We use Python in several courses. It's great ecosystem which offers algebra/numerics/visualization/statistica/machine learning/optimization methods within various modules. And it is continuously growing...
We used MATLAB before, and the switch was great decision! Surprisingly, students accepts Python better then MATLAB!
I teach introductory quantitative methods in social sciences using R. I have been using Rcmdr (R Commander) for around 4 years with very good results. Students who have never seen SPSS do not complain, because the Rcmdr seems intuitive and easy to use. Those who have been spoiled by SPSS point-and-click-without-thinking-too-much procedures sometimes complain.
But I guess, each one of us will need to choose whatever makes him/her comfortable at first place
Dear @Gustavo, this is a very good thread to share experience about teaching numerical methods. I used the socalled computer algebra systems like Mathematica, Matlab, and Maple and think that they offer interesting insight the material in numerical analysis courses. For computer graphics courses, more specialized Softwares are needed.
Currently, I use SPSS only because it is what most of the other faculty use. If their students learn the same program, they can more easily work together. To be honest, I hate it. It's limited and gets more limited each year. I have used MYSTAT (the free version of SYSTAT) in lower-level statistics courses because it is free and similar to SPSS. However, it too has limitations.
I would recommend Matlab if your university has the licenses, but, if you want a free tool, the best one, in my opinion, is Scilab. I believe R is a good alternative too, but R is less matrix-oriented and more statistical-oriented, so, it depends on which kind of numerical methods you're teaching.
You could use python, or even FORTRAN, but, probably, you will lose more time teaching programming than numerical algorithms
Since a long time, I use SPSS for all computations and statistical tests. I started to utilize AMOS fro structural equation modeling since three years only.
I've used SAS when I've taught in the past, mostly because of my own familiarity. R seems a little more difficult to me, at least in terms of reading in data, etc., although I know many people like it. I'd probably make more of an effort to learn it if I weren't a long-time SAS user.