The presentation/paper reports on mathematics and science teachers’ beliefs and concerns using inquiry-based strategies in their teaching. Two different surveys were conducted, one with 24 teachers to become future instructional leaders on Inquiry Based Learning (IBL), and one with 75 teachers as part of an international baseline study. The authors found that mathematics and science teachers in Norway would like to use more IBL strategies in their day-to-day teaching, and they were asking for more, and more relevant, continuous professional development courses with IBL as a focus. Textbooks were not seen as a hindrance to the use of IBL, but teachers wished for more IBL approaches to be used as tasks and examples. Although the curriculum, particularly in the natural sciences, did not represent an important constraint for its implementation, it would need to advocate IBL more explicitly. The results provide deeper insights into teacher concerns related to IBL, in particular the constraints they perceive to prevent them from working in such manners, and into potential ‘openings’ for working in IBL ways, both for more pupil engagement and deeper learning, as well as for the development of teacher professional knowledge in/for mathematics and science teaching.