mostly hate you (because _they_ suck), and the whole system is not designed to improve, but merely to survive financially.

          I wasn't exactly in the public sector, but it was one of the cheaper and thus more popular private vocational colleges. My already modest expectations were far beyond what this enterprise was offering, which is probably why all the grads wound up either in brainless government jobs (lucky them), or call centers.

          The day we rid schools of the financial burden, is the day they will start churning out smarter grads.
      • by lpq (583377) on Thursday June 05, 2008 @02:36AM (#23664519) Homepage Journal
        It's pretty bad being a teacher. Had a partner teaching first then second grade -- not all of the kids, but enough to create a problem had the rebellious chip-on-the-shoulder attitude that came around 7-8th grade when I grew up. One issue is there is no way to discipline the children that they care about. Since corporal punishment was stricken, I don't think teachers have found an effective replacement. But "time-outs"...they don't care, their minds are off most the time anyway -- and sending them out of class, or suspension/expulsion -- many of them don't care -- they don't want to be in school anyway. Many of the kids had behavior issues that might have put them in a remedial class (apparently, like Bush was). That's a major problem that's come up in the past several years since Bush's "No Child Left Behind" act. Instead of holding kids back or allowing kids to progress at different rates, all must wait for the slowest child (little Georgie). The regular testing of the kids is more or seems more to evaluate the teachers than the children. Now, it's no longer a child's responsibility to behave or learn -- it's the teachers responsibility to "emote" knowledge into them...kids are simply being trained to be passive receivers and the learning is predictably suffering.

        That's been a bad trend over the past ...several or dozen or more years -- too much focus on remedying the lowest rung at the expense of dragging down the whole -- but that's part of the "false dichotomy" -- that there has to be a trade off.

        It's the same "root cause" as teacher's not being able to afford to live in the communities they teach in. Not enough resources into education -- too many resources invested in high-end of life and the adult stages (including, recently, this war that is causing oil prices to go up (war->deficit spending->'printing' money (how close is US debt to 3 T$ (Tera-$)?)->dollar deflates in value as massive 'unbacked-money' is created, commodities (incl oil) go up) -> US goes bankrupt)). But look at how much the rich spend on luxury goods --- increase in cruise ships, vacation spots -- extremely expensive hobbies/sports...so much wealth concentrated in top 1% people -- but it's the 'masses' that are taught in schools -- and that's where the dollar share has been shrinking the most.

        There was an opinion piece in the WSJ that tried to show how increasing the top tax rate didn't increase the government's tax-income as a percentage of GDP -- what it unintentionally showed, actually was GDP going up as
        the top tax rate rose, and GDP going down as it fell -- so the % going to government appeared level. GDP going
        up or down reflects almost directly goes into a rise or fall of the "standard-of-living" of the nation. That meant that as the top tax rate fell, the average standard of living for the nation as a whole fell -- and vice versa.
        GDP has fallen to lowest levels in my lifetime under the top tax rate falling from over 70% to the 20-25% it is now. All that was Reagan-& the Bushes rolling back taxes on the rich while using government deficit to inflate the economy. While Clinton didn't raise taxes -- he did manage to get the deficit from around 2-billion to almost breaking even by the time he left office -- now it's up higher than ever.

        Bush needs to be out of office so yesterday. I think my postings are too long and people don't get this far...
        *sigh*...just supposed to shut-up while the nation is tanking to hell...

    • General request! (Score:5, Insightful)

      by xaxa (988988) on Wednesday June 04, 2008 @05:22PM (#23659267)
      Could everyone put their country in the comment, if applicable? It saves people arguing back-and-forth about the same point, when both are correct for their own country and experiences, but on opposite sides of the world ;-).
    • by shadowkiller137 (1169097) on Wednesday June 04, 2008 @05:29PM (#23659381)
      instead of a dumbing down I would say that there is more of a split happening between the people in advanced courses and those in the lower level courses. those in the lower courses are not being taught as well and like you said basic concepts are being removed but those in the higher level courses I think are being taught more advanced concepts than previously at that level and age. The standardized tests however must be able to access the whole range of people taking the test so they must be made easier because if the people with the lower training in math got all 0's on the test it would not show at all what they learned, in their own basic way.
      • by hedwards (940851) on Wednesday June 04, 2008 @08:54PM (#23662109)
        I'm not sure about other areas, but around here we switched to integrated math at the start of the 90s, and you'd be lucky to learn anything like that.

        Rather than algegra, geometry, etc., as discrete courses, they get jumbled together and reintroduced each year through 3 years. The problem is that there's never enough of it at any given time to actually stick, so you get a lot of students who are going through the motions.

        On top of that you get a lot of group work, which basically ends with the one or two students that actually get the course material providing answers to the entire group.

        In an atmosphere like that, where the basics aren't really ever taught, I'm not really sure that most students could cope with anything particularly challenging. And that's not even bothering with the switch from more more theory and analysis to more focus on useless proofs.

        Proofs can be valuable, but only when the students are being taught to understand the reason why certain corollaries, postulates and theorems have been put forth. Mindlessly regurgitating them without an understanding of the implications isn't particularly worthwhile.
    • by sedmonds (94908) on Wednesday June 04, 2008 @05:29PM (#23659391) Homepage

      I don't think teachers are being paid enough and they are certainly not valued enough by the community. Once upon a time, the best and brightest minds went into the teaching profession; it had respect and was highly valued. Now, it's whoever wants to become one, winner by default. The best and brightest need to be attracted back. Why would somebody who has the ability to earn more than four times the national average wage go into a job that earns less than the average wage?


      Not only do teachers not get paid enough to attract and retain the good ones, but teachers unions and the fear of lawsuits make firing the awful ones nearly impossible.
      • Re:Pay teachers more (Score:5, Informative)

        by Changa_MC (827317) on Wednesday June 04, 2008 @05:35PM (#23659493) Homepage Journal

        ...teachers unions and the fear of lawsuits make firing the awful ones nearly impossible.
        I call B.S. on that one. In my time teaching, I saw several bad teachers let go. Problem was, there wasn't anyone better to replace them.
      • I know my fellow coworkers would crucify me for this, but I think the biggest problem with teachers getting a fair wage is the Unions. Are teachers at private schools getting screwed over so bad? I have been working in public education for 7+ years, and the unions have fought hard to ensure that kindergarten and high school teachers of any subject all get the same pay. And what has happened as a result of that? In the democratic process of wage negotiation, few grammar school teachers really care a lot more
      • by Xandar01 (612884) on Wednesday June 04, 2008 @06:12PM (#23660141) Journal
        I too have a belief that the system protects teachers too much. However this year my Daughter's eighth grade Math teacher was awful and could not even attempt to keep control of the class. He was let go about 1 month before school was out and it was his first year.

