We had a thread about this topic several months ago, and it turned into a rather heated debate.
Here is the way that I think of dots:
***A "normal" note divides into 2 of the next smaller note value. A dotted note divides into 3 of the next smaller note value. So...for example...a "normal" quarter note divides into 2 eighth notes. A dotted quarter note divides into 3 eighth notes.***
To me, this way of thinking is SO much easier than "A dot adds half the value" or "A dot increases the value by 50%" or any of the other ways that the concept is sometimes worded. These various ways of wording it are mathematically correct, but they are much more difficult for many people to understand and remember. PLUS, perhaps more importantly, the way that I have explained it above is rooted in the historical origins of music notation. I have done quite a bit of research on this. Here is a link to one small example of my findings on the subject:
http://en.wikipedia.org/wiki/Mensural_notation
In case you don't want to read the whole article, here is an excerpt that is particularly relevant:
"In order to avoid remaining ambiguities, a separator dot (tractulus) was introduced to make clear which notes were supposed to form a triplex group together. It could be placed between a long and a breve to enforce perfect (triplex) value on the former when the latter would otherwise have imperfected it (signum perfectionis)."
As many of you probably know, "perfect" refers to things that are grouped or divided into 3's, while "imperfect" refers to things that are grouped or divided into 2's. So, you see...the idea of a dot indicating 3 is rooted in the ancient origins of music notation. And it is SO easy to grasp! I truly wish my first teacher had explained it that way to me. Instead, he told me "A dot increases the value of a note by 50%"...and I was confused for about a decade. Thankfully, my own research led me to the historical roots and this other way of looking at it.