The importance of interplay between mathematical forms of expression for students learning of number sense

Number sense refers to an understanding of, and the ability to use, numbers and arithmetic operations. Meaningful knowledge of numbers and arithmetic operations requires different forms of expressions, such as symbols, words, and images. For example, in subtraction, there is an interplay between symbols (4–3), words (decrease), and images (such as illustrations on number lines). We know that students find it difficult to deal with different forms of expressions in mathematics, but there is limited research focusing on the interplay between different forms of expression in relation to number sense.

The purpose of the project is therefore to clarify the role of the interplay between different forms of expressions in students’ learning processes related to number sense. This is addressed through the following research questions:

(1) How can key aspects of number sense at different educational levels be made explicit through different types of interplay between forms of representation?

(2) How is students’ understanding of key aspects of number sense affected by different types of interplay between forms of representation?

The project aims to develop design principles for how teaching at different educational levels can be structured to support students’ learning of number sense. Different types of interplay between forms of expressions provide a basis for specifying such design principles, particularly with regard to how teaching materials can be designed and used to support students’ learning processes.

The project is conducted in collaboration with Örnsköldsvik municipality and is linked to one of the municipality’s priority areas concerning the progression of number sense. By developing design principles for teaching number sense, the project can generate findings that address the municipality’s question of how teachers can build a solid foundation for students’ number sense. Progression is investigated by studying teaching and learning over the course of a full academic year in classes from several different grades.