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, Offtopic) by Anonymous Coward on Thursday August 09 2018, @07:11PM
Who woulda thunk that.
(Score: -1, Offtopic) by Anonymous Coward on Thursday August 09 2018, @07:13PM (2 children)
It helps you to model boobies in VR.
(Score: 1, Funny) by Anonymous Coward on Thursday August 09 2018, @08:32PM (1 child)
Unless you're from Indiana and you think Pi == 3 in which case your booby skin will be missing some pieces or weirdly folded in on itself.
(Score: 3, Touché) by Alfred on Thursday August 09 2018, @08:52PM
(Score: 1, Interesting) by Anonymous Coward on Thursday August 09 2018, @07:15PM (10 children)
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.
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.
(Score: 3, Insightful) by fyngyrz on Thursday August 09 2018, @07:25PM
Calculus:
(Score: 1, Interesting) by Anonymous Coward on Thursday August 09 2018, @07:25PM
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
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
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)
It's not just that, I'd modify the quote to:
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)
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."
(Score: 2, Insightful) by Anonymous Coward on Thursday August 09 2018, @07:20PM (1 child)
People who were no good at the prerequisites, but took high school calculus anyway, did not do well in college calculus? Big surprise...
(Score: 0) by Anonymous Coward on Thursday August 09 2018, @07:43PM
Behold! The results of post-modernism, where deductive reasoning holds no value.
(Score: 4, Interesting) by Thexalon on Thursday August 09 2018, @07:34PM (9 children)
My high school calculus course was lousy, mostly because the teacher had the serious drawback of not having a good understanding of calculus. As in, she knew the formulas and notation and such, but didn't understand how they came about or how to really think using them. My college-level calculus profs did have that understanding, and as a result while I got similarly good grades in both courses, I didn't feel like re-taking calculus in college was a waste of time by any means.
Although I'll also mention that discrete math was a lot more fun and useful than any of the calculus I took. There'd be a good argument for making that the top high school course instead of calculus.
The only thing that stops a bad guy with a compiler is a good guy with a compiler.
(Score: -1, Flamebait) by Anonymous Coward on Thursday August 09 2018, @07:46PM (7 children)
Young
menminds need to know that they're working on something demonstrably useful. All teaching should be about solving some actual problem.Pure mathematics should be something left to be pursued by those few
menminds who can perceive its importance without encouragement.(Score: 2) by Thexalon on Thursday August 09 2018, @08:15PM (6 children)
I can genuinely say I've made use of all the math I studied in both high school and college in my post-academic life. Yes, I work in software, so math is more likely to come up in my profession than, say, marketing, but it has real applications.
For instance, to make geometry into applied math, just do anything related to construction.
The only thing that stops a bad guy with a compiler is a good guy with a compiler.
(Score: 0) by Anonymous Coward on Thursday August 09 2018, @08:22PM (5 children)
That's the point.
Also, either your sector of programming is quite niche or your studies of mathematics weren't as advanced as you seem to think; most programmers never touch mathematical thinking beyond basic "business logic".
(Score: 2) by Thexalon on Thursday August 09 2018, @08:51PM (4 children)
The extent of my math education was mid-level undergraduate and a fairly prestigious college (USA Today top 25 in its group). Of those courses:
Calculus doesn't come up all that often, but is involved in some analytical contexts where you need to track rates and totals of variable things. Linear algebra comes up when maximizing one variable in the face of a bunch of others that affect it, e.g. trying to maximize server throughput while minimizing the number of servers, the electricity to supply them, and the cabling to hook them all together. Discrete mathematics is heavily connected to programming, to the point where much of CS can be described as "applied discrete mathematics". And set theory is vital for understanding databases, which even the most code-monkey of code-monkeys has to be able to handle.
You still think math is useless?
The only thing that stops a bad guy with a compiler is a good guy with a compiler.
