This study investigated elements of pedagogical knowledge when students’ higher order thinking was an explicit and focused instructional goal. The findings suggest a model that consists of 6 elements. It seems that, for all these elements, the source of differences between teachers’ various pedagogies may be tracked to the basic distinction between a traditional transmission-of-knowledge approach to instruction versus a reform oriented constructivist approach. The findings portray how these two pedagogies are played out when higher order thinking is viewed as a distinct educational goal. Appropriate activities are insufficient for students’ active thinking. In the absence of adequate pedagogies, teachers adopt algorithmic approaches for teaching thinking that decrease the cognitive demands of tasks. Practical recommendations are discussed.