THE tragic failure of mathematics education in the United States is the absence of referents for the symbols that get shoved around by the seemingly mindless rules. A more concise way to say this is mathematics is taught as though the symbols refer to themselves rather than to quantities or processes. The Mathematician will scoff at me while the Physicist will applaud. In Physics, we deal with quantities; whereas in Mathematics, we deal with … uh … hmmm … rules and symbols! Yes! Rules and symbols.
I could drone on in writing here; but I think that it will be more efficient if you watch this quick little video that I made that proves that numbers do not add. Enjoy.