In relation to an international concern to encourage inquiry-based pedagogies in Science Technology, Engineering and Mathematics (STEM) subjects and the issues of transfer in teacher professional development (PD), we report on the aspirations and perceived challenges of teachers in Qatar as they embark on PD to introduce inquiry-based learning into their mathematics and science classrooms. Data from initial interviews with eighteen teachers, with Grades 4 to 8 mathematics and science classes, were analysed in relation to challenge factors from inside and beyond their classrooms. The findings are used to provoke our awareness and understanding of the issues of shifting pedagogies that might arise during PD programmes.