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