Unpacking Primary Teachers’ Initial Knowledge of Realistic Mathematics Education: A Case of Iceberg Model of Fraction Division

Abstract

Iceberg model of realistic mathematics education (RME) is known as a metaphor to illustrate how informal, pre-formal, and formal mathematical models and strategies are used by students to develop a "floating capacity" for the understanding of formal representations of mathematics. This is a survey study that explores Indonesian primary teachers' initial knowledge of RME through iceberg model created for learning fraction division in primary classrooms. A total of forty-five elementary school teachers in Sidoarjo, Indonesia worked on a questionnaire about creating an RME iceberg in the initial agenda of teacher professional training. The created iceberg models were analysed based on the extent to which the learning stages meet the admitted learning trajectory of fraction division in RME. Results indicate the iceberg models created by the primary teachers tend to illustrate the skeleton of learning stages in formal mathematics, instead of pre-formal mathematics. Most of the teacher participants concern with providing a learning experience on the formal operation of fraction division at the beginning of learning stages followed by contextual learning experience, which is inversely related to the standard model of iceberg in RME.