The idea that the educational needs of secondary school students are best met by providing them with learning experiences that are both intellectually challenging and connected to the world beyond the classroom underpins several recent pedagogical initiatives in Australia. However, such learning experiences are rarely found in practice. Many reasons for this have already been identified, but we suggest there may be another dimension to this problem. From our experience of trialling a similar pedagogical approach with Years 8 and 10 students, the participating teachers seemed to be struggling with a conceptual dilemma that interfered with creating learning experiences that are both intellectually challenging and relevant. We suggest this dilemma was generated by a dualistic framework of thinking and practice, endemic in education systems, which constructs academic rigour and relevance as incompatible with each other. We conclude that there is a need for more extensive teacher professional development in pedagogies which attempt to integrate intellectual rigour and relevance. (Contains 1 table.)