Higher order thinking skills are prominent as curricular goals internationally, but creating the conditions conducive to their occurrence remains a challenge for teachers of mathematics. We report teachers’ attempts to develop higher-order thinking in classrooms in six countries: China, Japan, Sweden, Singapore, Australia and the U.S.A. Data from the Learner’s Perspective Study (LPS) (Clarke, 2006) was used to study lesson sequences in geographically and culturally diverse classroom settings, where multi-camera video documentation of classroom practice was supplemented by post-lesson video-stimulated interviews with teacher and students. In each identified attempt to promote higher-order thinking, we examined the tasks employed, the associated mathematical activity (action), and related these to the creation of conditions conducive to higher-order thinking. Conditions that appeared essential for the promotion of higher order thinking involved: The lesson goal (intention): Teacher questionnaire responses revealed a common commitment to the development of higher order thinking skills. The mathematical task (action): Mathematical tasks were carefully chosen to lead to a legitimate abstraction. The modeling of critical reasoning and meta-cognition (disposition): Student mathematical activity associated with student reflection and metacognition was highlighted by the teacher as desirable. In combination, these elements created a classroom environment that promoted higher-order thinking.