The phrase "a student to explore" is correct and usable in written English.
It can be used in contexts where you are referring to a student who is encouraged or given the opportunity to explore a subject or experience.
Example: "The program is designed to create a student to explore various fields of study and discover their passions."
Alternatives: "a learner to investigate" or "a pupil to discover".
A new scholarship has also been announced for a student to explore Ho Chi Minh's relationship with Sussex.
There will be opportunities for a student to explore an advanced topic in great depth, possibly for a junior project.
The five concentrations are designed to allow a student to explore one area of the department in greater depth.
Sample thematic concentrations and courses that allow a student to explore them are available in the American Studies Office in Building 460.
I have realized that the music program is very flexible in allowing a student to explore different aspects of the musical world and through course work, to build an education that satisfies each of our individual interests and ambitions.
In certain situations, the ARC may initiate contact with a student to explore his or her needs and offer support.
I doubt that learning to write a standardized test essay, especially one written for a computer, will encourage any student to explore the beauty of the written word.
If Christakis wants student to explore being "a little bit obnoxious... a little bit inappropriate or provocative or, yes, offensive," then release the hounds.
The primary purpose of the major is to encourage each student to explore a subject area in considerable depth.
Even if you haven't gotten to the genetics or space chapter in your science book, allow the student to explore a topic that you haven't covered or may not plan to cover (as long as it is appropriate).
The project, Microsoft says, "is a chance for students to explore a different professional path".
