Aparent who demonstrates to a child how to tie their shoes and then gradually turns over the responsibility of the task to the child is

scaffolding            

Explanation:

Scaffolding: In psychology, the term scaffolding is defined as an instructional method or phenomenon in which a teacher describes the problem-solving process for his or her students and therefore every step as they keep moving.

Gradually, the teacher then disappears from helping or guiding the students and allows them to solve or work on tasks independently and hence the teacher provide guidance only when requested by the students.

In the question above, the given statement signifies the process of scaffolding.