## 4 Discussion  
This study aimed to assess the effectiveness of training programs designed to enhance teachers' knowledge and self-efficacy in helping those with mathematics learning disability (MLD). Specifically, it examined the comparative effects of IOL and face-to-face training and analyzed their impact on teachers' professional development. The findings indicate that while both training modalities support teachers' professional growth, they exhibit distinct dynamics. The results reveal that, prior to the implementation, teachers in the IOL group had significantly higher knowledge and self-efficacy levels compared to those in the face-to-face education group. This may suggest that teachers opting for IOL have higher individual learning motivation or are better prepared for the training process due to their greater familiarity with technology [32]. Additionally, prior experience with digital learning platforms may have facilitated smoother adaptation to the IOL format. However, the post-intervention results indicate that the knowledge and self-efficacy levels of both groups became comparable. This suggests that both training approaches effectively contribute to teachers' professional development and that initial differences in learning processes tend to balance out over time. This finding aligns with previous research demonstrating that IOL and face-to-face education can yield equivalent outcomes in teacher development [32; 37]. Factor-level analyses indicate a significant increase in teachers' personal teaching competence and instructional support competence. Following the training program, teachers demonstrated greater proficiency in recognizing the needs of students with MLD, utilizing appropriate instructional materials, and developing individualized teaching strategies. The improvement in instructional support competence suggests that teachers enhanced their ability to implement in-class adaptations and provide guidance services for students. These findings align with previous research indicating that training programs designed to enhance teachers' competencies in special education are effective [25; 29]. The training program proved to be highly effective in increasing teachers' knowledge and self-efficacy. The mode of participation, whether remote or face-to-face, did not significantly influence the program's effectiveness, as both groups achieved comparable levels of success. This finding is particularly important for the accessibility and scalability of the training program. The fact that similar outcomes can be achieved regardless of the training format presents a significant advantage in addressing teachers' professional development needs under varying circumstances. The differences observed before the implementation may be due to the teachers' professional experience levels, learning styles, motivation, or previous professional development training. The higher level of knowledge and self-efficacy of teachers who participated remotely in particular may be explained by the differences in the technological aptitude of this group or their self-learning skills. In this context, analyzing the reasons for these differences before the implementation in more depth may contribute to the development of different strategies according to the needs of teachers in the preliminary preparation process of the training program. Designing training programs in an individualized manner may help to eliminate such differences. The findings further contribute to the discussion on the effectiveness of IOL and face-to-face education. According to [PERSON]'s d analysis, the initial difference observed in the IOL group before the intervention had a medium effect size. However, no significant difference was found between the two groups after the training. This suggests that both educational modalities were equally effective in enhancing teachers' knowledge and self-efficacy.