Recent decades have witnessed a global expansion of private supplementary tutoring, known as shadow education--additional support in academic subjects that takes place outside of regular school hours. Using the data of 55 countries from the Programme for International Student Assessment (PISA) 2022, this study examines the association between students' participation in shadow education and their academic achievement in mathematics and how these relationships change for developed, developing, and East Asian regions. This study also sheds light on the moderating effect that socio-economic status has on the relationship between engagement in shadow education and math performance. Multilevel regression analyses revealed that, at the between-school level, only one of the five forms of shadow education, namely the degree to which students received "asynchronous" video-recorded instruction, was associated with improved math performance. Similarly, at the within-school level, only the degree to which students received video-recorded instruction was statistically significantly associated with improved mathematical outcomes. Incidentally, we find that institutional-related school-level factors such as the overall quality of student-teacher relationships, provision of math-related extra-curricular activities, and support in terms of peer-to-peer tutoring appear to be associated with improved school math performance, while the quality of student-teacher relationships and level of math teacher support also feature positively for students within-schools. Regarding differential effects by region, at the between-school level, only the degree to which students received large-group study or practice was associated with math performance in East Asian countries. With regards to the moderating effect of SES on the positive relationship between "asynchronous" shadow education and math performance, we find the effects to be negative, suggesting that "asynchronous" engagement might be more beneficial for students from lower SES backgrounds. Finally, while the overall negative relationships between synchronous forms of shadow education and math performance appear counter-intuitive, we speculate that this may reflect the use of such tutoring for remedial purposes. We suggest that further research into these "remedial reverse effects" in post-COVID AI-bot-capable educational contexts may provide a more definitive understanding of the role that student engagement in shadow education has on their academic performance.