This is a slight tangent because it is about mechanical computational skills rather than formulas, but the idea is the same. I am currently teaching a bunch of

This is a slight tangent because it is about mechanical computational skills rather than formulas, but the idea is the same. I am currently teaching a bunch of very bright graduate students from a number of countries. On the most recent midterm, students from countries that force people to learn to compute and learn some formulas finished in an hour, while US students and some others took two. US students in particular were caught up on figuring out the solution to x+y+z=1, x=y+z, y=4z. Just impossible. US students in my class are wasting time on mechanical calculations rather than understanding the meanings of the theorems they illustrate, because they have weak computational skills. I can't write problems that are computationally easy enough. They are unable to apply their much-vaunted "creativity" and "critical thinking" because even once they Google a formula they can't carry out meaningful work with it. I can Google how to use a hammer and a table saw, but I'll produce a crappier table than the person who has so much practice she can use them without thinking. That person can think about the final design while I think about not hitting my thumb or slicing off a digit. The argument about knowing how and when to apply formulas misses the fact that practice in applying those formulas is essential to competence.