This article focuses on the challenges faced by educational leaders of international schools in conceptualising international mindedness. Further articles are planned which will focus on how the wider social and school context influence educational leaders' promotion of international mindedness, and on why educational leaders are drawn to values-leadership models in its promotion. The use of the term international mindedness has grown significantly over the last thirty years. It is now in common usage in many international schools (Hayden et al, 2015), and is used specifically by both the International Baccalaureate and the International Primary Curriculum to describe the core values that underpin the educational programmes they offer. It is a broad concept whose advocates claim it encapsulates the values and ideals of international education that seek to promote greater global understanding and awareness (Hill, 2014). However, the value and appropriateness of the term remain contested (Haywood, 2015; Savva and Stanfield, 2018).