(Score: -1, Flamebait) by Anonymous Coward on Thursday August 09 2018, @09:02PM
Also, I doubt you approached any of those computing problems in the way that a student of mathematics or even computer science would. I suspect you basically looked around for software or formulas or excel sheets or StackOverflow posts, etc., that gave you readily applicable (and perhaps parameterizable) solutions that you could just crank, thinking all the while "Yeah, I kind of remember stuff about this. Thank goodness I did me some learning."
(Score: -1, Redundant) by Anonymous Coward on Thursday August 09 2018, @09:49PM
Also, I doubt you approached any of those computing problems in the way that a student of mathematics or even computer science would. I suspect you basically looked around for software or formulas or excel sheets or StackOverflow posts, etc., that gave you readily applicable (and perhaps parameterizable) solutions that you could just crank, thinking all the while "Yeah, I kind of remember stuff about this. Thank goodness I did me some learning."
(Score: 0) by Anonymous Coward on Friday August 10 2018, @12:06AM
Also, I doubt you approached any of those computing problems in the way that a student of mathematics or even computer science would. I suspect you basically looked around for software or formulas or excel sheets or StackOverflow posts, etc., that gave you readily applicable (and perhaps parameterizable) solutions that you could just crank, thinking all the while "Yeah, I kind of remember stuff about this. Thank goodness I did me some learning."
(Score: 0) by Anonymous Coward on Friday August 10 2018, @01:21AM
He didn't say that math is useless, only that schools teach it very poorly by not having students solve real, practical problems.
(Score: 0) by Anonymous Coward on Thursday August 09 2018, @10:59PM
Around here teaching High School math only requires mat up to linear algebra, differential equations and calculus 3. I blame the state for being too cheap to pay teachers to develop their skills more fully.
(Score: 2) by MichaelDavidCrawford on Thursday August 09 2018, @07:53PM (1 child)
While my high school taught calculus its schedule interfered with the student newspaper class.
At UCD we derived integrals and derivatives.
At Caltech we did proofs.
Really my high school Geometry course did more to prepare me for Caltech's calculus than did UCD's Calculus.
Yes I Have No Bananas. [gofundme.com]
(Score: 2) by KritonK on Thursday August 09 2018, @08:49PM
I took calculus at 17, too. Back then, it was compulsory in Greece, if you followed the "practical" direction of studies, as opposed to the "classical" direction, where students were taught Latin, with a more generous helping of ancient Greek than what we got in the "practical direction".
The teacher was great, we got to understand exactly what differential calculus was about, and we got to solve all sorts of problems in almost magical ways using derivatives. At the end of the school year, we dabbled a bit with integral calculus. Although I understood what it was about (sort of the reverse of differential calculus), I found it way over my head.
As to whether it helped me with my university engineering courses, I'm not sure it did. Our four semesters of math were on linear algebra, not calculus, and what courses did require calculus, involved some other, more complicated calculus, that we were somehow supposed to pick up on our own, without being given any tutoring or explanation. We were taught Maxwell's equations, e.g., which involved dels and line integrals, which we had not been taught at high school, but were somehow required to understand and be able to handle with ease, just by being given a definition.
(Score: 0) by Anonymous Coward on Thursday August 09 2018, @08:17PM
I would have to agree that mastering the basics is more important than getting exposed to it all before end of high school.
Did okay upto year 12, but never did an undergrad degree. So 25 years out, i kept tanking a few graduate level stats courses, always playing catch-up on the basic stuff, leading eventually to attempt at a first year calculus course. This i chose to abort before midterms, firmly placing myself in the interested but not capable group - thus exiting with grad.dip. Killing all intentions for a masters.
My lesson was that i should have dumped the early advice to skip over a bridging course and insisted on re-doing the basics. May never have improved my outcome, but my experience rings true to the concepts in the article.
(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...
"Don't you ever miss the days when you used to be nostalgic?" -Loiosh
(Score: 0) by Anonymous Coward on Thursday August 09 2018, @09:13PM (3 children)
and in fields of nuclear engineering, consumer electronics and space (engineering and physics), the only time I've ever had to use calculus was to pass tests in college. It helps to have a deep understanding, but not required, especially now that computers do all the work.
