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Systems thinking (ST) skills are often the foundation of sustainability science curricula. Though ST skill sets are used as a basic approach to reasoning about complex environmental problems, there are gaps in our understanding regarding the best ways to promote and assess ST learning in classrooms. Since ST learning provides Science, Technology, Engineering, and Mathematics (STEM) students' important skills and awareness to participate in environmental problem-solving, addressing these gaps is an important STEM learning contribution. We have created guidelines for teaching and measuring ST skills derived from a hybrid of a literature review and through case study data collection. Our approach is based on semi-quantitative cognitive mapping techniques meant to support deep reasoning about the complexities of social-ecological issues. We begin by arguing that ST should be evaluated on a continuum of understanding rather than a binary of correct/incorrect or present/absent. We then suggest four fundamental dimensions of teaching and evaluating ST which include: (1) system structure, (2) system function, (3) identification of leverage points for change, and (4) trade-off analysis. Finally, we use a case study to show how these ideas can be assessed through cognitive maps to help students develop deep system understanding and the capacity to propose innovative solutions to sustainability problems.