Constructions in mathematics text – a crucial foundation in mathematics education

The researchers in the project aim to identify and describe typical building blocks in mathematics text, known as constructions, with both words and symbols. The results are expected to form the foundation for a transformed approach to mathematical education.

When we learn everyday language, we not only learn words and grammar but also the building blocks of language, known as constructions. For instance, we know how to interpret “25 kronor per kilo” as well as “one piece at a time.” We recognize the particular wording as a building block, a construction, with a specific meaning.

Within construction grammar, the focus is on identifying the constructions present in a language, as it provides a clear picture of what it means to master a language. Since symbols are essential in the specialized language of mathematics, many typical constructions in mathematics naturally include symbols.

We are all familiar with dictionaries that describe words, but a “constructicon”, which describes constructions in a similar way, is less known. A general Swedish constructicon is currently being developed, and the project team’s findings will contribute by identifying building blocks typical of mathematical language.

Constructions can range from fixed expressions to categories representing various words or symbols. Many of the most intriguing constructions consist of a combination of fixed words or symbols and general categories. An example of a construction, where general categories are capitalized, is [QUANTIFICATION of a FIGURE]. Instances of this construction in mathematical texts include “the volume of a sphere” or “the area of a trapezoid”.

In this project, researchers will identify typical constructions by processing large amounts of text. A limited selection of the identified constructions will also be analyzed in textbooks to describe their role and function in mathematics text.

Many relatively simple constructions are already known, such as technical terms and general ways of writing symbolic expressions in mathematics. What distinguishes these straightforward constructions is that they often consist only of words or only of symbols. By including symbols in the analysis of mathematics texts, the project team intends to ensure that constructions combining general categories of both words and symbols are also described. Computer-driven methods are required to identify constructions of this kind.

Surely it would be easier to learn a language if generalized patterns were presented rather than having to discover them independently from all individual instances?

The project’s findings are expected to contribute valuable empirical, theoretical and methodological knowledge. An important contribution will be made to mathematical education by providing reliable knowledge about central mathematical constructions. The understanding of constructions offers an entirely new foundation for teaching 
mathematics.