Language and communication in curricula for mathematics education. The problem of disciplinarity versus discursivity

Mathematics education begins in language, it advances and stumbles because of language, and its outcomes are often assessed in language (Durkin, 1991:3)

The ‘nature’ of mathematics is closer to language than to science

On the relationship between the concepts of language, communication and disciplinarity

Tendencies from compatative studies of four national curricula

Key competencies/basic skills (related to language & communication)

What and where is 'disciplinarity'?

Challenges?

Key competencies/basic skills

Being able to express oneself orally in the mathematics subject means making up one's mind, asking questions, reasoning, arguing and explaining a process of thinking using mathematics. This also means talking about, communicating ideas and discussing and elaborating on problems and solution strategies with others.

Being able to express oneself in writing in the mathematics subject means solving problems by means of mathematics, describing a process of thinking and explaining discoveries and ideas; one makes drawings, sketches, figures, tables and graphs. Furthermore, mathematical symbols and the formal subject language are used.

Being able to read in the mathematics subject means interpreting and using texts with mathematical content and content from everyday life and working life. Such texts may include mathematical expressions, graphs, tables, symbols, formulas and logical reasoning.

Being able to do mathematics in the mathematics subject is, needless to say, the foundation of the mathematics subject. This involves problem solving and exploration, starting with practical day-to-day situations and mathematical problems. To manage this, pupils must be familiar with and master the arithmetic operations, have the ability to use varied strategies, make estimates and assess how reasonable the answers are.

Being able to use digital tools in the mathematics subject involves using these tools for games, exploration, visualisation and publication, and also involves learning how to use and assess digital aids for problem solving, simulation and modelling. It is also important to find information, analyse, process and present data with appropriate aids, and to be critical of sources, analyses and results. (LK06)

Mathematical competencies according to Niss (2003) (...)

(...) Handling mathematical symbols and formalisms such as

• decoding and interpreting symbolic and formal mathematical language, andunderstanding its relations to natural language;

• understanding the nature and rules of formal mathematical systems (both syntax and semantics);

• translating from natural language to formal/symbolic language• handling and manipulating statements and expressions containing symbols and

formulae.

(...) Communicating in, with, and about mathematics such as

• understanding others’ written, visual or oral ‘texts’, in a variety of linguistic registers, about matters having a mathematical content;

• expressing oneself, at different levels of theoretical and technical precision, in oral, visual or written form, about such matters (Niss, 2003:8-9).