From the book What is Mathematics? A few interesting snippets from the Foreword and Introduction:
The teaching of mathematics has sometimes degenerated into empty drill in problem solving, which may develop formal ability but does not lead to real understanding or to greater intellectual independence.
Formal mathematics is like spelling and grammar—a matter of the correct application of local rules. Meaningful mathematics is like journalism—it tells an interesting story. Unlike some journalism, the story has to be true. The best mathematics is like literature—it brings a story to life before your eyes and involves you in it, intellectually and emotionally.
when I was about to be married, my father challenged my wife-to-be to read What Is Mathematics. She did not get far, but she was accepted into the family nonetheless.
Mathematics links the abstract world of mental concepts to the real world of physical things without being located completely in either.
So what do you need to get a great deal of pleasure and insight from the book? According to Ian Stuart:
You do need a modest attention span, an interest in mathematics for its own sake, and enough background not to feel out of your depth. High-school algebra, basic calculus, and trigonometric functions are enough, although a bit of Euclidean geometry helps.
Yesterday, I read a news item and tweeted it:
“American students lag behind most other nations in math skills: Only children from Italy and Spain performed worse” http://bit.ly/1ax7tht