The Role of Language in Teaching and Learning Mathematics

The purpose of this paper is to emphasize the role of language in the process of teaching and learning mathematics. We will begin with the definition of mathematics given by Cassiodorus (in its essential features repeated in Kolmogorov's famous article "Mathematics" from the "Great Soviet Encyclopedia" and explored in the author's book "Humanitarian oriented mathematics teaching in general school" (Ryazan, Ryazan Institute of Education Development, 2000, 112 p.). This definition illuminates the exceptional role of language in the building, discovering, understanding, teaching, and learning of mathematics. We show that this role is predetermined by the abstract character of mathematics. The abstract object cannot be shown; it can only be described with the help of language. This gives rise to the problem of identifying abstract entities on the grounds of their descriptions. We accentuate the way the language of set theory helps finding the solution to this problem. We illustrate this through the examples from elementary geometry and elementary algebra. And we especially underline the importance of this solution when working with events in the probability theory. After that, we are going to show how proof and language help to form and develop imagery thinking and, thereby, illuminate the possibility of the left brain hemisphere to participate in the formation of imagery thinking. Keywords: mathematics, teaching, and learning, language, imagery thinking, functional brain asymmetry