The duty of care as applied to school hours is written in Statute, you can look it up.
Your comment 'but the teacher can teach them wrong things without consequences' is not so, you could argue for example that if a teacher directed one child to hit another or taught for example religious intolerance in breach of the law (and leading to some trauma for the pupils) that that might be without regard for duty of care.
When your lecturer said that the school does not have a duty of care, is it possible that he may have only meant this in the context of your original question about following the correct syllabus? If so you need to ask your lecturer to clarify this and to ask why. Ask if there is precedence.