## 1 Introduction
In contrast, current challenges, particularly in the post-COVID-19 era, necessitate remote teacher training programs that are sustainable, effective, and inclusive [37]. The influence of interactive online learning programs on teachers' knowledge acquisition, their impact on self-efficacy beliefs, and the characteristics that shape these outcomes remain crucial areas for further investigation [32]. One of the most important ways to enhance sustainable teacher preparation is through interactive online learning, especially when it comes to preparing teachers to help kids who struggle with math. The COVID-19 pandemic's shift to online learning highlighted the necessity of customized instruction that includes appropriate, cutting-edge approaches for these pupils [40]. In the context of helping children who struggle with mathematics, interactive online learning has become an essential tool for teacher preparation. The use of interactive online learning approaches necessitates a review of their sustainability and efficacy in pedagogical practices, particularly with regard to the distribution of resources meant to enhance these students' academic performance. The COVID-19 pandemic hastened the use of interactive online learning and forced teachers to find creative ways to teach math to kids who struggle with it. The necessity of adapting conventional teaching strategies to properly address the requirements of secondary students with learning disabilities in an online setting is emphasized by [PERSON], [PERSON], and [PERSON] [41]. The significance of teaching teachers to use differentiated pedagogic tactics that take into account the varying cognitive profiles of pupils in a virtual environment is underscored by their findings. Since these methods aim to enable educators to design inclusive learning experiences in spite of physical classroom limitations, they have a direct impact on the sustainability of educational practices. [PERSON] et al. [42] further examine the difficulties of teaching mathematics remotely, emphasizing that standard pedagogical approaches frequently do not translate well into an online setting, especially for disciplines like mathematics that call for practical involvement. Acknowledging the challenges faced by educators, the authors recommend that teacher training programs and resource distribution should change to incorporate technology and pedagogical approaches tailored to online settings. In this context, sustainability refers to both the efficacy of teaching methods and the ongoing professional development of teachers, which is crucial for meeting the complex requirements of students with learning disabilities. This research is expanded upon by [PERSON] et al. [43], who looked at the educational resources and tactics that arose throughout the COVID-19 pandemic. According to their study, educators have implemented a number of creative methods that could be used as a foundation for future teacher training cadres. The focus on developing accessible learning environments emphasizes the necessity of a resource allocation approach that encourages an increase in the variety of instructional strategies and resources available to teachers. Sustainable teaching methods that may be tailored to the specific requirements of math students with disabilities can be informed by the insights gathered by these initiatives. Another way to achieve educational sustainability is by integrating adaptive technologies into teacher preparation programs. According to [PERSON] et al. [44], adaptive technology-enabled personalized learning benefits students with learning disabilities and fosters a more sustainable model of teacher education by enabling teachers to modify their lessons to fit the needs of various learning profiles. This strategy encourages participation and long-term success among students who struggle with mathematics by supporting the creation of customized learning pathways.