[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] Research in physics education has contributed substantively to improvements in the learning and teaching of university physics by informing the development of research-based instructional materials for physics courses. Reports on the design of these materials have tended to focus on overall improvements in student performance, while the role of theory in informing the development, refinement, and assessment of the materials is often not clearly articulated. In this article, we illustrate how dual-process theories of reasoning and decision making have guided the ongoing development, testing, and analysis of an instructional intervention, implemented at three different institutions, designed to build consistency in student reasoning about the application of Newton's 2nd law to objects at rest. By employing constructs from cognitive science associated with dual-process theories of reasoning (such as mindware and cognitive reflection), we were able not only to examine the overall improvement in student performance but also to investigate the impact of the intervention on two aspects of productive reasoning--mindware and cognitive reflection. Our analysis showed that the intervention strengthened students' mindware such that students were able to apply it as a criterion while checking the validity of their intuitive responses. Moreover, logistic regression revealed that the success of our intervention was mediated by the students' cognitive reflection skills. Indeed, for students with comparable mindware, those who demonstrated a weaker tendency toward cognitive reflection were less likely to initiate conflict detection and therefore never had the opportunity to utilize their mindware. We believe that this kind of integrated, theory-driven approach to intervention design and testing represents an important first step in efforts to both account for and leverage domain-general reasoning phenomena in the learning and teaching of physics.