Pre-service teachers have an extensive opportunity to observe real teachers in action for approximately 13 years, a phenomenon termed the "apprenticeship of observation." However, this prolonged exposure is limited to a learner's perspective, excluding the behind-the-scenes work teachers engage in with knowledge, learners, and context. As a result, pre-service teachers often develop a superficial view of the teaching profession, focusing more on imitative practices than a comprehensive understanding of the teacher's role. University methodology courses help pre-service teachers begin to appreciate the full scope of a teacher's responsibilities.

In South Africa, the mathematics curriculum aims to foster critical and creative thinking among learners. However, traditional teaching methods, which emphasize procedural knowledge and test preparation, remain prevalent. These methods are what pre-service teachers predominantly observe, limiting their understanding of the true nature of mathematical work. Consequently, pre-service teachers' conceptions of mathematics often diverge significantly from those of professional mathematicians, influencing their future teaching practices and identities as mathematics educators.

This research explores the perceptions of second-year pre-service teachers regarding their roles as both mathematicians and mathematics teachers using the specialization dimension of Legitimation Code Theory. This theory helps analyze the epistemic (knowledge-related) and social (knower-related) relations that pre-service teachers identify as essential in both roles. The study also examines whether these descriptions contribute to the development of pre-service teachers' identities as mathematics educators.

Using qualitative methods, the study analyses responses from 60 pre-service teachers about their perceptions of mathematicians and mathematics teachers. The findings reveal that second-year pre-service teachers do not recognize the differences between the work of mathematicians and grade 9 mathematics teachers, often describing their roles under relativist codes, indicating a lack of recognition of the importance of specialized content knowledge and personal dispositions. This aligns with the suggestion that learners only see the 'finished product' of teachers' work, leading to the misconception that "anyone can teach."

The analysis also showed that some students prioritize social relations over epistemic relations when envisioning a career as a mathematician. A small percentage of codes fall within the elite codes quadrant when students discuss their roles as grade 9 mathematics teachers, where both specialized content knowledge and personal attributes are valued. This indicates that these pre-service teachers, although few in number, demonstrate a strong ability to integrate these perspectives when describing their work as grade 9 mathematics teachers. This study suggests that methodology courses should introduce pre-service teachers to the work of mathematicians to foster their development as educators who promote critical and creative thinking.

Keywords: Pre-service teachers, Mathematicians, Mathematics education, Apprenticeship of observation, Legitimation Code Theory, Teacher identity.