On the Nature of Algebraic Language

Source abstract

Among the practical aims of mathematical instruction recommended by the National Committee we find the following: “An understanding of the language of algebra and the ability to use the language intelligently in the expression of simple quantitative relations; appreciation of the significance of formulas and ability to use this language intelligently.” The ability to understand a language and use it as a means of expression is indeed very important, and in the educational process specific provisions have been made for its development. The person who is equipped with this ability is in a position to use it as a study tool, and the more abilities one has acquired in understanding different languages the better prepared is he to engage in extensive studies effectively. But is the language of algebra really a language, and is the understanding and intelligent use of it analogous to the understanding and use of an ordinary language?