Education systems worldwide are being challenged to re-examine the statistical and mathematical capabilities needed for an informed and critical citizenry, in light of disruptive phenomena such as global warming and climate change, migration, and pandemics. These phenomena are having a significant impact on the quality of life and wellbeing of citizens across the globe—and likely to continue to do so into the future. This article outlines the findings of a joint qualitative study in three countries (Brazil, Australia, South Africa) that focused on mathematics teacher autonomy during a time of disruption. The study draws on focus-group interviews with teachers regarding perceptions of enacting changes in content (what) and methods (how) they were teaching in response to the new mathematical and statistical demands associated with the COVID-19 pandemic crisis. The results contribute to new knowledge by highlighting the complex nature of teacher autonomy via a mapping of eight enabling and inhibiting influences affecting perceived situational freedom, at four levels: Classroom (curriculum demands; students’ knowledge), School (school leadership; time pressure), Profession (teacher self-efficacy; perceived responsibility for change), and External influences (from outside the school system, e.g., pandemic effect on students, parents, community; politicized sensitivities). Each influence was found to act in a dual fashion as both an enabler and inhibitor in relation to teacher autonomy. The discussion and conclusions reflect on implications for theory and practice, and point to directions for educational systems that can support the autonomy that teachers need to make changes when responding to (future) disruptions.