This study explored the teaching and learning beliefs of qualified (in-field) secondary science teachers who were teaching mathematics out-of-field that is, without qualification. The relationship between secondary teachers' beliefs about their in-field subject--science and their out-of-field subject--mathematics was examined. The theory of boundary crossing and frameworks of beliefs about science and mathematics teaching and learning were used to explore continuities of beliefs when crossing disciplinary boundaries to teach mathematics out-of-field. Individual semi-structured interviews and video-stimulated interviews were used to collect data about teachers' beliefs and teaching practice for science and mathematics. Continuity of beliefs across science and mathematics was more likely when teachers held traditional beliefs about science. Continuity of non-traditional beliefs about learning and teaching science and mathematics was less likely, though some teachers did show evidence of beginning to adopt, or exhibit a desire to learn more about, constructivist approaches to teaching mathematics.