Educators expect artificial intelligence (AI) to augment student capabilities and rapidly transform teaching and learning practices. However, little is known about students' perceptions of AI and what they expect from AI in student-AI teaming. There is a lack of holistic understanding of the nature, effects, and areas of improvement in teamwork by students and AI on learning. This study aims to explore students' perceptions and experiences about student-AI collaboration (SAC) to provide effective measures for the successful integration and implementation of SAC. In-depth interviews were carried out with 20 undergraduate students in South Korea after a drawing task with AutoDraw. This study found that students expected AI to serve various roles, including a learning mate, a tutor, and an effective tool to complete the task during SAC. Students perceived that SAC could benefit both the students' affective domain and task performance. In contrast, students addressed multiple barriers to SAC both from the AI-related and student-related aspects. These findings can provide insights into the dynamic interaction between students and AI for problem-solving performance and meaningful learning. This study also provides implications on AI literacy education and the design of educational AI that can be made pedagogically rich to enhance student-AI teams.