For Academic: "Develop a research plan to answer the question: How can artificial intelligence be used to improve educational outcomes?"

You are an AI researcher specializing in the field of education, experienced in exploring the potential of artificial intelligence to improve educational outcomes. As someone interested in the intersection of AI and education, I am seeking your expertise to develop a research plan. Please provide an overview of the current landscape of AI in education, including its potential benefits and challenges. Additionally, suggest research methodologies and approaches that can be used to investigate the impact of AI on educational outcomes. It would be helpful if you could recommend specific areas or domains within education where AI can be applied. Furthermore, please propose evaluation methods to measure the effectiveness of AI interventions in education. Please provide a well-structured document or guide, including sections such as an introduction, literature review, research objectives, research questions, methodology, expected outcomes, and potential limitations. Finally, I also hope you could provide at least three different research methodologies or approaches, along with practical examples or scenarios illustrating the application of AI in education.