Is It Time To De-Emphasize The AP Calculus Test?

IN a recent WSJ op-ed ('Who Needs Calculus? Not High Schoolers', May 15, p. A11) James Markarian (chief technology officer of SnapLogic) made the case that AP calculus is overrated for most high school students. This despite the fact that nearly 450,000 took the exam in 2016.   This is relevant now as perhaps nearly the same number sat down to take the test last week Tuesday.

But why? Why all the emphasis on AP calculus?  Markarian's theory is perhaps as good as any for the radical expansion of calculus teaching in high school, namely it's taught  because of the "intense competition for elite colleges". So hundreds of thousands take it, though they may even hate it, because "they hope it will increase their chances of admission."

The problem is that high school math classes then veer dangerously close to 'teaching to the test" which is actually adverse to genuine learning and critical thinking (which also, btw, emerges in many math problems). In addition, how many students will actually use it in their professional careers? As Markarian observes:

"Students need skills to thrive in the 21st century workplace but I'm not convinced calculus is high on that list. Sure calculus is essential for some careers, particularly in physics and engineering, but few high schoolers are set on those fields."

What to take instead of calculus? Well statistics!  As Markarian notes:

"The Labor Department estimates that 'statistician' will be one of the fastest growing job categories over the next decade, faster than software developer and information security analyst. The pay isn't bad either: The median statistician made $84,000 in 2017."

Sounds like the teaching of AP Calculus needs to be de-emphasized in favor of statistics.  Note that Markarian, like yours truly, isn't saying high schools ought to stop teaching calculus. As I wrote in an earlier post, e.g

http://brane-space.blogspot.com/2016/04/calculus-is-so-last-century-hardly.html

"Calculus then, ought to be here to stay, certainly for most college math and science majors and perhaps even some others (e.g. Philosophy) interested in exploring the role of quantum mechanics in modern expositions, say involving quantum nonlocality and entanglement. "

But also having noted,

" I've always been skeptical of the high school AP Calculus curricula and whether students are really of sufficient mental maturity that the courses serve any useful purpose (apart from the usual academic 'feather' in the cap to expand their choice of college). And I never saw the reason for pre-med students to be taking calculus. In each case then, perhaps some finite math course or statistics would better serve these populations as opposed to differential and integral calculus."

The key point which Markarian hits on and with which I concur:

"Changing the incentives could encourage students to take subjects relevant to their ambitions. Statistics and probability are much easier to apply to real world problems such as traffic analysis or election polling, which helps keep adolescents engaged."

Now, to be sure, it is possible to teach oneself statistics on one's own time. I did it in preparation for completing the extensive statistics sections (e.g. Poisson statistics) in my  solar physics dissertation. However, that was done at the post graduate level and statistics itself was not a course requirement. The point here is that if one is serious about statistics as a career choice then he will be doing the subject as a major, so self teaching will clearly not be enough.

In addition, let's note that an academic route that includes both calculus and statistics may be optimal. One WSJ letter writer picks up on this (May 21, p. A16):

"Calculus in conjunction with statistics is a vastly superior skill than statistics alone and the proof is the proliferation of extremely profitable high frequency trading and finacial modeling. Statistics on its own can really only tell you about past processed  but you need calculus to understand how something will change over time."

On the other hand another letter writer (Sean Campbell, Ph.D.) warns:

"Almost nobody should learn calculus at the age of 17 or 18 with the expectation it will advance one's career ten years in the future.  The reason to learn calculus is to think rigorously and analytically in a structured environment."

 The implication here appears to be that few 17 or 18 year olds are  really mentally equipped (e.g. their prefrontal cortex is still growing) for rigorous analytical thought of the type required to master calculus. If they do take AP calculus most are likely trained to memorize mechanical techniques,such as for differentiation and integration - then working  as many problems as possible to  reinforce the techniques.

But if that is the case, the high school  population taking AP calculus may be vastly inflated, i.e. over what it realistically should be.  This is especially in terms of realizing there are currently some 30 million jobs available in the U.S. that pay an average of $55,000 a year and don't  require a bachelor's degree  - far less calculus, or even statistics  This according to the Georgetown Center on Education and the Workforce. .

This begs the question of whether it is worthwhile to get a college degree at all,  if the  post-secondary object is simply to get a good paying job minus the onerous burden of student loan debt. The total of that debt now stands at nearly $1.4 trillion, and defaults are also growing at an unnerving pace. These will continue given the interest on most student loans are set to increase by 50 or more basis points,. 

The determining answer to the previous question  may have been provided by Dr. Steven Mason ('The Myth of Higher Education', Integra , No. 9, Oct.  2010).  He argued that that the only real reason to attend college isn't to snag a job afterward, but  "in the quality added to one's life".

