The article discusses a policy enacted by an elementary school in the US stating that in order to continue to the next grade students must fluently recite or calculate based on rote memorization. There is a ubiquitous tweet from Jo Boaler (mathematics educator and author) lamenting this school's policy. Check out the replies for some interesting argument and discussion.
Mathematics is much larger than simple computation and rote memorization. As the example in the article says, if you just multiply 2 x 2 you should yield 4, but that is only in the Base-10 number system. For a Base-2 number system, same computation has an output is 11. So we really need to train our youth to understand the origin of this content so they can build on it and recognize whatever patterns come out.
Mathematics is the science of patterns. Analyzing weather patterns; looking at increasing tile patterns; and more. Keith Devlin wrote an interesting introduction to his mathematics course coming up in Fall 2015 that elicits some light on this subject as well as the history of mathematics overall. In it he describes the origin of certain pieces of mathematics and how important it is to know where it comes from so that we can use it better. I hope I am able to teach my students the same way.