There seems to be two schools of thought when it comes to teaching numerics. You either teach how to effectively implement the algorithms or you teach how to effectively select and apply the algorithms. It seems to be tied to if the computational science department comes out of the Computer or Math department.

I'm personally of the opinion that knowing how to select and apply the right algorithm is far more important to learn for undergraduates. Implementing numerical algorithms correctly and efficiently is serious high level PhD territory, and if you're not going to learn how to do it right you're much better off not doing it at all and leaving it to the experts.