The General Education program 2018 defined the requirements to be achieved on students’ quality and competence, educational content, educational methods, and methods of evaluating educational results. Currently, at the primary level, the implementation of the new program has been implemented in grades 1, 2, and 3. The teaching activities need to focus on realizing the goals and requirements of the formation and development of specific competencies as well as core competencies for students. The ability to self-study and self-improvement belongs to common competencies, which plays an important role in helping each person have the ability for lifelong self-study to self-develop themselves. Along with other subjects and educational activities in primary schools, Vietnamese language has many advantages to help students practice and develop their self-study and self-improvement competence through contacting, comparing, and connecting in reading comprehension text. Understanding the teaching content and organizing methods for students to make comparisons and connections of the learned texts with historical, cultural and social contexts, as well as readers’ personal experiences will help students develop both subject-specific competencies and self-study and selfimprovement competence.