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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: 0) by Anonymous Coward on Thursday August 09 2018, @08:26PM (8 children)
Even if you're learning from Spivak's book, algebraic operations remain the only algorithm. Later when you pick up more differential equations and Laplace transformations it becomes clear just how much that is true and how all those layers upon layers of identities are really just memorization first, comprehension second.
The problem is institutional. Without high-school calculus teachers slack around algebra and don't build up kids' skills rigorously enough since they find the subject boring. But, when trigo is just around the corner and calculus is soon to follow, teachers are pressured into actually teaching those skills instead of messing around.
Look up how many STEM undergrads high-schools without a calculus class produce. That's where you'll get your answer.
(Score: 2) by Snotnose on Thursday August 09 2018, @08:36PM (6 children)
Math major here. My big understanding of Math was you got one or two balls of gibberish, and you had to use every identity you could remember to convert them into balls of different gibberish in the hope you could do that thing you needed to do with the gibberish to get an answer. Why is, say, the Law of Cosines important? Because sometimes you can use it to transform a ball of gibberish into a different, more tractable ball of gibberish.
Well, it's gibberish nowdays. But 40 years ago I actually understood it.
When the dust settled America realized it was saved by a porn star.
(Score: 0) by Anonymous Coward on Thursday August 09 2018, @09:25PM
Welcomen to the world of Wittgenstein.
There are now a number of software packages that translate forms of gibberish back and forth.
(Score: 1, Insightful) by Anonymous Coward on Thursday August 09 2018, @09:26PM (3 children)
That's what separates understanding from application.
If you can't derive those things from first principles, then it's true: You don't really know what you're doing, and your never did.
(Score: 2) by Ken_g6 on Thursday August 09 2018, @10:49PM
Hee, hee, did someone say something about deriving mathematics from first principles? That only takes a few thousand pages. [wikipedia.org]
I would say most math students shouldn't dive into that.
(Score: 0) by Anonymous Coward on Thursday August 09 2018, @11:32PM (1 child)
This was the pedagogical position among mathematics lecturers right up until computer assisted proves forced them to accept derivation is just a more computationally intensive stat based pattern matching algorithm that, despite previous claims to "understanding", merely demands even more practice and memorization before the personal capacity of one's individual genes is met.
A shame von Neumann's generation failed to pass on just how exceptional is the exception to the rule and how the rest of us should stay humble and don't get too proud about deriving a few proves where a true genius would derive a whole new field and will blatantly tell you it's all just raw computations.
(Score: 0) by Anonymous Coward on Friday August 10 2018, @12:01AM
Fine. Either you can do that pattern matching, or you can't. What's your point?
(Score: 0) by Anonymous Coward on Thursday August 09 2018, @11:04PM
That's usually because the balance wasn't right. To properly learn math you need to be taught things that you mostly just memorize at first. You take those things and you build your own connections between them by way of playing with them and analyzing them, generalizing them and figuring out how they fit together.
Personally, I've been doing math professionally for years, but rarely need my calc 3 work, but the more of it I do, the more connections that I discover for myself and the more efficient I get at predicting what methods might work for a given question or situation that I haven't seen before. But, it took years of work and it only happened because I started to pay more attention to the actual math language being used. If I handled it the way a lot of students do where they just memorize it all and try things until something works, but not bothering to figure out why, I'd still be rubbish.
IMHO, flow charts and mind maps are essential for most people to grasp the relationships between various bits of math that they're being taught and keeping things straight.
(Score: 1) by nitehawk214 on Thursday August 09 2018, @08:46PM
So, you are saying if we take the rate of students graduating without high school calculus over time...
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