I sometimes think how getting a degree in applied mathematics was almost a complete waste
(Score: 1) by Ethanol-fueled on Friday August 10 2018, @01:48AM (1 child)
I been working in high-tech gadgetry for 15 goddamn years and ain't ever seen a mathematician at all. I've worked with physicists, engineers, comp-sci monkeys, Ph.D oceanographers, technical people who studied Mandarin in college, and talented salaried autodidacts -- but not once have I seen a single fucking mathematician in industry.
(Score: 0) by Anonymous Coward on Friday August 10 2018, @05:16AM
I've seen one, with phd even, but working as an engineer...tracking parts and QA test results I think.
Good friend from undergrad got a full ride NSF scholarship to anywhere in the world, went to podunk state college, started working on elliptical integrals, dropped out a semester later to go to wall street and retired the following year to a big custom built mansion.
(Score: 2) by maxwell demon on Friday August 10 2018, @08:28AM
If everything you learned in your life were just for being useful in your job, your complete life would be a complete waste.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 4, Insightful) by jdavidb on Thursday August 09 2018, @09:36PM (1 child)
This sounds to me like an excuse to not master the prerequisites and not take Calculus. Look, if you don't want to take Calculus, don't take it. And definitely don't take it if you haven't mastered the prerequisites - doesn't that go without saying? You absolutely cannot progress in math if you don't master one topic before proceeding on to the next ones. Any good math teacher should tell you this.
I am my childrens' math teacher, and we're going to shoot for Calculus for all of them. For now we're working on the basics.
ⓋⒶ☮✝🕊 Secession is the right of all sentient beings
(Score: 0) by Anonymous Coward on Thursday August 09 2018, @11:08PM
It should go without saying, but it doesn't. Most of those students are taking it in high school either because it looks good on their transcript or in the mistaken belief that they'll be able to skip the course in college. Neither of which are particularly true and schools should stop suggesting they're true.
Unfortunately, whole generations of school children have been raised to consider the grade to be the important thing rather than a signifier of learning. And unfortunately, that's also how the grading schemes have tended to be as well. To make matters worse a lot of people treat this stuff like something they'll never use, so don't bother to take it seriously and wind up in over their head as the things they didn't master, but should have, start to crop up.
There's a reason why math courses are commonly used to weed out weaker students.
(Score: 2) by AthanasiusKircher on Friday August 10 2018, @04:21AM (2 children)
Okay, I'll admit to being genuinely confused by what the point of this study is. TFA seems to spend an inordinate amount of time setting up a conflict between high-school math teachers and college professors. To paraphrase: "The high school teachers want to believe their calculus courses are useful, so of course they think their courses are useful! While the college profs think prep for calc is more important! And our study [notably written by college profs] finds the college profs are right!" [Except the high-school teachers are partly right too... but they'll get to that later...]
What the hell?
Shouldn't the point be to determine the best pedagogy, rather than who is "right"? What even bother with this sort of useless rhetoric? Already something sounds seriously off about the tone of this study.
Then, you get into the details. The actual study seems to be paywalled, but I found a PDF that contains a summary report based on this study (which was in press), starting around page 53 of this PDF [maa.org].
And the more I read, the more bizarre this study seems to be. If I'm reading their summary correctly, they didn't care about what grades or other performance students had in their high school calc classes. They didn't differentiate between whether the students took some form of AP calc or "honors calc" or some random "calc" their high school teacher offered that may not be rigorous at all or may not complete 25% of the AP curriculum. In their terms, "the taking of high school calculus is a simple dichotomous variable..." (p. 56). Well, they may treat it that way, but the analysis seems like it shouldn't be so "simple" to me.
Because I'm pretty sure that I've seen multiple prior studies showing that IF a student takes a RIGOROUS high school calc class (say, AP BC) AND earns a high score on it, THEN they are likely to do better in college calculus. If a student takes some crap half-ass calc class that doesn't get very far and does poorly in it to boot, why the hell should that student's performance in college calc be significantly improved??
