This study proposes a framework for examining ways in which prospective teachers integrate mathematical knowledge acquired in advanced topics courses into explanatory knowledge for school teaching. Participants, all of whom had recently completed coursework in abstract algebra, were asked to explain concepts connected to the school mathematics curriculum, such as division by zero and even numbers. The analysis shows that students used three distinct explanatory strategies: "Abstract Mathematical Argument," "Analogy", and "Rules". Students experienced competition among and within strategies. Moreover, students often derived different conclusions using different strategies. When faced with this conflict, they felt compelled to choose a strategy and to draw a conclusion derived from applying that strategy, regardless of sense-making. Students' ability to integrate explanatory strategies appeared to depend on their possession of coherent mathematical meanings, suggesting that strategy integration is indicative of students' having a key developmental understanding of the underlying mathematical ideas.