Your newspaper has recently carried a number of articles and letters discussing the teaching of mathematics. I spent many years teaching math (from Grade 8 to first-year university), and I am always amused and slightly irritated at the polarization of opinion between those who want to "go back to the basics" and those who use denigrating terms such as "drill and kill."
I always agree with both sides. As a math teacher, I was greedy for my students -- I wanted it all.
I wanted them to have a deep and thorough understanding of what they were learning. I wanted them to see how various concepts tied together. I wanted them to have great quantities of important facts and information at their fingertips. I wanted them to be fast and efficient with their algebraic and arithmetic skills.
And I especially wanted them to be good at creative problem-solving, able to solve challenging problems that were new to them, not just knock-off versions of problems they had solved before.
To be good at solving problems, I wanted my students to have what I sometimes called a "well-stocked mind" -- a mental tool kit that gave them a wealth of information to draw on. I also wanted them to be able to concentrate on analysing the problem without getting hung up on more trivial matters -- such as how to do the arithmetic or algebra required in the solution. That is where fast and efficient skills were essential.
My advice to teachers of today is this: You do not have to decide between teaching for understanding and teaching for skill proficiency. You can be greedy. You can do both.