The purpose of this study is to explore the existing problems associated with using generative AI in education and to propose a potential solution for addressing those issues through the design of pedagogical AI agents. The existing problems are examined from two different perspectives: those of teachers and students. The proposed solutions for designing pedagogical AI agents are systematically presented, including main concepts, design considerations, functions, procedures, and structure/templates. An example of how to apply the proposed solution in designing a pedagogical AI agent is provided, illustrating its application in teaching order words (or sequencing words). Finally, the paper concludes with a discussion of potential topics for further research.