## 1 Introduction
In recent years, various in-service training programs, professional development workshops, and online training courses have been developed to meet this need [30]. The widespread use of interactive online learning technologies, especially during the COVID-19 pandemic, has accelerated the transfer of teacher education programs to online platforms. Face-to-face and interactive online learning programs may have different effects on teachers [31]. Face-to-face education offers participants direct interaction, immediate feedback, and application-oriented learning opportunities, while interactive online learning provides flexibility in space and time, a diversity of resources, interactive communication, instant messages, and the opportunity to reach a wider audience [32]. However, the question of which model increases teachers' knowledge and self-efficacy levels in MLD more effectively has not yet been clarified. The literature takes into account various variables when evaluating the effectiveness of in-service training programs [33]. These variables include teachers' educational status,length of professional experience, age, previous in-service training in special education, and educational background in learning disabilities. For instance, in a study conducted by [PERSON] [34], it was determined that vocational high school teachers' level of knowledge about learning disabilities showed significant differences according to their branches, the presence of students receiving inclusive education in their classes, and their previous participation in in-service training on special education. This finding shows that the effectiveness of in-service training programs may vary depending on the professional and personal characteristics of teachers. In addition, teachers who have previously received training in the field of special education may initially have an advantage in recognizing and intervening in students with MLD. Such teachers may benefit from the training programs offered, especially in terms of strategy development, material design, or integration of new technological tools [35]. On the other hand, teachers who have not received any training in special education or vocational education before may need to be given basic conceptual information first. Training teachers in MLD is essential to the success of inclusive education policies. International organizations and educational policies emphasize the importance of providing inclusive and equitable learning environments that address the diverse learning needs of all students [36]. Teachers who understand the academic, cognitive, and affective needs of MLD students are crucial for fostering an inclusive and high-quality education. Thus, focusing on MLD within teacher education programs can be seen as a strategic approach to improving the quality and equity of education systems globally. However, there is a limited body of research examining the effects of interactive online learning and face-to-face mathematics learning disability education programs on teachers' knowledge and self-efficacy. In particular, the post-2020 surge in digitalization and interactive online learning has created new research demands in this area [32; 37]. Comparative studies can offer valuable insights for both policymakers guiding teacher education programs and teacher training institutions. For instance, the study by [PERSON] and [PERSON] [38] demonstrated the effectiveness of an in-service training program aimed at enhancing teachers' adaptive expertise in relation to students with learning disabilities, yet it did not extensively explore the impact of face-to-face versus interactive online learning delivery formats. Similarly, while [PERSON]'s [39] research on mathematics intervention strategies for primary school students informs teacher education models, it does not sufficiently address the comparative analysis of interactive online learning and face-to-face education programs.