^ This is the best comment of all the various replies, as it directly addresses the actual content of the thread: it wasn't that "oh no I had to spend so much time learning the mathematical basis of computer programming and I just wanted to throw together a shopping cart in Ruby" it was "most of my time was wasted learning about the task I was given as the goal of the program--which happened to be math but could have been something inane like the physics of a roller-coaster--instead of about the meta-task of how to actually analyze, automate, or implement arbitrary tasks".

The problem is, people don’t learn well when they’re taught general things and are told to specialize on their own. People learn best from examples and then generalize using their general purpose jumping to conclusions machine called the brain.

I agree simple math problems may not be the best exercises to program, but the point is you should be doing a lot of such specific (but diverse) exercises to get the general idea.