This year I have been teaching maths course to liberal arts and linguistics students. My practice is: tell them what maths appears in our everyday life -- tell them the *.mp3 and *.jpg files in computer are actually using the idea of function approximation; tell them the varietyvarious application of maths in contemporary information technology field such as the self-error-correcting-code system, the Code-Dividing-Multiple-Address cellphone technology, etc.
When the students know maths is around themselves, not just laying in the textbook, their interstinterest will automatically come out. Even they cannot understand the logic and the principle finnally, they at least get an impression that maths is very useful in modern technologies.