The authors assessed five commonly perceived barriers to increased use of conceptual teaching in mathematics in the United States related to teacher autonomy, trade-offs with computational strategies, student achievement, class size, and teacher qualifications. These barriers were examined through the use of data from nationally representative samples of eighth-grade mathematics classrooms across 38 nations that took part in the Third International Mathematics and Science Study in 1999 and follow-up analyses involving data from the high-achieving nations of Japan and Singapore. Findings suggest that most of these perceived barriers are not impediments to the use of conceptual teaching strategies in other countries, and the comparative findings hold promise for alternative paradigms for organizing better mathematics instruction in the United States. (Contains 10 notes, 3 tables, and 3 figures.)