die Schule
school
An institution where children and young people are taught according to a plan.
In Deutschland beginnt die Schule für die meisten Kinder mit sechs Jahren.
In Germany, school begins for most children at the age of six.

school
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school
An institution where children and young people are taught according to a plan.
In Deutschland beginnt die Schule für die meisten Kinder mit sechs Jahren.
In Germany, school begins for most children at the age of six.

The word family of 'die Schule' includes important related words such as 'der Schüler' (male student/pupil), 'die Schülerin' (female student/pupil), and the adjective 'schulisch' (school-related).
Die schulischen Leistungen meines Sohnes haben sich verbessert.
My son's school performance has improved.
You use 'in die Schule gehen' (accusative) to describe movement toward the building. 'Zur Schule gehen' (dative) means more generally that someone is of school age and attends school.
Jeden Morgen gehe ich mit dem Fahrrad in die Schule.
Every morning I go to school by bike.
The preposition 'auf' is used to express attendance at a particular type of school. For example, you say 'auf die Realschule gehen' (to go to a Realschule) or 'auf dem Gymnasium sein' (to be at a Gymnasium).
Nach der Grundschule möchte sie auf das Gymnasium gehen.
After primary school, she wants to go to the Gymnasium.
To talk about the time after daily lessons, you use the phrase 'nach der Schule' (after school). Colloquially, people also often say 'Schule aus haben' (to be finished with school for the day).
Was machst du heute nach der Schule?
What are you doing today after school?
The meaning 'Denkrichtung' (school of thought) is limited to contexts from art, science, or philosophy. It is often connected with a name or place, e.g. 'die Frankfurter Schule' (Frankfurt School, philosophy) or 'die Wiener Schule' (Viennese School, art).
Dieser Komponist gehört zur Zweiten Wiener Schule.
This composer belongs to the Second Viennese School.
The idiom 'Schule machen' means that an idea or behavior is so successful that it is copied by many others. The thing being copied is the subject of the sentence.
Sein innovatives Geschäftsmodell hat schnell Schule gemacht.
His innovative business model quickly caught on.
direction
'die Schule' and 'die Richtung' can both mean a kind of style or way of thinking in art, science, or philosophy. 'Schule' fits better when it is about a group of people, a tradition, or a doctrine with similar ideas. 'Richtung' is more general and means more of a tendency, style, or movement. They can be confused because both occur in texts about art or thought. As a practical rule: a 'Schule' often has representatives and a shared doctrine; a 'Richtung' describes more where ideas or styles are developing.

Diese Malerin gehört zu einer bekannten Schule des 20. Jahrhunderts.
This painter belongs to a well-known school of the 20th century.
In der modernen Kunst gibt es viele verschiedene Richtungen.
In modern art, there are many different movements.