there were zealots then who believed that if you understood these sorts of mathematical derivations and used language correctly, then you would be more skillful. They neglected to realize that not only does skill require practice, but skill also requires flexibility,a quality that the mathematical derivations and precision of language do not convey. Imagine taking the seven different ways of multiplying fractions given in the previous section and subjecting each of them to careful mathematical analysis as was done earlier. Few would want to do this.