Academic priorities 318
Probably the "standard" solution using a square root.
Even when it is wanted to find the solutions, describing the process sufficiently to carry it out on a computer which does not already have the algorithms to solve it would be adequate.
There are computational aspects like these, and they are now rarely taught. However, if you have every tried to get teachers or prospective teachers to understand the structure of the integers, or get students who have taken the full calculus sequence to understand any of the concepts, even though they know how to calculate, you will know that the ability to calculate is of little importance, and it may well hinder the learning process.
It can also lead to poor application; if an engineer who knows how to solve certain differential equations chooses only among them, I do not want to have to use his bridge.
It is not impossible, and some of it will be picked up along the way. Some have the ability, and some do not. I can often mentally come up with an estimate; others cannot. So what? It does not help understanding.
-- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University
Academic priorities 319
I agree. That's why I lost it in my second year of university. Math turned into a series of seemingly arbitrary steps that I couldn't relate to the real world - and at that...