The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21) understand the concept of division. The data was collected over six…

This paper explores languages for communicating precise ideas within limited domains, which include mathematical notation and general purpose and high level computer programming languages. Low-level properties of such natural artificial languages are discussed, with emphasis on those in which names are chosen for concepts and symbols are chosen…