The question of whether Calculus should or should not be made mandatory in High Schools bags the perennial question of whether any other subject should or should not be made mandatory in High Schools. I mean, certain subjects are mandatory for obvious reasons: English, Algebra, History, Geography, and some other subjects are compulsory courses, at least in some High Schools. However, there is a hidden issue which not many educators and students alike are aware of but choose not to delve deeper into it or ignore it entirely. The issue is this: even among the mandatory subjects, not all their course contents are going to be useful to students at any stage of their lives. So my point is that whether a particular course should or should not be taught in High Schools has little to do with the usefulness or usability of the course contents.
One studies History and English at High Schools but are you saying that the knowledge gained by studying these courses ( like History of US, Canada; World History; solving simultaneous equations in 2 or more unknowns, etc ) will enable one to make use of the knowledge gained thereby, now or in the future? The answer is obvious: not necessarily so. The objective of studying these mandatory subjects is broadly similar to the objective of studying any other subject: to stimulate students intellectually and to raise their level of general understanding and appreciation of the world we live in, no more and no less.
It is upon this premise that I base my arguments on the issue of whether Calculus should or should not be taught at all in High Schools. I contend that, in the light of my aforementioned points, there is no simple or straight-forward answer to this question. The answer to the question depends on a list of factors- factors that favour or work against the teaching of the subject; the circumstances of the High School concerned, the strength of the faculty, availability of funds, etc.
One of the most important factors in determining whether Calculus should be taught in High School is the question of whether the High School has well-qualified, competent, teachers who could deliver interesting and content-rich lectures; I agree that this is tall order to demand from a teacher. The teacher must not only possess the core knowledge of Calculus but must be able to take the students to a fun-tour of Calculus, from its very beginnings ( a brief historical outline of the discovery or invention of Calculus by Leibniz and Newton will be appropriate ) to its development into more complex ideas ( the idea of a derivative, or differential coefficient etc and its applications; the converse process of integration etc ). Along the way the teacher has to introduce fundamental concepts of the subject augmented by illuminating and interesting illustrations of the concepts. I believe that Calculus, like any other divisions of Math, is not intrinsically a difficult subject and yes – the concepts involved may appear at first glance to be quite difficult – but I opine that it does not take a Math whiz-kid to grasp the principles of Calculus.
Of course ideally no student should be coerced into taking up a subject he or she dislikes or has little inclination for. But this argument does not address the possibility that there are students who may want to challenge themselves intellectually but are mistaken or mis-informed about the subject matter and as a result worried that Calculus is akin to rocket science or is so difficult that they won’t be able to do well compared to some other non-Calculus options. That, to my mind, is a pity and could be detrimental to the long-term well-being of the nation. Too many High School students are opting for so-called ‘soft’ subjects – subjects which are not Math related and not Science-associated ( whether Physical or Biological Sciences ). The nation’s educators and decision-makers should take cognizance of the fact that America is now lagging behind in the quality and standard of Math education among developing nations. In many international Math quizzes and competitions US students have not done very well; in fact it is countries like Singapore, China, Korea and other Asian nations whose students, of any age group, consistently come up top in international Math competitions like the Math Olympiad. If this is not alarm bells ringing for the nation, what is?
Arguments against the mandatory teaching of Calculus in High Schools elude the fact that in almost all fields of engineering, knowledge of Calculus is a pre-requisite. And it is safe to say that all engineering schools require its student to have solid foundation in Calculus. I am sure you don’t want to see that the nation’s top engineering schools are populated by mainly foreign students? And while we should remain firm opponents of parochialism and narrow nationalism, we must redress this issue by encouraging more High School students to take up Science and Math, including Calculus. What should be done is not to scrape Calculus as a High School course, even as an elective, but to revise the course materials of Calculus so as to leave out the more difficult components ( e.g higher derivatives, applications in vectors, higher order differential equations ) and instead concentrate on the fundamental concepts and their simple applications.
My contention therefore is that, on balance, Calculus should be made mandatory in High Schools, with the qualifications that schools ought to have Math teachers with the requisite qualities and that the course contents of Calculus be modified so as not to over-burden the average students who should be exposed to this great and important subject.