This paper reviews the research on mathematics teacher education and mathematics education reform to provide a possible foundation for educating mathematics teachers in rural Appalachia. The paper takes the position that teacher change has certain characteristics and impediments that are not limited to any particular circumstance. Research on elementary mathematics teachers in various countries reveals teacher misconceptions and lack of knowledge about mathematics, their difficulty in appreciating its connectedness, and their beliefs about mathematics as a frightening subject. Research on secondary mathematics teachers suggests that secondary teachers' beliefs about mathematics and the intensity of their beliefs impede reform efforts. Commonalities found in research into preservice and inservice teacher education focus on difficulties teachers have in knowing mathematics, knowing about mathematics, and knowing about the teaching of mathematics. From these commonalities, three principles are identified for teaching mathematics to preservice teachers: that preservice teachers should experience mathematics as a pluralistic subject, should explicitly study and reflect on school mathematics, and should experience mathematics in ways that support the development of process-oriented teaching styles. Barriers to school improvement in rural areas are discussed, followed by implications of the rural circumstance for improved teaching/learning of mathematics and improved training of rural mathematics teachers. (Contains 60 references.) (SV)