        Interestingly the High School that she is going to is aware of that teachers failings and identified all of his students as likely needing extra help in ninth grade.

        This was supposed to be the GATE class too. Now most of these advanced math students have lost the edge they had and are behind other GATE students in the district.

        Glad they got rid of him.
      • by Solandri (704621) on Wednesday June 04, 2008 @07:05PM (#23660993)

        I don't think teachers are being paid enough and they are certainly not valued enough by the community. Once upon a time, the best and brightest minds went into the teaching profession; it had respect and was highly valued. Now, it's whoever wants to become one, winner by default. The best and brightest need to be attracted back. Why would somebody who has the ability to earn more than four times the national average wage go into a job that earns less than the average wage?
        Not only do teachers not get paid enough to attract and retain the good ones, but teachers unions and the fear of lawsuits make firing the awful ones nearly impossible.
        Another consequences of the "not paid enough" line of reasoning is that if we did raise teacher pay, we'd have to fire most of the current teachers and hire new ones. The teachers unions get in trouble with this double-edged sword since ultimately their goal is to increase pay for the current crop of teachers, the ones the pay increases are supposed to filter out by attracting more capable teachers.
    • by homer_s (799572) on Wednesday June 04, 2008 @05:38PM (#23659545)
      ...can keep up with the shear numbers of parent classified geniuses.

      Clearly, your English teacher wasn't paid enough.

      But other than that, the problem I see in this country is that the consumers of education have no choice. And like in any other monopoly, the provider gets away with poor quality.
    • Re:Pay teachers more (Score:5, Informative)

      by Coryoth (254751) on Wednesday June 04, 2008 @05:40PM (#23659577) Homepage Journal

      I don't think teachers are being paid enough and they are certainly not valued enough by the community. Once upon a time, the best and brightest minds went into the teaching profession; it had respect and was highly valued. Now, it's whoever wants to become one, winner by default.
      That seems to be true for mathematics tyeachers in the UK; conveniently the BBC is also covering the rather glaring fact that the majority of people teaching mathematics aren't experts [bbc.co.uk]. That is, the majority of people teaching mathematics have degrees (if any) in unrelated subjects. Mathematics isn't the only subject that has a shortage of people actually qualified to teach; most of the sciences do apparently. Mathematics is far and away the most glaring case however (only 47% of maths teachers had a relevant degree, compared to 85% for biology, 83% for chemistry, and 72% for physics). Throw in the fact that mathematics is one of those subjects where a student can be permanently set back by just one bad teacher and you have a decent part of the problem.
      • Re: (Score:3, Insightful)

        by Kopiok (898028)
        It depends on what a relevant degree is, and if that even matters. My AP Calculus teacher was an ex-engineer, and she was fantastic at teaching the subject. Knew what she was talking about and made the class interesting. On the other hand, my ex-engineering Pre-Engineering teacher was a joke and couldn't teach his way out of a paper bag. I believe they were both certified for education. It all depends on who the teacher is, not their credentials (though those certainly help).
      • by AK Marc (707885) on Thursday June 05, 2008 @02:38AM (#23664525)
        the majority of people teaching mathematics aren't experts.

        Um, So? Why should a teacher master differential equations to teach algebra? I'd rather have a good teacher that knows enough math, than a great mathmetician that can't teach. When you require degrees, you restrict more than you enable. My high school physics teacher had a biology degree (and wasn't the biology teacher, but did teach chemistry) the French teacher had an economics degree. The economics teacher had a masters in political science, but no high school diploma or bachelors from college. Oh, and the political science teacher had a degree in education, not political science. Amd they were all good at what they taught.

        Throw in the fact that mathematics is one of those subjects where a student can be permanently set back by just one bad teacher and you have a decent part of the problem.

        Which is why you need a person at the front of the class that connects, and their knowledge of the material is secondary. I know from personal experience tutoring, that I've actually tutored someone successfully in a subject I had no knowledge of. I talked them through, asked them questions, and they were able to learn what they needed with direction, but not someone just giving them answers. Math teachers eed to be teachers first, and mathmaticians low on the list, at least until up until the last coule years of high school and beyond, where the math gets more complicated.
        • Re:Pay teachers more (Score:4, Interesting)

          by Coryoth (254751) on Thursday June 05, 2008 @07:26AM (#23665997) Homepage Journal

          Um, So? Why should a teacher master differential equations to teach algebra? I'd rather have a good teacher that knows enough math, than a great mathmetician that can't teach.
          Having both taught math, and known many math teachers, I can say that in general it is very helpful to have mastered mathematics at least 2 years beyond what you are trying to teach, preferably more. Math is a subject where things come together in surprising ways, and higher level material can and does connect together various different earlier subjects in new ways. Learning more advanced mathematics usually creates a broader and much deeper understanding of what came before. A simple case: knowing calculus and linear algebra can give you a much better appreciation for the value and use of basic algebra and trigonometric functions. More advanced: knowing some topos theory can give you a much better appreciation of numbers, addition, multiplication and exponentiation.

          Knowing more advanced math is not required to be able to teach high school mathematics; it does, however, make a teacher better able to teach high school math by giving them a better and richer understanding of the material they have to teach. Sure, a terrible teacher who has that extra appreciation of the material isn't a great substitute for a fabulous teacher who doesn't, but in general I think we can expect the distribution of quality teachers to be roughly the same between those who seek a degree in math and those who don't... given that, on average, those with a degree in the subject will be that much better.
    • Re: (Score:3, Informative)

      by clampolo (1159617)

      Ok time to take a Karma hit for telling the truth. Minorities have been screaming for years that the SAT Math section somehow discriminates against them because their scores are so low. So they had no choice but to dumb them down. The more you lower the maximum score, the more equal everyone's score is.

      Welcome to the wonderful world of multiculturalism and affirmative action.

      • by vidarh (309115) <vidar@hokstad.com> on Wednesday June 04, 2008 @07:20PM (#23661215) Homepage Journal
        Nice try. In the UK at least the various ethnic groups have been jockeying for position as the "worst" group for a long time. A few years ago it was west-indian black boys that did worst. Lots of effort was put in to improve the situation, and then white boys suddenly did worst.

