Are people still teaching that mass increases as speed approaches c?

An interesting phenomenon around here... LOTS of people answering relativity questions referring to the increase of mass as speed approaches c.

This is an obsolete interpretation. In modern physics literature, the word "mass" always refers to rest mass. The variable M always refers to mass, which always refers to rest mass.

It's obsolete for very good reasons: you can't correctly calculate effects of gravity using "relativistic mass;" relativistic mass is not invarient, but rest mass is. Even if you're using it to illustrate changes of inertia, it's different in different directions: you'd have to give a particle a different mass for each of x,y, and z motions. Scalar, invarient mass becomes a noninvarient vector. Messy.

When you explain that bodies cannot travel at c by explaining that they get more and more massive, it easily misleads the asker into thinking that if they were to travel at c they would become fatter and fatter in their own reference frame, which is clearly untrue.