the meaning of "Hauptschule" at the time you refer is a school in the village
where the church is located, i.e. in the principal village of the parish.
There were additionally to the Hauptschule some so-called "Nebenschulen" in other
smaller villages of the same parish which I would translate into secondary
In case of Osten the situation abt. 1840 was the following:
There was one "Hauptschule" in Osten itself. Since 1838 Johann Friedrich
Flickenschildt was teacher of this school. He was born on 25.05.1811 at Neuhaus on
the Oste. In 1838 he married Sophia Dorothea Schulte from Bargstedt. They had
9 children. J.F. Flickenschildt (who died on 05.07.1879) was the best known
teacher in the nothern part of the Kingdom of Hannover. He published
school-books in mathematics which were used even in foreign countries.
Additionally following "Nebenschulen" existed in the parish of Osten:
in Achthöfen, Altendorf, Nord-Isensee, Süd-Isensee, Obernaltendorf, Oberhüll
Moreover, the village Osten had 4 private schools with few pupils only.
Albin von Spreckelsen