In this paper we report the results of a study in which we investigated how formal education and shadow education in Taiwan provide students opportunities to learn mathematics. Based on the conceptual framework of Opportunity to Learn (OTL), aspects specific to formal education, including mathematics curriculum, mathematics textbooks, and teachers' competence, and their teaching, were reviewed. Two national projects identified under shadow education were examined. The results revealed significant features of the mathematics curriculum, textbook design, and the quality of mathematics teachers in Taiwan that constitute a lived space where teachers with their knowledge and beliefs, curriculum, textbooks, and school settings, can generate cognitive and affective learning outcomes in students. Further analyses of the two above-mentioned projects showed how Taiwan extended learning opportunities to motivate students to learn and understand school mathematics. Based on the review, challenges were also identified.