The analogy in the English language arts would be to teach children to decode words so that they could read them without giving them any sense of what they mean. For example, what does "Splad the yuricles into the bundecloupus ando tpzig" mean? We can decode words in any language so that we can pronounce them but without knowing what those words mean it is pretty much a fruitless exercise. So in math, when we say "carry the one" or "invert and multiply" or six fours are twenty-four" without any sense of what these phrases actually mean we might just as well be using a foreign language or gobbledegook. By the way, David Pimm called this "teacher patter". The result of this is to develop dis-empowered learners. If we know something but don;t understand it there's not a whole lot we can do with it. If you know that pi is 3.14 and goes on for ever without recurring but have no idea what pi is then you can do little more than reply 3.14 when asked what pi is on a test.
If we teach math with understanding then learners are empowered to use the knowledge they are developing. If you understand that pi is the ratio between the circumference and diameter of a circle then you can apply this understanding to all kinds of situations involving round things. The advent of technology has significantly improved out ability to teach math with understanding as these Math Gifs my daughter Marie recently sent me show. Once you understand the visual/spatial relationships of a particular mathematical phenomenon it then becomes much easier to abstract or "mathematize" it through the use of a symbolic relationship such as an equation or set of symbols.