        So "they" had a choice, and blaming minorities is just a way of deflecting from lack of investment in combating the real problems: Poverty - because the common theme when it comes to who underperfom is social situations, not race -, and too little investment in education.

    • Re:Pay teachers more (Score:5, Interesting)

      by NeilTheStupidHead (963719) on Wednesday June 04, 2008 @06:17PM (#23660221) Journal
      I can attest to that first hand: When I started my engineering program [only 1.5 semesters to go :)], I had never heard of imaginary numbers before. Granted, I was able to grasp the concept rather readily, but even am I shocked at the inability of some of my peers to perform basic algebra. I spent most of my first semester trying to explain, repeatedly, the distributive property to one fellow (who is still enrolled, and who still fails to grasp the concept).
      Part of the problem, as seen from my view, is the complete and utter dependance on calculators, especially those fancy, programmable Texas Instruments ones, that can practically do the work for you. I have one (it was considered 'required course materials') that I have used maybe a handful of times, preferring my old two-line Casio scientific calculator, particularly now that I know what the little cursive 'i' does. :)
    • Re:Pay teachers more (Score:4, Interesting)

      by blahplusplus (757119) on Wednesday June 04, 2008 @07:05PM (#23661003)
      "Pay teachers more..."

      Sorry but I don't believe this is the case at all, the culture of "pay me more" is bullshit. Many teachers and experts can't teach, but there are those in both groups who can. Paying teachers more is not the issue in many places, in Canada highschool teachers after a good decade or so can pull in 60,000-100K per year and student disengagement is at recrod levels. The idea that the private sector will 'solve everything' is also bullshit, it's cultural and it's complicated, people have made the same argument your making throughout history, yet the same problems occur you're not a unique snowflake here.

      The problem is really about the culture itself, it goes deeper then that though it's north american insitutional and business culture that is the problem. See here:

      See: http://www.youtube.com/watch?v=gG3HPX0D2mU [youtube.com]

      Listen to the comments of "calcification" of kids in the school system and adults in the workplace. It makes a lot of good points about self management and responsibility.

      I don't agree that all kids are just "lazy", they are disengaged because most of the time we don't allow their curiousity to blossom by killing it early through 'school'. The other problem is that we don't have a place for certain kinds of people in the job market that will pay decent wages. That is the REAL problem, technological displacement, and trying to achieve the impossible (i.e. raising the bar and expectations to unreasonable levels and then being disappointed when kids don't meet them)

      Modern schools are often harmful and disengaging enviornments, for many it's positively toxic to someones development. No amount of paying teachers more, or accountability will deal with forced schedules and irrelevant curriculum, the lack of alignment of student curiousity and interest with what they want to learn vs the boring pablum clueless teachers, businesses and government elites, pushing their pablum as 'education'. Many slashdotters can no doubt attest to the low quality of the curriculum and their teachers and school simply not being relevant to what they are interested in, so they 'carve their own path'.

      I think something is to be said by not killing childrens motivation and curiousity, which we do very young.
  • by spir0 (319821) on Wednesday June 04, 2008 @05:10PM (#23659055) Homepage Journal
    we don't want to upset the poor children or make their lives too difficult. their parents might sue.
  • First post! (Score:5, Funny)

    by Harmonious Botch (921977) * on Wednesday June 04, 2008 @05:10PM (#23659075) Homepage Journal
    They had to lower the standards because the kids today can't handle simple math.
    • by NewbieProgrammerMan (558327) on Wednesday June 04, 2008 @05:12PM (#23659107)

      They had to lower the standards because the kids today can't handle simple math.
      Does that include concepts like, "what 'first' means?"
      • by Sponge Bath (413667) on Wednesday June 04, 2008 @05:29PM (#23659395)

        Don't bruise his self esteem you brute.
        Here on /. in the 21st century, every post is first post.

        • Re:First post! (Score:5, Insightful)

          by Anonymous Coward on Wednesday June 04, 2008 @05:55PM (#23659839)
          You're modded Funny, but that's worryingly accurate. Today's kids like being told they're number one, and if they get dragged down for poor marks, they'll just complain to their parents, who'll complain to the schools, who'll start making cutbacks for other similar children until everyone is told they're outstanding when they clearly are not. I can't talk, though - that sentence was huge. Sigh.
  • Finally (Score:5, Insightful)

    by Zelos (1050172) on Wednesday June 04, 2008 @05:12PM (#23659109)
    I'm glad somebody finally pointed this out in black and white. I remember lining up A-level (UK age 18 exams) maths papers from the 80s and 90s, you could see the questions get easier almost year-by-year.

    Yet every year the exam results get better and the government congratulates itself on improving standards while denying the exams are getting easier.
    • Re:Finally (Score:5, Funny)

      by eln (21727) on Wednesday June 04, 2008 @05:36PM (#23659515) Homepage
      Tell me about it. It's pathetic how easy math exams are these days. I mean, I really struggled in math in the second grade, and I was lucky to get average grades. Imagine my surprise when I decided to take my son's 2nd grade math test, and I got an almost perfect score! It was so easy! Clearly these kids are being spoiled by lower expectations.
    • Re: (Score:3, Insightful)

      by afidel (530433)
      Yeah, I'm sure you would see a similar result in the US. The reason being that you now have to pass the exams to even graduate and simple jobs like working at McDonalds require a high school diploma so making the tests too difficult for the majority to pass is simply unreasonable.
  • by amrik98 (1214484) on Wednesday June 04, 2008 @05:12PM (#23659113)
    There is strong pressure on the education system to "improve"; and these improvements are measured by tests. Students are generally not going to get smarter, so why not make the tests easier to make it seem like you are doing your job?
    • by Swizec (978239) on Wednesday June 04, 2008 @05:21PM (#23659235) Homepage
      In Slovenia I'm noticing quite a different trend and it also seems to be making the policymakers look good ... or something. My sister is 8 years younger than me and is now in primary school - she's learning stuff I only learned in high school. She was being taught things like fractions in third grade, I didn't even know what the hell fractions were back then.

      But maybe we're just being weird here.
  • tools (Score:5, Interesting)

    by bsDaemon (87307) on Wednesday June 04, 2008 @05:13PM (#23659119)
    back in the 50s, 60s, 70s, and 80s kids got a slide rule, protractor, compass, and graphing pad. Now it's ti-83+ for algebra class and the ti-89 has more computing power than the original Macintosh.

    doing the math is going to be easier, even if they didn't ask harder questions. However, the amount of automation these days means that most people aren't ever going to have to do the harder math in their daily lives.

