The concept of globalisation stands for a variety of discourses. Although globalisation has been impacting on education, it has been rarely problemitised and researched in mathematics education. This paper presents an analysis of a discussion held with a number of mathematics educators from Brazil. It is one of a series of such conversations being held with groups of leading educators in South America, South-East Asia and Australia concerning their perceptions of the impacts of globalisation on their professional lives, and on mathematics education in their country and region. The analysis shows that these mathematics educators understand globalisation in terms of two differing discourses of economic colonialism but also in terms of the awareness of the world as one. It will be demonstrated that the different discourses will yield different moral stands one can take on the issue of globalisation. The paper argues that the constructs of the local and the global can not be posited as dichotomies if we were to understand the complexity of identity formations in late modernity. Lastly, this paper discusses new narratives on the role of the Internet in the globalisation of mathematics education.