Instead, they claim pre-calculus prep is more important. But how did they measure that? Page 56-57 again: "The preparation for calculus variable is a normalized composite constructed after a factor analysis that showed a strong relationship between high school grades in non-calculus mathematics (i.e., algebra I, geometry, algebra II, precalculus) and students’ SAT or ACT quantitative score."
In other words, the take-away is: students who got good grades in math AND scored well on standardized tests in math likely continued to better in college math. Who knew?!? Meanwhile, the question of whether a student merely ENROLLED in a prior math class (not whether that math class was rigorous nor whether that student even did well in it) is NOT as good a predictor of future math performance! Stop the presses!! What an amazing insight! [/sarcasm]
But hey, at least those darn high school teachers have been proven wrong, and the college profs are right! Right??
Uh... [page 57]: "Even students with relatively weak preparation in mathematics appeared to benefit from taking a calculus course in high school. [...] The result also supports calculus professors’ views that a strong background in algebra and precalculus is more important than taking calculus in high school. [Huh? That seems an odd conclusion based on the earlier sentence in the paragraph.] We take from this that high school students should not be prevented or dissuaded from taking calculus in high school solely based on weak performance in earlier coursework. [Huh?]"
So, if I'm reading this right, the study says the following:
(1) High school math teachers like to teach calculus and think their courses are valuable. College profs think they're less important.
(2) College profs are more right because precalc grades are better predictors than whether a student registered for some random crap calc course.
(3) BUT it turns out there are still apparent benefits for most students who take high school calc, and the biggest benefits are apparently to those who do worst in math. (!)
(4) BUT college profs STILL are more right, because (this was in the ellipsis in the quote above) the worst math students still get pre-calc skill reinforcement by taking a high school calc class. (!!)
(5) SO, even though college profs are the rightest most rightety-right of all people in the universe, and even those high-school math teachers are wronger than wrong for believing that their high-school calc classes are worthwhile, we STILL encourage lots of students to take calc in high school, even for the weaker students.
Sorry, but WTF?!?
Seriously. That's what this study appears to say, based on multiple bad choices of study design, bad logic, and bizarre repeated non sequiturs about how right college profs are. I'm trying to decide between whether the study authors just have a serious agenda or whether they're complete morons.
(Score: 2) by AthanasiusKircher on Friday August 10 2018, @05:04AM
Also, I'd encourage everyone to take a look at the authors' figure 3 on page 58 of the PDF I linked in my previous post, and see if you can figure out how that's supposed to square with their conclusions. Basically, at every level of prior math performance, students who enrolled in high school calc did better in college calc than those who didn't. The gains are not particularly large, but the trend is consistent. (The only exception appears to be the very lowest performing in prior math, but the error bar is huge there, I assume because there aren't enough students in that category to draw clear conclusions.)
The caption to figure 3 also notes that those who enrolled in high school calc in the first place tended to have better performance in prior high school math. (Duh.)
Based on that graph (assuming I'm reading it right), a more reasonable study summary might say the following:
(1) Students who had better performance in pre-calculus high school math tend to enroll in high-school calculus at higher rates.
(2) No matter what their level of pre-calculus knowledge, those who take high-school calc almost always tend to perform better in college calc. (Though the gains are not always substantial.)
(3) Almost all students who performed highly (i.e., got an A grade) in college calc had previously taken high-school calc. (See right side of the graph.) Even students who had an exceptional pre-calculus ability seem very unlikely to score an A in college calc unless they took it in high school, demonstrating that true mastery of the subject likely requires both exceptional prior knowledge AND repeated exposure to concepts.
(4) Also, in general, those who do better in math often continue to do better in math. (Duh.)
THE END.
[Unfortunately, that sort of narrative doesn't really work well with the whole weird "high school teachers are wrong and college profs are right" framing argument.]
(Score: 2) by AthanasiusKircher on Friday August 10 2018, @08:16PM
Just in case anyone else happens to read this -- I apologize for the tone of my post. It was late, I was tired. And bad science really annoys me, particularly when data is manipulated by people claiming to be math educators. But everything I said seems to be true of their study. Disappointing.