This article focuses on elementary school teachers' preferences for mathematically based (MB) and practically based (PB) explanations. Using the context of even and odd numbers, it explores the types of explanations teachers generate on their own as well as the types of explanations they prefer after reviewing various explanations. It also investigates the basis for these preferences. Results show that teacher-generated explanations include more MB explanations than PB explanations. However, many still choose to use mostly PB explanations in their classrooms, believing that these explanations will be most convincing to their students. The implications for teacher education are discussed.