Quote:Discussion is good, but there's nothing wrong with expecting a right answer.
I'll jump in on this one-- I worked on a project to develop a research based curriculum for high school algebra. There is clear research to show that while expecting a right answer may be good math, it is bad education.
For those of us who do math as a profession, math is more than a machine where you turn the crank and out pops an answer. Math for us is a language, a way of expressing ideas.
For example, I work as a software engineer where I need to propose and defend algorithms for large server based speech recognition. I rarely need a numerical answer-- and often, even with a room full of very smart, geeks with advanced degrees, we still argue over which solution is best (and often the answer is only found through experiment).
I need to be able to grasp a problem, and then express it mathematically. My ability to find roots of a polynomial doesn't matter. My ability to correctly identify an algorithm as O(N^2) -- and my ability to explain why this is relevant in terms of a specific problem is the most important thing of all.
When I was teaching high school physics, there was a class of student (with very good grades) who could do everything they needed to get an A in algebra. The solved simultaneous equations. They found roots of polynomials.
It was rote-- they were doing arithmetic (mechanically following steps they memorized) rather than math (using reason to develop and express ideas and solve new problems).
They had no clue of "Why" they would ever need to find roots of an equation... and they could never solve a problem involving a polynomial unless they had seen that exact problem before.
This was deeply frustrating to me.