    Slashdotters are an anomaly because our careers and interests require us to do maths all the time. If the future historians are allowed to slack off on their trig tests, so what? They weren't going to be engineers anyway.

    They probably should track out classes more than just "regular" and "honors/AP" though. That way the future nobel prize winning poet who is an over acheiver and the future NASA scientist don't have to compete for the teacher's attention to detail in Calculus.

    Just a suggestion.
    • Re: (Score:3, Insightful)

      by xaxa (988988)
      And you carry your TI-93 round with you? I don't, but I still use very basic maths at the supermarket.
      Brand X: "Buy one, get one free!"
      Brand Y: A few pence cheaper, and a larger pack too.
      Brand Z: "25% off!"
      How many people today can't work out which is best?

      (UK supermarkets even do most of the work for you, below the price for every product is printed something like "1.50 per kg", so it's very easy to compare prices -- you only need to work stuff out if there's an item on multi-buy promotion, in which case t
      • Re: (Score:3, Insightful)

        by everphilski (877346)
        WalMart here in the US generally has the price per unit marked.

        And yeah, I do carry my TI-89 with me, but I'm an Aerospace Engineer. Without that, my mechanical pencils and my ID card I'd be naked! :P
    • It's been said before, but (imo) today's students are essentially 'weaker' in 'doing' math simply because they don't have to do much of the doing. The result? Easier tests so that more, or at least the same number of, students pass. Schools funding is often determined on this criteria, so no one wants "below passing" students.

      When kids start Algebra I with a TI-89 that is drawing tangent lines and running linear regressions (in between games of tetris) for them, they don't learn any of the basic skills.
    • Re: (Score:3, Informative)

      by Mike1024 (184871)

      doing the math is going to be easier, even if they didn't ask harder questions.

      I agree with you; sporting records are regularly improved upon, but no-one is complaining about sprinting becoming easier.

      That said, in the linked PDF a 1951 question is stated as:

      Solve the equation:

      9 * (1-x^2)/(1+x^2) - 7 * 2x/(1+x^2) = 3

      A 1970 question is:

      Show that (x â" 3) is a factor of

      x^3 - 5x^2 - 18x + 72

      then find the three points where y = x^3 - 5x^2 - 18x + 72 meets the x axis

      While a 2006 question is:

      Find a and b when

      x^2 + 8x + 21 = (x + a)^2 + b

      Use your answer to find the minimum value of

      x^2 + 8x + 21.

      I can see why someone might say the 1951 question was harder than the 1970 question which was harder than the 2006 question.

    • Re:tools (Score:5, Interesting)

      by KefabiMe (730997) <garth@@@jhonor...com> on Wednesday June 04, 2008 @05:48PM (#23659709) Journal

      Calculators on tests have made tests easier, but this is a good thing. Can you imagine having to figure out sines and cosines by hand anymore? What calculators do is make it easier to get to more advanced topics. Knowing how to add 1234+2345 in my head is just no longer a necessary skill. I rather students practice the properties of math, and write things out on paper anyway. (#1 problem with algebra and calculus students, they try to do too much math in their head) Calculators are not going away any time soon, and anything that encourages the entire population to do more math is a good thing in my book.

      Secondly, while historians may not need to know trig, it is imperative that as a nation we raise our mathematical abilities. Great math and science students generally did not learn everything at school. Having a parent that can help out with some algebra homework (or even better understands the value of math) will make it much MUCH more likely that the child will grow up with an appreciation of mathematics. If we as a human race want to push the maths and sciences as far as we can, then we much raise the math and science ability of the entire population.

      Just so everyone knows where my loyalties lie, I am a mathematics major, I am a math tutor, and hopefully eventually you'll see me teaching mathematics at a University near you!

      • I went to HS in the mid 80's, undergrad (Physics) and grad (Unclear Physics) in the early 90's: I was APPALLED even in grad school at the people who were supposedly top of their undergrad class and unable to do simple DifEqs! The advantage I think? I had to learn to do it myself. Even in undergrad: I could use a calculator... but no whiz-bang TI-85 (I did end up buying a schweet HP clamshell my senior year - and learned to glory of reverse polish). So you used your Handy Dandy Math Handbook even in the e
      • Re:tools (Score:5, Informative)

        by digitrev (989335) <digitrev@hotmail.com> on Wednesday June 04, 2008 @06:32PM (#23660479) Homepage
        Actually, if it's a set of angles, you can do some cosines and sines by hand.

        Take an equilateral triangle of side length 2. Cut in half, so you have hypotenuse length 2, base length 1, and vertical length sqrt(3). Now you can find the cosines and sines of both 30 and 60 degrees (or pi/6 and pi/3 radians, respectively).

        Now take a right angle triangle with base and vertical length 1, and hypotenuse length sqrt(2). Now you can find the sine and cosine of 45 degrees (pi/4).

        So with a few simple skills: basic geometry, SOHCAHTOA, Pythagoras's theorem, you can find the sine and cosine of 3 different angles. Now learn your CAST rule (where the different trig functions are positive based on the quadrant) and you can do it for up to 12 different angles. Then learn your double angle formulas and you've got another 4 angles. Then learn the period of trig functions and you can now find it for any of those 16 angles plus the period of the function. Anything other than that, and yes, you'll need a calculator, but knowing those rules (which can be taught progressively throughout high school) and you'll find doing certain things much easier. Now, granted, trig isn't for everyone. However, it's not unreasonable to expect people to do certain calculations sans calculator. Like multiplication, addition, and division.
        • Re: (Score:3, Interesting)

          by KefabiMe (730997)

          I definitely agree with you, when tutoring trig students the first thing I do is have them reproduce the unit circle and the trig values for multiples of 30 and 45 degrees. Trig exams force students to learn this by asking things like, what is the sine of 60 degrees? sqrt(3)/2 is the correct answer, but generally not one that most calculators can spit out.

