This study examined the mathematics education curricula used in elementary teacher training institutions in Korea, classifying them according to a three-tier structure: liberal arts, subject pedagogy, and advanced courses. Using a document-based comparative analysis of the latest confirmed curricula from 13 institutions and a case study of one institution (A College), this study obtained implications for future curricular revisions. Changes in course titles, credits (or class hours), and grade-semester placement were coded in terms of addition, deletion, integration, renaming, and semester shift; following this, they were also categorized into AI/digital or edutech-oriented transition; enhancement of play-, experience-, and practicum-based courses; restructuring of the credit system; and reorganization of semester placement with reference to the examination of teacher employment and field-practice burden. According to the findings, liberal arts curricula tended to expand elective structures and to introduce digital-related courses, while subject pedagogy largely maintained a common core across institutions, and advanced courses showed substantial variation in credit systems and semester distribution. At A College, partial reorganization through course renaming, addition, and semester relocation influenced operational stability and strengthened practicum-oriented instruction. Advanced-course structures were further classified into three types: a fourth-year second-semester gap type, a standard distributed type, and an upper-year concentrated type, each reflecting a compromise between student workload adjustment and the operating conditions of the institution. Based on these findings, this study suggests expanding AI- and digital-based practicum courses, alleviating fourth-year course congestion, designing elective clusters, and introducing a shared structure of core and elective courses to create major directions for future curriculum improvement.