Despite the incorporation of mathematical modelling in the Singapore mathematics curriculum framework since 2007, Singapore teachers still face readiness issues concerning the use of open-ended real-world problems. This paper presents some preliminary findings from an exploratory study undertaken within a professional development programme on mathematical modelling for experienced secondary mathematics teachers who are tasked to lead their schools in mathematical modelling. The research aims to gain insights into teachers' efforts at designing and assessing modelling activities, and their perceptions about facilitation challenges, for the purpose of proposing future directions in professional development towards more sustained, concerted efforts at incorporating mathematical modelling in Singapore schools.