This article discusses the nature of the difficulty in learning and teaching elementary mathematics from the viewpoint of the psychology of learning, focusing on some key topics such as number operation and algebra and how children learn these concepts. The paper also seeks to examine the reasons why many topics in school mathematics seem difficult and to make the point that what is difficult can still be taught and learnt. What is required is often the coordination of a culturally developed sign system with an intuitive base. This coordination is a process that happens naturally and spontaneously if children are given opportunities and situations they find motivating.
