Вот отличное описание этого явления:
Today, someone asked me. What is the difference between personal study and private study. It did rather confuse me. I do know what they both mean. Personal study is the essay of your choice for higher english, and private study is when you sit in a room with your own work and a bunch of skivers from your year and the year above who try and make you study anything but private and far from a quiet, productive use of time. I am rather just blabbering now. But i have realised that it is quite easy to confuse the two of them. I often say 'i'm off to personal study' when i really mean private study, usually once a week when the bell rings for third period on a tuesday.
https://www.blogger.com/comment.g?blogID=7643389955768363502...

Вот пример подобного расписания:
http://www.camshill.com/bulletin/revisionprog08pupils.pdf

Присутствие преподавателей (в предыдущем примере - private study with a normal teacher) объясняется тем, что учащихся во время таких занятий отмечают (проводят перекличку):
A register will be taken when you are in private study so you must go to the
correct classroom.
http://www.cchs.co.uk/current-students/docs/year_10_exams_st...

Я работаю в школе и у наших студентов старшеклассников (Years 12-13) в расписании занятий довольно часто планируют самоподготовку. Я бы не стала называть" period" "парой" поскольку, как правило по продолжительности, "период" не превышает 1 академический час.