The Perils of Overreliance on Math

 On the Importance of Really Understanding Radio and Radio Circuitry 

In the first version of this book I included (in bold letters) sections in which I described my efforts to deeply understand how the circuits I was using really worked. I mentioned that this yearning for understanding probably had its roots in the influence of Jean Shepherd: Shep seemed to expect true radio hams to really understand the gear that they worked on. As a child, James Clerk Maxwell would often ask about how things worked: “What’s the go of it? What’s the particular go of it?” That is the kind of understanding that I wanted. But as I progressed, I would often come across hams who had other notions about what constituted “understanding.” These people were often Electrical Engineers, deeply schooled in mathematics. For them, knowing the math was synonymous with understanding how circuits worked. Asked, for example, how a mixer mixed, they would spit out trigonometry formulae. I found this kind of understanding insufficient and unsatisfying. I was not alone: 

In 1990, after seven years of teaching at Harvard, Eric Mazur, now Balkanski professor of physics and applied physics, was delivering clear, polished lectures and demonstrations and getting high student evaluations for his introductory Physics 11 course, populated mainly by premed and engineering students who were successfully solving complicated problems. Then he discovered that his success as a teacher “was a complete illusion, a house of cards.” 

The epiphany came via an article in the American Journal of Physics by Arizona State professor David Hestenes. He had devised a very simple test, couched in everyday language, to check students’ understanding of one of the most fundamental concepts of physics—force—and had administered it to 8 thousands of undergraduates in the southwestern United States. Astonishingly, the test showed that their introductory courses had taught them “next to nothing,” says Mazur: “After a semester of physics, they still held the same misconceptions as they had at the beginning of the term.” 

The students had improved at handling equations and formulas, he explains, but when it came to understanding “what the real meanings of these things are, they basically reverted to Aristotelian logic—thousands of years back.” 

To Mazur’s consternation, the simple test of conceptual understanding showed that his students had not grasped the basic ideas of his physics course: two-thirds of them were modern Aristotelians. “The students did well on textbook-style problems,” he explains. “They had a bag of tricks, formulas to apply. But that was solving problems by rote. They floundered on the simple word problems, which demanded a real understanding of the concepts behind the formulas.”

From: http://harvardmagazine.com/2012/03/twilight-of-the-lecture