Sorry for the weird words once in a while, my phone seems to second guess me once on a while.
Regarding the 2-track approach, I totally agree:
in the end mathematics has a huge marketing problem: it is "sold" the wrong way : it starts off with the excruciatingly boring stuff (trying to give people a "base") and only then tries real world problems.
People should be sold the other way around , find an interesting problem and then learn maths on a as needed basis .... check out Ricardo Semler and Lumiar (he has a TED. Com talk )