This article discusses the implications of sociopolitical and cultural challenges and complexity on educational leaders' use of strategic thinking skills in divided societies, using the case of Israel, a deeply divided society with a hegemonic Jewish ethno-national state and Bedouins -- a subculture of the minority Arabs. In the suggested model, we propose that, due to sociopolitical and cultural challenges, Bedouin school principals use 'systems thinking' skills as a holistic approach to coping with their complex environment. Jewish principals use the additional strategic skills of reflection and reframing. We provide the results of a preliminary empirical study, with 103 Bedouin and 67 Jewish principals, supporting our propositions. This article and its propositions open avenues for research into principals' perceptions in deeply divided contexts and contribute to cognitive characteristics of leadership by explaining the implications of specific contexts for strategic thinking.