> It would be preferable to teach about "form," and then about manipulating expressions to convert them from one form to another. Teaching, even defining, form

> It would be preferable to teach about "form," and then about manipulating expressions to convert them from one form to another. Teaching, even defining, form would not be so easy, either. In some cases, maybe for partial fractions decomposition or completion of the square, but generally, no. Instead there is an easier approach, plenty effective: Just present the student with two algebraic expressions that are equal and have the student show that the two are equaly. So, the student gets practice in manipulating algebraic expressions; the goal, show that the two expressions are equal, is clear; and there are no issues of style or form. Of course a lot of the work in a common course in trigonometry is of this form. So, sure, when a student gets to manipulating trig functions in calculus, they have lots of practice manipulating trig expressions, maybe even more than commonly needed! :-) Or, maybe a good trig course would trim back some of the manipulation exercises and, instead, move on to some of the trig applications, especially to signal processing, Fourier transforms (just the finite versions if want to avoid calculus), power spectra, etc. Heck covering just overtones in music, how a violin or organ is tuned, would be both good and fun.