He elaborated this means that completing college  "allows one to better appreciate music, art, history and literature. It contributes to a better understanding of language and culture, nature and philosophy. It expands rather than limits horizons and replaces faith and belief with reason and logic"

In essence, one attends college because "it teaches a person to live - not to earn a living" and that living encompasses an impetus for further learning just for its own sake. If a fantastic, well-paying job also comes with it, that's icing on the cake.  But it should not be expected because you are shelling out twenty grand a year to get your B.A. or B.Sc.

The takeaway?  If a high school student is confident of securing a good job without going to college and isn't particularly invested in "learning how to live", there's no reason  to take an AP calculus course.   I would, however, suggest still gaining a mathematical background at least up to Algebra II.  That course still imparts good thinking and analytical skills - but perhaps not as rigorous as calculus.

"Calculus is so last century"? Hardly!

Two months ago a WSJ op-ed ('Calculus Is So Last Century') by Tianhul Michael Li caught the eyes of many mathematicians as well as physicists (and I can assure you, many space and solar physicists). In it Li basically argued that calculus is primarily of the last century as it "is the handmaiden of physics - invented by Newton to explain planetary and projectile motion."

Adding:

"While its place at the core of math education may have made sense for Cold War adversaries engaged in a missile and space race, 'Minute Man' and 'Apollo' no longer occupy the same prominent role in national security and prosperity they once did."

Which makes one wonder what alternative universe and planet this guy is living on? Surely not the one that I'm on!

A feature story in Saturday's NY Times, for example, expatiated on the latest developments including "hypersonic targeted warheads" not only under development by the U.S. but China and Russia as well. The U.S. has a non-nuclear version but the take is that the Russians and Chinese are developing nuclear warheads- independent of missiles- that can be hurled into space then come down on an enemy with little or no warning time. This is in contrast to Cold War ICBMs that general gave about 30 minutes advance notice, unless launched by submarines)

Most alarming is the drive by a number of nations, including the U.S., China and Russia, to develop low yield nukes which - as the article put it- could make their use much more likely than the "mutually assured destruction"  (MAD) model of the past allowed. Indeed, the Russian already have a military posture firmly in place that permits the use of tactical nukes (with 10- 25 kt warheads) in the event that NATO forces overwhelm Russian positions in Eastern Europe. (And cruise missiles are also being outfitted with low yield nukes.)

The current U.S. proposal to "modernize" its nuclear warheads is also seen as possibly destabilizing the existing system and rousing the Chinese and Russians to action in their own warhead development.

Far from national security having switched away from H-bomb Cold War worries, we are evidently entering a new era wherein nuclear "swords of Damocles" literally hang over our collective heads, in the form of targeted hypersonic warheads, or even nuclear-armed satellites,

None of these systems will use linear algebra (the math Li mainly advocates teaching) to reach their targets, but plain old brute differential calculus, of a form I described in earlier blog posts, e.g. from May 6, 2013 (the rocket problem).

Surely then, Calculus isn't passé if it is still central to the ultimate form of nullifying any national security or 'prosperity': nuclear war,

Meanwhile, in fields as diverse as astrophysics, astronomy, quantum mechanics and plasma physics - not to mention climate science -  differential calculus is as critical as ever. While it is true algorithms and numerical simulations, models have been developed in all these fields, it is also true that differential calculus underscores that development and continued tweaking of those models depends on the actual math, not just crunching numbers into numerical or statistical data sets.

Li is correct when he asks at the outset 'Can you remember the last time you did calculus?'  But that question could also be asked about linear algebra or finite mathematics, or a course in multivariate statistics.  The point is that any form of advanced learned in high school or college will fall by the wayside if it is not used in some way later on, irrespective of how it was taught.

Li argues that he isn't saying calculus shouldn't be taught, as it is "great mental training" which is most gracious of him. But if nuclear warheads are going to be set off in detached form and land on my head, I'd be curious as to the math underlying the dynamics. I don't want to just read about it in the NY Times.

Where I do agree with him more, is when he criticizes the "single drive toward calculus in high  school and college" which "displaces other topics more important for today's economy and society".  These include "statistics, linear algebra and algorithmic thinking" (such as revealed in finite math.)

I concur because I've always been skeptical of the high school AP Calculus curricula and whether students are really of sufficient mental maturity that the courses serve any useful purpose (apart from the usual academic 'feather' in the cap to expand their choice of college). And I never saw the reason for pre-med students to be taking calculus. In each case then, perhaps some finite math course or statistics would better serve these populations as opposed to differential and integral calculus.

Calculus then, ought to be here to stay, certainly for most college math and science majors and perhaps even some others (e.g. Philosophy) interested in exploring the role of quantum mechanics in modern expositions, say involving quantum nonlocality and entanglement.