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.

在本文中，我们列出了澳大利亚课程中与无限概念有关的一些领域。我们这样做是为了促进关于无限的哪些方面应该让小学教师熟悉的讨论。在我们看来，无穷大与代数、艺术、几何与测量、概率、科学和技术有关，是小学数学教学中必不可少的组成部分。

这项工作的最初动机是担心对许多年幼的孩子来说，无穷大似乎是神秘的（参见 Pehkonen 和 Hannula，2006 年基于对 11 至 14 岁的 300 名学生的调查），但没有理由认为这是应该是这样。然后，当我们进一步研究课程时，我们发现无限与小学和中学课程的许多领域密切相关，并且理解无限的概念可以提高学生在许多主题上的学习。

我们首先考虑无穷大的性质来组织这篇论文。在无穷大之后的四个部分中，我们注意到课程数学的一些重要部分在某种程度上从根本上受到了无穷大的影响。在这些部分中，我们将讨论无穷大和收敛的附带概念对于几何、数（小数和测量）、代数和概率的某些方面至关重要的地方。随后讨论了这些与教学的相关性，以及教师可能需要了解这些概念中对无穷大的哪些理解，以帮助学生寻找知识并更深入地了解课程中的特定主题.