          However, eventually when most calculators are able to spit out an answer like sqrt(3)/2, students may no longer need to know their 30-60-90 and 45-45-90

    • Re:tools (Score:5, Insightful)

      by Coryoth (254751) on Wednesday June 04, 2008 @05:53PM (#23659787) Homepage Journal

      Slashdotters are an anomaly because our careers and interests require us to do maths all the time. If the future historians are allowed to slack off on their trig tests, so what? They weren't going to be engineers anyway.
      It's interesting you say that, because the actual report was noting the economic impact of the lower numbers of students actually going on to complete higher level mathematics (in part, they claim, due to poor preparation based on lower standards). Apparently there is actually quite a demand for the skills that mathematics education can impart; high enough demand that employers in the UK are noting the lack of suitably qualified candidates (apparently financial insitutions in the UK are looking to France these days, since they produce more and better mathematicians).

      Sure, not everyone is going to go on in mathematics; some will be poets, some will be historians, and so on. It is also true, however, that most people don't have their future that well written by the age of 16, and having a solid enough background in a variety of subjects, including mathematics, literature, and history, to be able to keep future options open to exploration is important.

      doing the math is going to be easier, even if they didn't ask harder questions. However, the amount of automation these days means that most people aren't ever going to have to do the harder math in their daily lives.
      No, doing the mathematics is not going to be easier; sure the computational grind is easier, but mathematics is not arithmetic. Constructing rigorous logical chains of argument, and symbolic manipulation within formally defined systems; understanding how abstraction can be used effectively, and how it can be taken too far; and being able to think coherently and correctly about abstract entities -- these don't magically become trivial given a calculator. Personally I think part of the problem is that we've lost sight of what mathematics is, and what mathematics is not [stuff.gen.nz]. Modern mathematics courses are simplifying away what matters in favour of shallow coverage of surface material.
  • Good Timing (Score:5, Interesting)

    by JamesRose (1062530) on Wednesday June 04, 2008 @05:14PM (#23659135)
    So I have my A level maths exam (core 3) in two days, taking it a year early, and I'm still finding it trivial, and thats because I'm working from '90s papers and they're so much harder. So basically yes, the exam I am taking has gotten easier over the past years. It's not that the questions are easier though, it's because year by year subjects get dropped so you can focus so much more time on one subject so you can quite easily perfect your understangin of it.
  • by Ynot_82 (1023749) on Wednesday June 04, 2008 @05:14PM (#23659137)
    This is trotted out every single year

    pass rates go up - exams are getting easier. education system in decline
    pass rates go down - teachers not able to communicate with students. education system in decline
  • by rjshirts (567179) on Wednesday June 04, 2008 @05:15PM (#23659153)
    I'm a licensed teacher - Social Studies, not Math - and I've seen many district personnel changing how tests are delivered or graded, simply to make sure that the school is meeting the NCLB standards. As a Social Studies department, we were asked to make certain questions easier to understand, or to eliminate hard to study areas all together in order to make sure that the results would be up to where they need to be. Math teachers in my district have complained a LOT that the district is forcing them to dumb down the tests simply to make sure that scores are where they need to be.
    Kids aren't dumber, they just aren't given the opportunity to fail. If they aren't given the chance to make mistakes, they don't learn from them, and unfortunately, that is where the NCLB is leading us.
    • Re: (Score:3, Funny)

      by StormReaver (59959)
      "...the district is forcing them to dumb down the tests..."

      We in the U.S. did the same thing to the Presidency eight years ago, and have gotten similar results.
    • Re: (Score:3, Interesting)

      I'm a licensed teacher

      Since surely this is at least in part teaching issue, and seems to be commonplace in most of western society (not just nations with the NCLBA or equiv.) doesn't this really suggest a drop in teaching quality/ability? Are we handing out 'licenses' to the wrong people, or too easily (to people with integrity issues who bend to NCLB standards) or some other flawed way? Should we be handing out 'licenses' at all? Can teaching ever be taught, really? Are teaching unions a help or a hindr
    • by dghcasp (459766) on Wednesday June 04, 2008 @06:17PM (#23660225)

      For people not in the U.S., NCLB is the controversial No Child Left Behind [wikipedia.org] act.

      As I understand it (I once dated a teacher,) the history of NCLB is basically:

      • Congresscritter 1: We should improve education.
      • Congresscritter 2: How about we tie test scores to school funding?
      • Rational Person: Wouldn't that just inspire schools to change the tests in order to improve the scores and maximize funding? That's far easier than improving the quality of education, yet it has the same rewards under NCLB.
      • Congresscritters: Shut up! We've got pork in this bill now!
  • by Anonymous Coward on Wednesday June 04, 2008 @05:18PM (#23659197)
    The problem is, our current bottom-to-top emphasis on mathematics and the sciences effectively ensures that all but the brightest, most driven students will be alienated from these core disciplines because of the minutae they are forced to memorize. The prevailing logic would seem to be that this creates a detailed knowledge base for higher learning.

    While this is true, very few actually pursue higher learning in these fields because all of the emotion and excitement is gone when math and science are taught in this way. The wonderment that inspired so many young engineers during the space race is gone. Teachers need to address and emphasize the larger concepts to get children excited about math and science.
  • by brycarp (336444) on Wednesday June 04, 2008 @05:20PM (#23659221)
    Our local school district has unfortunately adopted a math curriculum called "CPM" which is supposed to stand for "College Preparatory Mathematics" - an oxymoron if there ever was one. My wife is a licensed secondary-level math teacher, and does tutoring locally although she wouldn't be able to ethically work in the district if she was forced to use this horrible curriculum that amounts to educational malpractice.

    Because the government education establishment in many places has given up on any attempt to maintain the tried-and-true approach to math education that has been employed in the past - building skills step-by-step in such a way that the student's "toolkit" grows in a logical fashion through the different skills, now they are left with a very fuzzy approach that doesn't really build anything on anything, and mostly is concerned with keeping busy doing something that they can pretend is math and pretend that some sort of progress is being made.

    The most tragic part of it is that the kids who would have been the real math enthusiasts under traditional teaching methods never get the chance to see the order and beauty of math, because curricula like this completely hide it.

    For more info on this, see the Web site mathematicallycorrect.com .

    Because the poor government "education" establishment is failing to really teach math, of course they have to put a happy face on the situation by dumbing down the tests too.
  • by Kohath (38547) on Wednesday June 04, 2008 @05:22PM (#23659259)
    No one is going to say that the teachers are doing a better and better job every year. No one is going to say that the students are held to higher and higher standards in math and that they are achieving those standards more often than before.

    This is because it would be false. You might get arguments about the extent of the change, but none on the direction.

