Programming is an Art
And we need to start teaching it like one. Programming is related to mathematics, sure, but so is everything. Painters either intrinsically or explicitly use color theory, which is mathematics. Sculptors have to know the structural tolerances of their medium, or their sculpture will fall apart. Music just is mathematics, with the emotion added back in.
And programming is similar. We have reached a day and age where you can be an honest to goodness programmer with a limited understanding of quantitative reasoning. I should know; the last sixteen years of my career were spent writing code. You no longer need to know how to bit shift to write a website. Boolean logic is important, but it can be taught linguistically instead of arithmetically. Some people respond better to word-logic than number-logic.
This doesn't mean I think we should get rid of deeply algorithmic computer science; we most certainly shouldn't. People who can think in algorithms are advancing what our machines can do, and are moving the boundaries back on every form of innovation.