‘Infinity-based thinking’ in the primary classroom: a case for its inclusion in the curriculum

Abstract

In this paper, we list some of the areas of the Australian curriculum that have links with the concept of infinity. We do this in order to promote a discussion about what aspects of infinity should become familiar to primary teachers. From our viewpoint, infinity has connections with Algebra, Art, Geometry and Measurement, Probability, Science and Technology and is an essential ingredient in the teaching of mathematics in primary school. This work was first motivated by the concern that for many young children, infinity appears to be mysterious and mythical (see Pehkonen and Hannula 2006 based on a survey of 300 students aged from 11 to 14 years old), but there is no reason why this should be the case. Then, as we looked further into the curriculum, we saw that infinity was closely linked to many areas of both the primary and secondary curriculum and that an understanding of the concept of infinity could improve students’ learning in a number of topics. We organise the paper by first considering the nature of infinity. In the four sections following infinity, we note that there are important parts of curriculum mathematics that are fundamentally affected by infinity in some way. In these sections, we discuss places where infinity and the collateral concept of convergence are critical for certain aspects of Geometry, Number (decimals and measurement), Algebra and Probability. These are followed by a discussion of the relevance of these to teaching and what understanding of infinity in these concepts might be worthwhile for teachers to know in order to help their students’ search for knowledge and to gain a deeper understanding of specific topics in the curriculum.