Darren

I like to focus on the trends that run throughout mathematics. Showing these to students is one of my great joys. This also grants great efficiency to students, instead of learning whole new concepts. The ability to re-use residual knowledge from other areas of mathematics and adapt them to suit, is a win-win as previous knowledge is now re-enforced and a new concepts can now be dealt with from a familiar and stable foundation.
I like to think of Mathematics as a Language. To expand this analogy I like to minimize time spent reading through the dictionary and remembering definitions of words, but to have natural conversations through mathematics.
Conversing through the language of mathematics truly is a wonderful thing. Languages other than mathematics, (like the one you are reading here) they suffer from the problem of ambiguity and imprecision.
The language of mathematics great advantage is to be completely devoid of any ambiguity or imprecision. Granted the goal of elimination of all ambiguity is often impractical in mathematics (take for example a whole book dedicated to proving one plus one is indeed two) and it is often seemed to be practical for teachers or students alike to gloss over any such ambiguity or imprecision, but as we all know, (or ought to have known) as with glossing over ill-prepared surfaces in painting. We find the paint will flake, so without clearing all ambiguity in the infancy of learning the language of mathematics. We find that as with the paint not adhering to the ill-prepared surface. The time spent practicing mathematics without routing all ambiguity and imprecision is time spent ill-efficiently.