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posted by chromas on Thursday August 09 2018, @06:49PM   Printer-friendly
from the mathses dept.

Contrary to widely-held opinion, taking high school calculus isn't necessary for success later in college calculus—what's more important is mastering the prerequisites, algebra, geometry, and trigonometry—that lead to calculus. That's according to a study of more than 6,000 college freshmen at 133 colleges carried out by the Science Education Department of the Harvard Smithsonian Center for Astrophysics, led by Sadler, the Frances W. Wright Senior Lecturer on Astronomy, and by Sonnert, a Research Associate.In addition, the survey finds that weaker math students who choose to take calculus in high school actually get the most benefit from the class. The study is described in a May 2018 paper published in the Journal for Research in Mathematics Education.

"We study the transition from high school to college, and on one side of that there are college professors who say calculus is really a college subject, but on the other side there are high school teachers who say calculus is really helpful for their students, and the ones who want to be scientists and engineers get a lot out of it," Sadler said. "We wanted to see if we could settle that argument—which is more important, the math that prepares you for calculus or a first run-through when you're in high school followed by a more serious course in college?"

The study's results, Sadler said, provided a clear answer -a firmer grip on the subjects that led up to calculus had twice the impact of taking the subject in high school. And of those who did take calculus in high school, it was the weakest students who got the most from the class.

To get those findings, Sadler and Sonnert, designed a study that asked thousands of college freshmen to report not only demographic information, but their educational history, background and mathematics training.

https://phys.org/news/2018-07-mastering-prerequisitesnot-calculus-high-schoolbetter.html


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  • (Score: 1, Interesting) by Anonymous Coward on Thursday August 09 2018, @07:15PM (10 children)

    by Anonymous Coward on Thursday August 09 2018, @07:15PM (#719547)

    Contrary to widely-held opinion, taking high school calculus isn't necessary for success later in college calculus.

    I have literally never met a mathematician with that opinion. In fact, my first year undergraduate professor believed that high school calculus was actually counterproductive.

    In addition, the survey finds that weaker math students who choose to take calculus in high school actually get the most benefit from the class.

    No shit? The students who already do well in mathematics probably don't need high school-level instruction and likely consider it to be a bird course. They show up to class and don't give a shit.

    The weaker students nevertheless picked this as one of their electives. This indicates that these students are interested in mathematics, which I expect is the single biggest indicator of future success in mathematics.

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  • (Score: 3, Insightful) by fyngyrz on Thursday August 09 2018, @07:25PM

    by fyngyrz (6567) on Thursday August 09 2018, @07:25PM (#719550) Journal

    Calculus:

    The agony and dx/dc

  • (Score: 1, Interesting) by Anonymous Coward on Thursday August 09 2018, @07:25PM

    by Anonymous Coward on Thursday August 09 2018, @07:25PM (#719551)

    These results mirror my experience. I was a goof-off in 9th grade geometry, never did my math homework, and ended up getting C's and D's. Back then (early '80s), there was still vestiges of that "new math" stuff going around, and they had two tracks. The "good" students went on a track of new math where they were trying to teach things from the standpoint of group theory lite and stuff ( "In the new approach ... the important thing is to understand what you're doing, rather than to get the right answer"), and my friends complained a lot. I was put on the old fashioned track (how many around here learned how to calculate using log tables?) where I went into algebra and trigonometry. We converged back in calculus senior year and I had such a good foundation of algebra and trig (especially all those trig identities that were drilled into my head) that calculus was an enjoyable class. I did better than most of my friends who went through on the "smart" path.

  • (Score: 0) by Anonymous Coward on Thursday August 09 2018, @10:56PM

    by Anonymous Coward on Thursday August 09 2018, @10:56PM (#719665)

    Same here, in fact, most of the math professors wind up having to redo all the calculus that was taught in high school because it either isn't right or doesn't go into enough detail to be useful.

    There's also the issue that students that are in high school aren't necessarily at the developmental stage that it would take to make meaningful use of calculus yet.

    Calculus itself usually isn't that hard, what makes it seem that way is that it torture tests your algebra skills. When I'm working with calculus students, most of what I'm helping them with isn't calculus, it's algebra that they should have already mastered, but for whatever reason didn't.

  • (Score: 0) by Anonymous Coward on Friday August 10 2018, @01:13AM

    by Anonymous Coward on Friday August 10 2018, @01:13AM (#719717)

    The students who already do well in mathematics probably don't need high school-level instruction and likely consider it to be a bird course.

    They do well in mathematics according to the schools, which have extremely low standards and focus almost entirely on rote memorization. Most of the A+ math students do not understand the math, because they don't need to understand it to get a good grade.

