Modelling operations: Counting-based and collection-based approaches to computation

Abstract

This paper focuses on different ways of modelling operations in mathematics; namely, counting- based and collections-based models. The two models are examined in relation to the literature on diagramme literacy, as well as New Zealand's mathematics curriculum document. Implications for the Numeracy Development Project and the New Zealand Number Framework are also considered. The value of presenting collections- based models in addition to the (counting-based) empty number line models in materials for teachers is discussed. Splitting diagrammes are presented as a collections-based alternative to empty number line models.