In piano education for preschool to early elementary school-aged children, both weekly lessons with a teacher and daily home practice supported by parents are fundamental for skill advancement. However, the nature of students' home practice, often unseen by teachers, has been less examined. This paper aims to (1) identify challenges inherent in home practice and (2) develop a system to mitigate these issues, enhancing teachers' understanding and support of students' home practice to improve piano performance skills. Through observing actual lessons and analyzing 177 days of practice videos from 30 students, this study identifies effective strategies, such as assigning appropriately difficult pieces and rewarding with stickers or stamps. It also highlights obstacles, including student tension under parental guidance and repetitive, unproductive practice. The insights from field study suggest the potential of third-party(system) feedback, practice segmentation, reporting practice records to teachers, and rewards for practice sessions. We developed a system incorporating these solutions and examined with 80 children over four months. Results showed increased teacher engagement with students' home practice, improved student motivation and practice duration, and enhanced sight-reading skills, demonstrating the system's effectiveness in supporting piano education.