Mathematics teaching is challenging particularly for teachers who have just started their careers. Research on this sort of teacher has focused separately on their knowledge, identity, or instructional quality. Yet, teaching mathematics as a profession requires synthetic and comprehensive competency. To fill this gap, this study investigates the relationship between changes in instructional quality and professional competency for teaching mathematics in terms of knowledge, skills, and identity. The current study recruited two beginning mathematics teachers who had the same teacher education backgrounds and worked at the same high school. We collected and analyzed video and audio recordings of their instruction and meetings and interviews about instruction. The findings reveal how their instructional quality changed during the first 3 years of teaching in addition to their heterogeneous professional competency for teaching mathematics. While both had high levels of mathematical knowledge for teaching, they differed in the extent of their skills for ambitious teaching and identity concerning mathematics instruction. Based on the findings, we argue that teacher education needs to value all aspects for professional competency synthetically, for indeed possessing mathematical knowledge alone is insufficient for a high quality of instruction. We also discuss approaches in teacher education about skills and identity for teaching mathematics.