Too much algorithmic honesty?
Today, mid-polynomial unit, I taught a class polynomial long division and polynomial synthetic division. Side-by-side, actually. Preceded by arithmetic long division (Greenleaf – an unfamiliar repeated subtraction without place value algorithm (how I was taught)), and the standard American algorithm. Opening examples were 279/13 and (2x^2 + 7x + 9)/(x + 3).
Which is better [long division or synthetic division]?
I froze, and then answered.
“In most high schools, polynomial long division is taught first, in an earlier course. Once synthetic division is taught, many teachers expect that it is the method to be used, all the time. But me, I never use synthetic division. Polynomial long division uses a familiar algorithm from arithmetic, and that is too big an advantage to ignore. In tonight’s homework, you have to do some of each, but for your own work, and on tests, you may choose which you are more comfortable with.”
Was I too honest?