This study uses the 2011 Trends in International Mathematics and Science Study to investigate the relationships among students' and teachers' computer use, and eighth-grade students' mathematical reasoning in three high-achieving nations: Finland, Chinese Taipei, and Singapore. The study found a significant negative relationship in all three countries between out-of-school computer usage of eighth-grade students and their mathematics reasoning scores. The study points to the fact that computer use out of school does not improve students' development of mathematics reasoning across the three contexts. Additionally, the more teachers had students use computer technology for higher-order thinking skills, such as for processing and analyzing data, the higher their mathematics reasoning scores in Finland, but the lower the students' reasoning scores in Singapore. The contrasting relationships in Singapore and Finland indicate the need to further study the nature of the activities related to computer use for higher order learning skills in the two countries. Implications for policy and research are further elaborated.