The values of mathematics in STEM education have become an issue that needs to be considered by mathematics educators. To address this issue, this qualitative study explores four Indonesian high school mathematics teachers' values of the relationships between mathematics and integrated STEM education. The phenomenography research approach was adopted as this study investigated participants' perceptions of the relationship between mathematics and integrated STEM education. The primary research tool was semi-structured interviews. To analyze the data, qualitative content analysis was performed using an abductive thematic approach. Three main findings were obtained in this study: (1) there were three categories of teachers' orientations of the values of the relationships between mathematics and STEM education: core, peripheral, and reciprocal; (2) there were six types of values of STEM education for mathematics education: application, integration, interest, performance, usefulness, and implementation; and (3) there were four types of values of mathematics education for STEM education: resolvable, supported, modellable, and thinkable. Additionally, it was interesting to see the teachers' different perspectives on the importance of highlighting mathematics in STEM education. Three teachers agreed that mathematics should be displayed explicitly, while one teacher believed that STEM activities are more successful if mathematics is only implicitly included. The findings and discussions contribute to the further design of an instrument to measure a variety of teachers' values of mathematics in STEM education.