In a message dated 5/2/2001 1:13:52 PM Eastern Daylight Time, firstname.lastname@example.org writes:
> When math teachers are only interested in the > solution, and not in the method, it is a very sad day. > > I thought mathematics was about processes, patterns and problem solving. If > it > is, then the METHOD of solution is an interesting process. I salute Joan > Reinthaler for her eloquent statement on the usefulness and purpose of the > quadratic formula, and I agree with her 110%. >
As to patterns, I agree that the QF is an elegant pattern. As to the process of doing a problem and the methods of problem solving: the QF is one of several (factoring, complete the square, Newton's Method, bisection, synthetic division, and several approximate and exact methods using computers, calculators and CAS-- to name a few). When you are considering process and problem solving then the criteria are different. The QF in most (all?) situations is not the "best," most efficient or most elegant. Also (still in the process and problem solving realms) it is very limited, working only on quadratic polynomials whereas many of the other methods work on a much wider variety of equations. No one solves quadratic equations for a living; they may solve quadratic equations as a step in doing the problem they are actually trying to solve. But they are after the solution.