    And nothing in education will ever improve in the US as long as the system is union-controlled.
  • by tsstahl (812393) on Wednesday June 04, 2008 @05:22PM (#23659269)
    has demonstrated that curriculum's have been dumbed down to accommodate a greater breadth of material. The students I see are exposed to more Stuff, but never have any in depth mastery. I am in the U.S., not UK.
  • Students are dumber (Score:5, Interesting)

    by dostert (761476) on Wednesday June 04, 2008 @05:23PM (#23659277)
    I'm a math professor and I must say, just in the past 10 years, I've noticed the "average" undergrad is A LOT worse at basic math than they used to be. I don't know which was cause and which was effect, but students are worse at math and we're teaching them less up through high school. This needs to change very soon or we're going to be a nation of mathematical idiots in another few decades. It has already started... just look at the percentage of American math PhDs coming out each year.

    I agree with everyone else, we need to pay math teachers more. In states like TX a public school teacher makes barely enough to live poorly, and with a math degree, they can make double working in private industry. It is a very hard sell to convince mathematicians to go into education.

    The other thing we need to do is not be afraid to actually fail someone. This society has made it so that everyone feels its their "right" to graduate high school and go to college. We need to change this and actually fail people when they can't do the work. If someone doesn't earn a degree, they shouldn't be "awarded" one.
  • Mensa and testing... (Score:5, Interesting)

    by jddj (1085169) on Wednesday June 04, 2008 @05:23PM (#23659293) Journal
    Mensa won't take SATs from later than 1/31/94 as an indication of your IQ. That says something about changing test difficulty...
    • by Smurf (7981) on Wednesday June 04, 2008 @06:23PM (#23660343)

      Mensa won't take SATs from later than 1/31/94 as an indication of your IQ. That says something about changing test difficulty...
      It sure does.

      On the other hand, they should be smart enough to know that the SAT was never meant to measure your IQ. In fact, they should be smart enough to know that IQ tests themselves only measure certain abilities, and are not really a good measure of intelligence.

      I normally score around 135 in IQ tests (of course it depends on things like time of the day, quality of sleep on the previous night, BAL, etc), and in my opinion IQ tests and Mensa-like organizations are only good to inflate egos, as they have little relevance to real life.

      By the way, did you know that "mensa" means "fool", "stupid", or "jerk" in Spanish? [wordreference.com] How fitting...
    • by delibes (303485) on Wednesday June 04, 2008 @06:54PM (#23660837)

      Mensa won't take SATs from later than 1/31/94 as an indication of your IQ. That says something about changing test difficulty...
      1, 31, 94, ?
      x(n) = [3 * x(n-1)] + x(n-2) , where n>3
      So it's 313 next, right? Next question please :)
  • by IP_Troll (1097511) on Wednesday June 04, 2008 @05:25PM (#23659323)
    Looking at the example questions, the earlier questions look difficult, but unnecessarily so. What I mean by that is, they take what could be a straight forward question and then obfuscate it behind a bunch of random noise merely to confuse the test taker.

    The newer example questions seemed more rationalized, they test whether you know the theory or formula needed to solve the question without throwing you a curve ball.

    Would you rather encourage people to continue studying onto more advanced levels with easier tests, or throw them a GOTCHA question which will totally turn them off to the subject matter?

    There is a difference between testing knowledge of the subject matter, and giving the test taker a hard time. A "difficult" question might be great to ponder when you have unlimited time, but in a time pressured test, it is not appropriate.
    • by Coryoth (254751) on Wednesday June 04, 2008 @07:00PM (#23660909) Homepage Journal

      The newer example questions seemed more rationalized, they test whether you know the theory or formula needed to solve the question without throwing you a curve ball.
      More specifically, they test whether you know the formula. That is, they test whether you have memorized the appropriate recipe. They don't test whether you know mathematics, they test whether you know facts about mathematics. The earlier questions require you to actually put together a multi-step process to get to a result rather than hand-holding you through it. They also tend to require you to actually lay out the line of reasoning you had to use. That actually requires some mathematics -- actually using and mentally manipulating abstract objects in a logical fashion; constructing lines of reasoning yourself to solve problems rather than just using fixed recipes. I'm not saying the early exams are perfect, but they do have a very distinct requirement that the later ones do not -- they require you to actually think and reason. The later tests are akin to history tests that are nothing but questions like "In what year did Columbus sail to the Americas"; they only require you to be able to regurgitate facts. Now such history exams exist, but they suck too. A real history exam should test your understand of meaning of events (both contextually at the time, and for us today), not just raw facts about events. Likewise a real maths exam should ask for more than just regurgitation of facts about mathematics.
  • by Manip (656104) on Wednesday June 04, 2008 @05:25PM (#23659329)
    I'm sorry but what do we really expect to learn from this research?

    Maths in the 1950s was designed for engineers and scientists in that generation. They learned what they needed.

    Maths today is exactly the same. The fact is you can't use 1950s standards to evaluate today's exams any more than you can use today's standards to evaluate 1950s exams.

    The only real question is - Are engineers and scientists finding their maths education weak?

    The answer in my view is no in most cases. In a limited number of careers the maths they received isn't nearly advanced enough but that would have been the case in the 1950s too.

    As I said they're using the wrong measuring stick to measure the difficulty of exams. Nobody needs to know half of the useless junk that kids learned in the 1950s when frankly it is less time consuming and more accurate to use a calculator.

    That's just my opinion. I honestly think a lot of this kind of "research" is a result of much older people looking at today's maths and thinking "Why aren't they learning what I did?" While completely ignoring what they're learning that the 1950s students didn't.
    • by Sycraft-fu (314770) on Wednesday June 04, 2008 @05:52PM (#23659769)
      Also, in general, we are slowly getting away from this idea that memorization is what is important and what makes you smart. Part of that is simply that these days it is much less useful, but there has also been development in educational theory. We do not need or want our children memorizing tons and tons of facts. That really isn't helpful. If I need something remembered, I'll have my computer do it. It's way better than you. We need them learning how to think.

      Well, since education used to be so much heavier in the memorization it is no surprise that the tests are "hard" for people today. I remember getting in to this argument with someone I knew. They'd found a test posted online that was a highschool graduation test circa 1900. They used it as an example of how much "harder" school was then and how I couldn't pass it. Well, turned out I could, but only because I'm a trivia junkie. I know lots of useless facts, and there was a whole lot of the test that was full of it. The geography and history sections were nothing but. Things like matching capital cities to states.

      Ok, well that's neat and all, but it is quite thoroughly useless. There is no reason to know that. If you want to, great, but don't pretend like it is useful knowledge or that you are smart because you can do it.

