In the best professional practice, it is advisable for a fellow teacher who notices a mistake made by another teacher to follow these steps:

1. **Private Communication**: Initiate a private conversation with the teacher who made the mistake. This conversation should be respectful, supportive, and focused on resolving the issue constructively.

2. **Provide Constructive Feedback**: When discussing the mistake, offer constructive feedback. Clearly outline the nature of the mistake, its impact (if any) on students, and potential solutions.

3. **Maintain Confidentiality**: Respect the privacy of your colleague. Avoid discussing their mistake with students or other colleagues unless it's necessary for the students' well-being or academic progress.

4. **Collaboration**: Encourage a collaborative approach to problem-solving. Work together to find a solution or rectify the mistake, keeping the best interests of the students in mind.

5. **Professionalism**: Uphold high standards of professionalism by addressing issues directly with colleagues rather than resorting to public exposure or criticism.

6. **Documentation**: If the mistake is related to a critical matter or policy violation, it may be appropriate to document the issue and any discussions or resolutions for reference.

By following these best professional practices, colleagues can maintain a supportive and respectful working environment while addressing and rectifying mistakes effectively.