In an attempt to address shortcomings revealed in international assessments and lamented in legislation, many schools are reducing or eliminating elective courses, applying the rationale that replacing "non-essential" subjects with core subjects, such as mathematics and language arts, will better position students in the global market. However, there is evidence that systematically pairing a core subject with another, complementary subject, may lead to greater overall learning in both subjects. In this paper, we analyze two subject area pairs--first and second language, and computer programming and mathematics--to demonstrate in what ways two subjects might complement each other. We then analyze the relationships between these pairs to better understand the principles and conditions that encourage what we call "convergent cognition," the synergistic effect that occurs when a learner studies two complementary subjects.