This paper describes the evolution of "recognition of need for data" and "strategical thinking", two types of thinking identified by Wild and Pfannkuch in their Framework for Statistical Thinking in Empirical Enquiry, as well as its relevance for math teacher professional development. The research was carried out with ten in-service secondary-school math teachers during an educational experience (at Bogotá, Colombia), who, in the beginning, showed high performance in procedural knowledge of data analysis. The experience was founded on project-based learning that participants proposed and conducted via a survey concerning implications of a Bill, relevant for their job context. These teachers made mistakes and showed difficulties during the two first stages of the investigative cycle, problem formulation, and research planning, due possibly to their inexperience in designing an empirical inquiry. Teacher educator's guidance, to turn mistakes into learning opportunities and teachers' active participation, promoted the development of statistical thinking, especially linked to the types aforementioned.