The current state of growing connectivity in society calls for a security mindset for K-12 and post-secondary (K-12+) populations. A security mindset offers an important approach to support security and can usefully be understood through the lens of complexity theory. Complexity theory also provides a helpful lens for identifying limitations inherent within some common pedagogical frameworks and practices in K-12+ education systems that may pose challenges for the cultivation of a security mindset. Hence, this paper brings awareness to examples of some of the most prominent pedagogical frameworks and practices that stand in potential misalignment with a security mindset when they are implemented in an imposing, monolithic manner. These include: rigid, prescriptive curricula; binary thinking, compliance, and standardized assessments; and disciplinary constraints. By identifying ways that common pedagogical practices stand to potentially undermine the cultivation of a security mindset, this paper contributes to clearing the way forward for K-12+ educational systems to design for emergence in support of building a more secure society.