  • (Score: 2) by driverless on Friday August 10 2018, @02:07AM (5 children)

    by driverless (4770) on Friday August 10 2018, @02:07AM (#719740)

    It's not just that, I'd modify the quote to:

    Contrary to widely-held opinion, taking high school calculus isn't necessary for success later

    unless your definition of success is "becoming a math teacher". I'm a scientist. I took calculus at school and university, encouraged by curricula that said you needed to take calculus in order to...uhh... in order to be able to take even more calculus afterwards. I have never, ever needed even the tiniest piece of it, it was years and years of totally wasted effort.

    What I really should have taken instead, and what I think everyone should take at least a year of, was statistics, so you know when you're being lied to by politicians/the media/PR people/etc. You probably won't ever use statistics either, but at least you've armed yourself with enough knowledge to cut through an entire class of BS.

    • (Score: 2) by bzipitidoo on Friday August 10 2018, @07:08AM (4 children)

      by bzipitidoo (4388) on Friday August 10 2018, @07:08AM (#719832) Journal

      The biggest problem I've seen with calculus is recognizing when it can be applied to a problem, and then understanding how to apply it. It's also rather easy to do without. You can do a sort of brute force calculus with computers. For instance, make a computer actually calculate the area of each very narrow slice, rather than simply integrate the function. It's little wonder you've never found it useful.

      Calculus is poorly taught. Every calculus class I had skipped over the rationale and reason behind it all to dive head first into the gory details of how to take the derivative of this and that kind of function. Once you get past polynomials, trig functions, and natural logarithm and e, it can get a bit tricky. Ultimately, they throw functions at the students for which there is no direct way to take a derivative. That's when they drag out the Laplace and Fourier Transforms. Throughout the entire series of calculus I, II, and III, students may never see a real world problem. Most of the exercises are thoroughly artificial, stuffed full of equations that mean nothing. Or if they do mean something, there's not the slightest hint of it to the students. Where is the orbital mechanics? The civil engineering bridge support problems? The classic RLC circuit from EE? And, how could they go on and on about the Fourier Transform, but do little more than mention the FFT? Have to press on to differential equations to finally start seeing real world calculus.

      • (Score: 0) by Anonymous Coward on Friday August 10 2018, @02:47PM (1 child)

        by Anonymous Coward on Friday August 10 2018, @02:47PM (#719927)

        For instance, make a computer actually calculate the area of each very narrow slice, rather than simply integrate the function.

        Simply?! Come on. Most functions cannot be integrated simply. Numerical methods (such as "calculat[ing] the area of each very narryw slice") are much more practical for computers, and can solve a much wider variety of problems. That's why basically everyone using computers to solve problems like this use numerical methods.

        • (Score: 2) by bzipitidoo on Saturday August 11 2018, @05:41PM

          by bzipitidoo (4388) on Saturday August 11 2018, @05:41PM (#720332) Journal

          > Most functions cannot be integrated simply.

          This is why you pick functions that can be integrated easily. Of course you might not have that option. If the function is unknown and all you have are data points, then, yes, you'll have to do something else.

          > Numerical methods

          Which methods do you mean? For instance, approximating the function you're working with, by sampling it at a bunch of points, then fitting an interpolating B-spline through those points? A B-spline is of course really easy to integrate as it's all polynomials. But if the original function can be integrated, why not just do so? Numerical methods are fine, sure, and good enough for all sorts of engineering work to the point they can be used to the exclusion of all other techniques. Yet it's still good to know about the methods and techniques of calculus.

      • (Score: 2) by driverless on Saturday August 11 2018, @02:14AM (1 child)

        by driverless (4770) on Saturday August 11 2018, @02:14AM (#720161)

        Calculus is poorly taught.

        "Calculus made Easy", Silvanus P. Thompson, MacMillan & Co, 1910. A significant improvement on any maths text published since, this actually makes calculus understandable. This is how you get people to understand calculus, not all the nonsense that's been tried on students since then.

        • (Score: 2) by bzipitidoo on Saturday August 11 2018, @06:28PM

          by bzipitidoo (4388) on Saturday August 11 2018, @06:28PM (#720339) Journal

          Thank you very much for telling me about that calculus book. I figured it had to be out of copyright, and sure enough, it is, and available on Project Gutenberg, here: http://www.gutenberg.org/ebooks/33283 [gutenberg.org]

          I read the prologue and the 1st first page and am impressed! This from the prologue sums up what I'm complaining about with the way mathematics is taught:

          "The fools who write the textbooks of advanced mathematics ... seem to desire to
          impress you with their tremendous cleverness by going about it in the most difficult way."