In the pre-calculus course I teach, two of the topics we cover are basic matrix operations (useful for solving systems of equations and later for determining the cross-product of two vectors) and linear programming (useful as a review of graphing linear inequalities, and then throwing a little something new on top).
The current masters course I'm taking is Discrete Optimization, and early on one of the things we've done is to describe linear programming problems with matrices. Wow, combining two of the things I teach into a single difficult problem, what could be more fun?!
I thought it might be interesting to show my students just how to use matrices to write the constraints of a linear programming problem, but after the "deer in the headlights" looks I was getting today when discussing linear programming without matrices I think I'll just keep that little bit of excitement to myself.
I'm pursuing this particular masters program, which will take me 5 years, rather than a 10 month generic masters in education from a diploma mill, because I want to learn more math and become a better math teacher. I've already moved forward towards both of those goals. The problem is that I get so excited about some of the things I learn that I want to share them with my students, who are nowhere near ready to hear or see that level of math. Even when it's appropriate to what we're doing in class, the background knowledge just isn't there to make the information accessible to students. I fear it might intimidate them unnecessarily and I have no interest in doing that.
So I get to enjoy those little connections all by myself. And sometimes I share them with other teachers.