We present findings from a study that guided and examined the design of an instructional module that aims to nurture high school students’ understanding of the meaning of measurements in physics. The module engages students in learning how to measure and conduct “error analysis” within a project-based learning environment, in which they build and calibrate measurement devices for various physics quantities. The module was implemented and studied in the physics teacher education program at the Technion. The participants were in-service and preservice physics teachers. Employing a design-based research (DBR) methodology, curriculum design, implementation, and a study of learning were conducted in three iterative cycles: One course for pre-service physics teachers (N = 21) and two professional development courses for in-service physics teachers (N = 19, and N = 13). The research questions were: (1) What are the design principles that characterize the teaching module and how their development during the various iterations correspond with and addressed the difficulties that were brought into the open during each implementation? (2) What were the conceptual difficulties related to the understanding of the meaning and role of measurements in physics, which were revealed during the learning process? The findings demonstrate how the module foster meaningful discussions of key concepts. They also suggest that preservice and in-service teachers often do not understand and are unable to explain the rationale behind the technical procedures they are required to do when analyzing data in the laboratory. We found that students and teachers tend to focus on the difference between the measured value and the theoretical value (i.e., the measurement error) and ignore the confidence interval in which they can report the measurement result (i.e., the uncertainty of measurement). An analysis of popular instructional resources suggests that part of these difficulties stem from the way the conceptual aspects of measurements are discussed in school and at the university.