Linguistic considerations in the acquisition and teaching of mathematics

Abstract

One of the most natural phenomena observed in humans, the acquisition of language, and its relationship to the development of written or symbolic expression, inspire a Model for the Acquisition of Mathematics. The abundance of work concerning (academic) second language learning is particularly applicable to this model. The present paper will draw parallels between (academic) second language learning and the ways in which learners master mathematics, as they move from the concrete to symbolic stage of conceptualization.

Abstract language is often viewed as developing from the oral (concrete) through formal or written (symbolic) stages. The oral stage is characterized by informal learning within a given environment. Academic second language learning begins similarly (although it may be complemented or interfered with by aspects of the first language). We maintain that in like fashion, mathematics learning develops from the concrete stage to the symbolic stage. On the formal side of mathematical learning, care must be given to the timing of the introduction of corresponding symbolic means of expression, and technical vocabulary.

Integrating observations on the mastery of mathematics with findings in first and especially second language learning, the present paper will use familiar topics in mathematics to introduce a model for the successful acquisition of mathematics at any level of complexity.