The Readability of Mathematics Textbooks Revisited

Abstract

All mathematics textbooks are written in more than one language. Each contains portions in a natural language, such as English, together with portions in one or more additional languages, such as HinduArabic numeration, various algebraic notational systems, the language of the sentential calculus, and the like. The mix of these languages varies greatly from book to book, topic to topic, and level to level. The natural language component often is replete with translations from one of the other symbol systems. For example, phrases such as if and only if, if … then, A and B are direct translations from the sentential calculus. Their precise meanings must be comprehended by the reader before he can hope to assign the author's intended meaning to the passage in which they occur.