SEMANTIC UNDER-LOADING: THE LESSON OF LOGS

The semantics of some of the most fundamental elements of arithmetic and algebra, rather than either modes of learning or teaching, or the conceptual complexity of the elements themselves, may be barriers to understanding. In the treatment of logarithms there is an over-supply and under-use of terms that describe the same concept. Power, index and exponent supposedly are synonyms and are invoked when logarithms are defined. There are supposedly distinct theories, "The Rules of Exponents " and "The Laws of Logs". Questions on logarithms in algebra are unpopular, although understanding the nature of logarithms does not seem to be a prerequisite for applying logarithms to numerical problems. Nonetheless the mystification that arises from poorly specified and "under-loaded " symbols in the theoretical treatment of logarithms must result in a disheartening loss of understanding. Students ’ difficulties with the semantics of elementary mathematics need to be acknowledged where possible and remedies sought, at undergraduate level if necessary. To this end a case is made for abandoning the term logarithm, despite its longevity, and for rationalising the terminology in the area of powers and exponents