Supervised self-study Imagine an education model in which teacher/supervisor/mentor does not teach the syllabus to students. Instead, just pushing them towards key topics, and students must study by themselves. The teacher only control/supervise students to keep studying in right direction, but no professional teaching.

This is something like supervising academic research projects at graduate level.

I am curious if there is a pedagogical model/category/method of this kind for education (at lower levels)? For example, is there any example for teaching by this method in any school or university around the world? If yes, what is it called? I had no appropriate keyword to search for it.
Problem-based learning is one approach that fits your description. From wikipedia


  Problem-based learning (PBL) is a student-centered pedagogy in which students learn about a subject through the experience of problem solving. Students learn both thinking strategies and domain knowledge. The goals of PBL are to help the students develop flexible knowledge, effective problem solving skills, self-directed learning, effective collaboration skills and intrinsic motivation. Problem-based learning is a style of active learning.


A related approach is inquiry-based learning, which allows the idea to be used on a much smaller scale than problem-based learning, which, based on what I have read, tends to be rather resource intensive and require vast amounts of planning from the teaching staff.