The article wasn't pointless at all. He's saying that a conceptual understanding is important, but so are things like flashcards. I know growing up my ability to quickly do simple math and recognizing patterns quickly always helped me speed along quickly.
The problem is that unless you are also able to approach things like a constructivist, you will end up with a bunch of disjoint facts. I think that most people just don't understand math well enough to understand this key. The more math I know, the more I wish I hadn't memorized anything, but derived more things. There are many cases these days that I will have to go back and derive an equation for the first time because I was never taught the equation.
Her department is "Industrial & Systems Engineering", she doesn't need to know much more math than how to do arithmetic and a Chai squared. Not that I know more math than she does, it's just not a true part of the mathematical disciplines. She and I probably both just use the tools handed to us and don't understand the beauty or the ugliness. One of the big problems with math today is that nobody understands that arithmetic isn't math. It would be like a baseball player being called a woodworker because she used a wooden bat.
