The author writes:
Lockhart begins with a vivid parable in which a musician has a nightmare in which music is taught to children by rote memorization of sheet music and formal rules for manipulating notes. In the nightmare, students never actually listen to music, at least not until advanced college classes or graduate school.
The problem is that this abstract memorization and formal-method-based "music" education closely resembles the "math" education that most students receive. Formulas and algorithms are delivered with no context or motivation, with students made to simply memorize and apply them.
Part of why many students end up disliking math, or convincing themselves that they are bad at math, comes from this emphasis on formulas and notation and methods at the expense of actually deep understanding of the naturally fascinating things mathematicians explore. It's understandable that many students (and adults) get frustrated at memorizing context-free strings of symbols and methods to manipulate them.I went through the standard 3 semester course on Calculus in college. With the exception of one professor (who did contract work for the Air Force and liked to occasionally gave us problems involving radar tracking aircraft), it was pretty abstract stuff. My wife, on the other hand, took a business Calculus course where everything they learned was correlated to useful tools in the business environment. She seemed to retain her Calculus better than I did.