Research project The subject of mathematics is characterized by a precise language where figures and mathematical symbols play an important role in the written discourse. Since learning mathematics involves both interpreting and using the language of mathematics, it is necessary to understand its typical features. This project identifies such conventional expressions in mathematics, referred to as constructions, and examines their form and function in mathematical texts.
Constructions in natural language are well-known in linguistics. This project examines constructions in mathematical texts, including their symbolic language. An example of a construction in mathematics is the way specific objects are referred to, such as “the angle α” or “the function f(x)”. We first identifiy constructions using a computerised method. A selection of these constructions is then analysed in textbooks with regard to their form and function. The aim is to contribute knowledge about constructions relevant to linguistics, mathematics, and teaching.
Lexicons and grammar describe the components and structure of language, but we do not learn a language as a word list and a grammatical rule system. Instead, we learn different languages as linguistic patterns stored in memory. These linguistic patterns are called constructions. Constructions in mathematical texts have so far been described to a very limited extent, and this is where the project aims to contribute. Some well-known constructions in mathematical texts have already been documented, such as [NUMBER + NUMBER = NUMBER], but these constructions are so familiar that they are not of interest from a mathematics education perspective. Instead, the project seeks to identify unknown constructions, in the sense that they have not previously been highlighted. This exploratory aspect of the project makes it both exciting and uncertain. However, we are convinced that mathematical texts are full of constructions where verbal language and symbolic language are used in mathematics-specific ways, just waiting to be discovered and incorporated into language-focused subject teaching.
The project begins with the iterative identification of constructions and examples of how these appear in teaching materials. A construction may consist of one or more words and mathematical symbols. There is also large variation in how many examples exist for a particular construction, as the components of a construction may be either fixed, such as ‘the angle’ and ‘+’, or categories, such as ‘noun’ and ‘operator’.
In the later stages of the project, we investigate and describe the use of a selection of important constructions in mathematical texts. Teachers will likely recognize these didactically significant constructions as typical of the language of mathematics. However, to design effective teaching about constructions in mathematical texts, detailed descriptions of how such constructions are used are required.
A presentation of the project can also be found at the funders webpage: https://maw.wallenberg.org/konstruktioner-i-matematiktext-en-viktig-grund-i-matematik-undervisningen