      So ya, people today had trouble passing the test, but that doesn't mean the test was hard, it meant the test was different.
    • by grgyle (538200) on Wednesday June 04, 2008 @05:55PM (#23659845)
      "...The only real question is - Are engineers and scientists finding their maths education weak?..."

      Absolutely. An engineer in the 40s/50s would need to have in-depth critical skills of geometrical proofs and relationships, nasty algebraic manipulations, and "bag of tricks" mathematics like series approximations, dummy variable substitutions, etc, because computing resources were rare and resource intensive. If you look at the older tests linked in the OP, you can really see a reflection of that need.

      As an engineer today however, I have zero need for knowing trig simplification identities, calculus proofs, and the like beyond a high conceptual level, but I have far more need and usage of logical and discrete math fields, programming concepts, vector operations, statistical methods, and other "math" topics that are still completely absent from any high-school math curricula that I've seen.

      My wife (a math degree and former teacher) suggested throwing out the "calculus path" of mathematics entirely and retool math education to a "discrete math path". It sounded heretical to me initially, but I've come to believe that she's correct.
      • Re: (Score:3, Interesting)

        by Jerf (17166)
        I've often considered how I would re-write the math curriculum if I had a chance, and while I take some things out and put some things back in as time goes by, I have two constants that never seem to change:
        • Trigonometric identities go bye-bye. Even real mathematicians consider them little more than curiosities. Bring them out when you do Taylor expansions, put them away again when you're done.
        • Game theory is in. I'd happily trade Calculus for Game Theory for "non-Engineering bound students". Game theory is
      • by pongo000 (97357) on Wednesday June 04, 2008 @06:33PM (#23660497)
        As an engineer today however, I have zero need for knowing trig simplification identities, calculus proofs, and the like beyond a high conceptual level, but I have far more need and usage of logical and discrete math fields, programming concepts, vector operations, statistical methods, and other "math" topics that are still completely absent from any high-school math curricula that I've seen.

        And I'm afraid that you are, indeed, a victim. You see, the reason why you learn geometric proofs and calculus proofs is to assist with developing problem-solving skills that require an individual to reason a problem from start to finish, much like real life. It scares me that you claim, as an engineer, that all you need to know are the rote mechanics of math (and yes, that is what you describe: number crunching as opposed to critical problem analysis).

        Unfortunately, at least in the US, proofs of any type are becoming rare to non-existent in many curricula. I see the direct result of this every day I'm in school and a student stares at me with a blank look on his/her face when I ask him/her to analyze and determine the best course of action for solving for some quantity X given Y and Z.

        You didn't mention what type of engineer you are. Computer/software/hardware, perhaps? Then yes, I'd agree that programming logic, vector operations, and the like are probably a valuable intellectual commodity. But I know many engineers who work day in and day out designing things, and this takes more than a simplistic knowledge of how to perform statistical computations.

    • Re: (Score:3, Interesting)

      by Coryoth (254751)

      Maths in the 1950s was designed for engineers and scientists in that generation. They learned what they needed.

      Maths today is exactly the same. The fact is you can't use 1950s standards to evaluate today's exams any more than you can use today's standards to evaluate 1950s exams.

      Well, perhaps the people to ask as to whether things are going well or not are professional mathematicians, physicists, and philosphers of mathematics. Conveniently, a bunch of them are busy discussing this over at the n-Category Cafe [utexas.edu]. And yes, there is an element of some material beign dropped in favour of other newer material. It's worth noting, however, that there is a real concern (particularly by Tim Porter and David Corfield) that core material (that is, the essence of mathematics) is being lost in t

  • by Shivetya (243324) on Wednesday June 04, 2008 @05:27PM (#23659363) Homepage Journal
    Look, you can read about it anywhere. We even had math classes in some cities where success was built around "best attempt" or other such non-sense.

    What it all boils down to is that no matter what standard the Federal Government tries to set someone tries to cheat it. That is why there is always such an uproar versus standardized tests. Down here in Georgia they failed nearly 40% of all students in tested grades versus a standardized test. They knew it was coming. They even had practice tests. Is it all the schools fault?

    No. Students seem have this sense of inevitability. They are still of the belief that they don't have to. After all anything else they complain about in school gets changed. I don't see their attitudes as defeatism, its entitlement that they suffer. They don't have to do this, that, or what not. We don't have the right culture in schools, especially city schools among minority students. Until we change the fabric of society the MTV generations will forever think themselves above "working hard". They are all going to be rap starts, professional sports players, or worse win the lottery!

    We gave up control of our schools to "feel gooders". Now its all about grief counselors and no winners allowed because no one should be a loser. When we removed the reward of success what did we expect? I have seen articles where every student got to walk the diploma line regardless if they graduated just so they didn't feel ostracized. Well tough shit. Your boss ain't going to worry about making a failure to feel good. If you don't perform your in for a world of hurt. I guess you could go into government work, of all categories in the job market they have added more jobs than anyone and everyone knows the saying about how its near impossible to lose a government job.

    Schools and students are simply trying to cheat the system. The problem is the schools encourage it because they don't allow for losers. They don't want to hurt little Bobby's feelings so they set him up to fail in life. If they want control of our kids then they should be responsible for them. They get hell bent if someone raises a finger about the Bible in school or complains about sex education yet they are completely aloof when it comes to holding the kids to a standard of education.

    Private school was the only recourse I found. Standards had to be met or we might not be allowed to come back. Students were encouraged to be better. I don't see that outside of a few select public schools; you know I hear it all the time how so and so's public school isn't like those others but sorry it is.
  • by hairykrishna (740240) on Wednesday June 04, 2008 @05:28PM (#23659379)
    I know that this story gets touted around every year but I think there's some truth in it. I tutor some 1st year physics students and their math skills are shocking. They can follow 'recipes' well enough to solve questions they're used to. However, present them with a problem where they have to actually think and they're stumped.
  • by hyfe (641811) on Wednesday June 04, 2008 @05:30PM (#23659405)
    First off, I teach maths/IT to 16 to 19 year olds in Norway.

