On 03/02/2013 11:06 AM, Chris Tofu wrote: I can do phasor math using a slide rule quite easily. I can also do it using trig tables. If I have to derive my own trig functions, it'll take considerably longer. Programmable scientific calculators reduce the slipstick or table lookup to a press of a button. The question is that does each successive level of automation erode the understanding of the underlying principles? In pedagogy, "getting the right answer" is secondary to understanding and demonstrating knowledge of basic principles. In the opinion of many teachers, for example, the math (particularly calculus (diffeq especially) taught engineers is "cookbook". It typically requires a math major two or three times as long to cover the same basic material that an engineer would cover in a math course. The math major isn't necessarily stupider--it's just that the material is covered *in depth*. Engineer's match is taught so that larger principles can be covered in reasonable time. A physics teacher in electromagnetics presenting a simple network for solution may well frown on a student solving the problem using Thevenin or Norton equivalents when said teacher expects Maxwell's equations. Even though the numerical answer may be correct, the student who employs the shortcut may well get a zero for the problem grade. Pedagogy has its own ends, very little of which involves getting the right answer. Thinking of this, are any of the list readers old enough to have been taught Trachtenberg math? I recall at the time that it was criticized roundly for depriving students of a deep understanding; rather concentrating on getting the right answer quickly. --Chuck