<![CDATA[Mathematics Teacher Educators (MTEs) play a crucial role in advancing effective mathematics education, as they are responsible for preparing future mathematics teachers. In recent years, increasing attention has been paid to investigating MTEs’ professional knowledge. However, most existing research has focused primarily on self-studies, wherein MTEs examine their own knowledge and practice, often without considering the perspectives of other professionals. This study addresses this gap by exploring how In-Service Mathematics Teachers (ISMTs) perceive the knowledge that characterizes a “good” MTE. Data were collected via open-ended written interviews with ISMTs working at various school levels and from different regions throughout Italy. The analysis was conducted using the Mathematics Teacher Educator Specialized Knowledge (MTESK) model and incorporated complementary frameworks to capture additional dimensions of MTEs’ knowledge not initially included. Findings indicate that ISMTs value not only strong mathematical understanding and pedagogical content knowledge but also relational, communicative, and affective qualities such as empathy, motivation, and the ability to foster collaborative learning environments. Furthermore, professional teaching experience and familiarity with mathematics education research were identified as important factors contributing to MTE effectiveness. Notably, ISMTs’ perceptions revealed some ambiguity in distinguishing knowledge intended to support teachers from that aimed at students, and highlighted tensions between the theoretical knowledge emphasized by MTEs and the practical, concrete support ISMTs seek. This study contributes to the understanding of MTEs’ professional knowledge by incorporating the perspectives of those they train, thus illuminating often undervalued affective and experiential aspects. The findings offer significant implications for the design of teacher education programs to better address ISMTs’ needs and enhance professional development.]]>
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