Despite the promises of ML in education, its adoption in the classroom has surfaced numerous issues regarding fairness, accountability, and transparency, as well as concerns about data privacy and student consent. A root cause of these issues is the lack of understanding of the complex dynamics of education, including teacher-student interactions, collaborative learning, and classroom environment. To overcome these challenges and fully utilize the potential of ML in education, software practitioners need to work closely with educators and students to fully understand the context of the data (the backbone of ML applications) and collaboratively define the ML data specifications. To gain a deeper understanding of such a collaborative process, we conduct ten co-design sessions with ML software practitioners, educators, and students. In the sessions, teachers and students work with ML engineers, UX designers, and legal practitioners to define dataset characteristics for a given ML application. We find that stakeholders contextualize data based on their domain and procedural knowledge, proactively design data requirements to mitigate downstream harms and data reliability concerns, and exhibit role-based collaborative strategies and contribution patterns. Further, we find that beyond a seat at the table, meaningful stakeholder participation in ML requires structured supports: defined processes for continuous iteration and co-evaluation, shared contextual data quality standards, and information scaffolds for both technical and non-technical stakeholders to traverse expertise boundaries.