A SERIOUS PROBLEM WITH MODERN EDUCATION
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There is a troubling trend in education that warrants further discussion because it is symptomatic of a very serious problem: The failure of our institutions of higher education, from high school on up, to distinguish between “being exposed to” and “actually learning”. As a result, we have people with diplomas and even advanced degrees, who have obtained them by parroting back statements and memorized procedures without ever having understood them. This is not just the dumbing down of public education, which has certainly been happening over the past fifty years due to over-crowding and lack of qualified teachers and the lack of physical facilities, but it goes much deeper than that.
This problem affects all fields of education, but let’s talk about mathematics, because that’s a discipline where ignoring the basics should never happen, and because math is one of my areas of interest and expertise. During my years of teaching mathematics, first at the secondary school, college-preparatory level, then at the college and university level, and later, teaching systems analysis math and optimization techniques to post-graduate scientists and engineers, I discovered that advanced math courses were being taught by people who had missed, or not understood some the basics during the early part of their education. It is possible to learn to apply mathematical formulas and procedures without understanding the basic concepts upon which they rest.
I was fortunate to have had a professor, Dr. Floyd Helton, the chairman of the Math Department where I earned my degree in mathematics, who emphasized understanding the basic concepts underlying mathematics. In calculus classes, e.g., he would not allow the class proceed until he felt that everyone who was capable of understanding, understood the basic concepts of enumeration, equivalence, inequalities, identity, constants, variables, functions, infinitesimals, and limits. And he discouraged students from enrolling in advanced math courses, unless they had more than a passing grade in college-level algebra, trigonometry and analytical geometry. This is apparently not often done in colleges and universities today, because there are hordes of people out there with advanced degrees in applied math, science and engineering who, surprisingly, do not understand the basics.
There are levels of understanding in any discipline, and it is especially important in mathematics and science to understand basic concepts. But the way math is taught in our schools today, forgoing thorough learning for expediency in processing students through the system, and confusing memorizing formulae with understanding logical processes, is a formula for disaster!
ERC July 19, 2017