"To teach is to learn twice" - Joseph Joubert
This quote from Joseph Joubert is the best I have seen about learning and about teaching at the same time. I don't think you can really separate the two. If I want to really and truly understand and know something, teaching it is the fastest and most effective way. There is something about trying to help others understand that causes the teacher to have to know more, and not just more, but more in more depth as if you were looking at something from many different angles.
As I teach, I learn more about the subject and more about teaching and more about myself. I cannot teach and not be learning at the same time.
If you want to see how well you know something, try teaching it. Go ahead. You may very well find that you don't know it nearly as well as you thought, yet in trying to teach it, you have automatically risen to a new level of understanding. Great. Now, teach it some more. You will find after a short time that you now have a far greater knowledge and understanding of the subject and that you know it from a number of different perspectives. You will also find it to be the best learning experience.