Mathematics education studies have shown that part of learning mathematics is learning its language. The language of mathematics is said to include specialised terms and ordinary language terms that have contextual meanings in mathematics. Considering the fact that learners in South Africa are performing poorly in mathematics in the international comparative studies, e.g. TIMSS, there was a need to investigate how teachers facilitate second language learners’ access to the meaning of mathematical terms in multilingual classrooms in South Africa. This study investigated a teacher’s practices in the facilitation of learner access to mathematical terminology in a Grade 11 multilingual class in a township school in Vosloorus, South Africa. The study employed a qualitative approach in investigating Discourse practices that the teacher used to define mathematical terms to second language learners in a multilingual classroom. Direct classroom observations and a teacher interview were the main data gathering methods. The main findings were that the teacher used a combination of interactive practices that involved group work, telling, individual student interactions and initiation, response and evaluation methods. Among definition teaching strategies used were the textbook procedural definition and the textbook descriptive definitions. The chalkboard and the textbook were the main artefacts of the Definition Discourse. The study concludes that the Definition Discourse of the multilingual classroom is a process that involves not only the definition of terms but also an integration of teaching methods and interactive practices where definitions of mathematical terms can be taught even through the eliciting of procedural methods of working out mathematical problems.

The aim of the study is to perform a linguistic analysis of mathematics textbooks. Mathematical text exercises are built up of linguistic structures which are significant for the pupil’s understanding of text exercises. Two different mathematics textbooks for grade three are analysed: Prima matematikand Tummen upp. The aim is to investigate how text exercises in mathematics textbooks are linguistically structured. The study analyses the style, form and content of the text and its relation to the reader. The result shows that the content of the text exercises is close to the pupil’s everyday reality, which ensures a close and strong relationship between the writer and the reader. Something which can entail difficulties for reading comprehension, however, is that the form consists of meaning-bearing mathematical terms which it can be difficult to relate to. Since the mathematical language and the everyday Swedish language meet in text exercises, it is important that they interact well with each other.

This diploma thesis is focused on study of cognitive and communicative phenomena, which appear at solving exercises in semantic and arithmetic environment First-Grade Students' Stepping. These phenomena are revealed by a set of quantitative analysis experiments undertaken with first-grade pupils. Theoretical basis, which make the description of revealed phenomena possible, are generic model theory and semantic embedding of number (Hejný), procept theory (Gray and Tall), mathematical schema building theory (Hejný) and didactic constructivism, structural and semantic conception of number, process, concept, procept.