The mathematicians concern themselves with doing mathematics at high level of abstraction. The mathematics educator concern themselves with what it is that one does when doing mathematics and what kind of experiences are propitious for a person’s later successes. - P. Thompson.
According to Thompson, the following quote is a paraphrase of what Winston Churchill said about mathematics and mathematics education.
There are mathematics educators who believe that mathematics and mathematics education are one and the same thing. Most mathematicians will hear none of this. But there are quite a number who now finds it part of their responsibility to educate as well.
As a mathematics educator, the most important part of teaching mathematics for me is to be able to provide learners with experiences to think mathematically and to develop their mathematical thinking habits even for those who would not be using hard-core mathematics in their lives. I believe that it should be one of every student’s inalienable rights – to learn to think mathematically. Sadly of course that most of the students, because of their traumatic experience with school mathematics, would rather go through life without math.