    Maths has definitivly become a lot easier here. It takes a lot less work to get good grades now, and there's an alarming lack of focus on basic math skills. There's plenty of A-students who can't do basic math. The norwegian school-system is really fucked up though. There's so much focus on getting the trouble-makers through school, so they're allowed to basically take over classes. I mean, we don't want to send them to special schools, because that would stigmatize them! Never mind the 25 other students in the class, they'll just have to sit there and feel neglected.. Not to mention, without consequences these students never learn. I've had students yell at me straight off at 08:15 in the morning because the last test had some questions which weren't exactly as the ones in the book. They're so mal-adjusted and unfit for real life it's scary.. (ohh.. and just for kicks.. 90% of the worst students are pakestani.. while they make up about 3-4% of Oslo in total..trying to teach them anything is basically a crash-course in becoming a racist)

    That said, I work with a couple of really old math teachers, and there's a few subjects like probabilites that are completely new them.. so math has changed. Don't be fooled though, they've replaced all the hard'n'gritty stuff with fluffy feel-nice stuff.

    In Norway, we've had two big reforms in the last ten years, and both made the hardest paths easier. Ironically, they also both made the maths for students taking vocational education harder. It's so tragic I want to cry :(.

  • Then/Now (Score:5, Funny)

    by Quiet_Desperation (858215) on Wednesday June 04, 2008 @05:43PM (#23659611)
    Then: Sally is twice as old as Suzy. Three years from now, the sum of their ages will be 42. How old is Sally?

    Now: Chloe has 7 apples. How many apples does Chloe have?

    Tomorrow: Write the number 5.
  • by rmcd (53236) * on Wednesday June 04, 2008 @06:07PM (#23660047)
    The recent report of the National Mathematics Advisory Panel [ed.gov] is mandatory reading for anyone concerned about math education in the US. The report details exactly how things are going wrong. Our school district (where I have kids in grades 5, 7, and 9) uses a program called "Everyday Math" [uchicago.edu], which is atrocious. (The University of Chicago should be embarrassed.) The emphasis is on breadth rather than depth, and there is a "spiral" so you learn a little bit every year about a lot of different topics. Students frequently have to write little essays explaining how they got the answer. (The linked report explains that spiralling is poor pedagogy, and that good math students can't always write an explanatory essay -- they just know what to do.) The high achieving families all have their kids tutored at the local Kumon center [kumon.com] so they can learn their multiplication tables. The low income families just suffer the consequences of inferior education. The school board and district administrators are clueless, having just agreed to try out 3 different math programs in 3 different middle schools. How on earth will they evaluate the results?

    In our district, the nonsense stops in high school (which is administratively separate), and and I actually think my ninth-grade daughter is learning more math than I did at the same age. But you have to survive elementary and middle school math to get to the high quality teaching. It's such a waste.
  • by jonaskoelker (922170) <jonaskoelker@gn u . org> on Wednesday June 04, 2008 @06:21PM (#23660307) Homepage
    There are problems beyond math.

    The biggest is that the school system is not a great way to learn stuff. I remember (but bear in mind that I'm your average slashdotter, not your average person) at a fairly early age drawing 6x6 grids which taught be that 7 has probability 1/6. I remember my father drawing circles in the sand with dots in the center, explaining the basics of chemistry (and he's not a chemist), and me completely getting it.

    I remember at age 14 (laughably late by slashdot standards) that a person I knew had written a program that played chess. Being a moderately skilled chess player at the time (1390), I thought that was awesomely cool and wanted to do that myself. That got me started writing C (I had dabbled in .bat "scripting" and javascript for ~2 years before that).

    Where am I? Studying CS & Math. Doing the things I chose to study in my own time, not the things I discovered in school.

    Contrast this with school. You're forced into confinement (it wasn't until grade 6 or 7 we were allowed to leave school grounds unsupervised) with a bunch of people that mistreat you horribly and wish you the worst, and another bunch of people who really don't give a rats ass. You're bored out of your mind in the classes that interest you because the material is easy and progress through it is slower than your pace. You're bored in the rest as well, because they don't interest you; the disinterest may arise merely from the fact that they are being forced upon you.

    And I went to a private school... with the things my mother has said about public schools (and she's worked at one), I think I should be glad to not have attended one. On top of that, I hear the danish school system is better than the one in USA.

    More edibles for cognition: John Taylor Gatto (English teacher [johntaylorgatto.com]) says that we he finds companies that don't mind having the kid do some work, the kids do more and better work than the paid staff. My ex-girlfriend (okay, so not completely an average slashdotter :D) has had the same experience (with her being the "kid", age ~15 at the time). This at least tells me that kids have an inherent drive to not waste their time. If that's true, then why are they so unmotivated to do schoolwork?

    Not wanting to be completely off topic, the article says that work needs to be done on making math chic. The question is: who has the credibility and influence with kids to make math cool? For young kids, the parents have some influence, although not much in the "cool" department. For teens, it's mostly the peers (not the kinds who reset the connection). That's a network effects problem you have to solve. Who else? Rock stars? Quaterbacks? Miss teen south carolina (everywhere such as maps)? I mean, having math be the Hot Stuff wouldn't be bad, but it would imply (not just suggest, as the decline in maritime piracy has) the existence of the flying spaghetti monster.

    (for those not picking up logician's humor, everything follows from a contradiction).
  • by Anonymous Coward on Wednesday June 04, 2008 @06:54PM (#23660835)
    Examples of the evolution in teaching math since the 1950s.

    1. Teaching Math In 1950:

    A logger sells a truckload of lumber for $100. His cost of production
    is 4/5 of the price. What is his profit?

    2. Teaching Math In 1960:

    A logger sells a truckload of lumber for $100. His cost of production
    is 4/5 of the price, or $80. What is his profit?

    3. Teaching Math In 1970:

    A logger sells a truckload of lumber for $100. His cost of production
    is $80. Did he make a profit?

    4. Teaching Math In 1980:

    A logger sells a truckload of lumber for $100. His cost of production is
    $80 and his profit is $20. Your assignment: Underline the number 20.

    5. Teaching Math In 1990:

    A logger cuts down a beautiful forest because he is selfish and
    inconsiderate and cares nothing for the habitat of animals or the
    preservation of our woodlands. He does this so he can make a
    profit of $20.

    What do you think of this way of making a living?

    Topic for class participation after answering the question:
    How did the birds and squirrels feel as the logger cut down their homes?
    (There are no wrong answers.)

    6. Teaching Math In 2008:
    Un maderero vende un camión de madera de construcción para $100. Su
    coste de producción es $80. Cuántos de su familia pueden usted alimentar
    desde los $20 beneficios?

"Atomic batteries to power, turbines to speed." -- Robin, The Boy Wonder

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