
korrigieren
to correct
To find and improve mistakes in a text, calculation, statement, or action.
Der Lehrer korrigiert die Klassenarbeiten der Schüler.
The teacher corrects the students' exams.
to correct
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to correct
To find and improve mistakes in a text, calculation, statement, or action.
Der Lehrer korrigiert die Klassenarbeiten der Schüler.
The teacher corrects the students' exams.

to adjust
To slightly change or adjust a position, course, attitude, or mindset in order to reach a desired state.
Der Pilot musste den Kurs des Flugzeugs leicht korrigieren.
The pilot had to adjust the plane's course slightly.

to correct oneself
To recognize a false statement you previously made and replace it with the correct information.
Ich sagte, das Treffen sei um 15 Uhr, aber ich muss mich korrigieren, es ist erst um 16 Uhr.
I said the meeting was at 3 p.m., but I have to correct myself; it's actually at 4 p.m.
Verbs that end in '-ieren' often come from Latin or French. In German, they are almost always regular (weak) verbs and form the past participle with 'hat' and the ending '-t' (e.g., korrigiert).
Hast du meine E-Mail schon korrigiert?
Have you already corrected my email?
The corresponding noun for this verb is 'die Korrektur' (correction). It describes both the process of improving something and the result of that process.
Der Autor hat die Korrekturen des Lektors akzeptiert.
The author accepted the editor's corrections.
In its main meaning, 'korrigieren' (to correct) is used with things that can contain mistakes. Typical objects are: 'Fehler' (mistakes), 'einen Text' (a text), 'Hausaufgaben' (homework), 'eine Rechnung' (a calculation/bill), or 'eine Aussage' (a statement).
Bitte korrigiere die Fehler in diesem Dokument.
Please correct the mistakes in this document.
When it is not about mistakes, 'korrigieren' means to adjust or fine-tune. In this context, the objects are often things that have a direction or state, e.g., 'den Kurs' (the course), 'die Haltung' (the posture/attitude), or 'eine Prognose' (a forecast).
Das Unternehmen musste seine Gewinnprognose nach unten korrigieren.
The company had to adjust its profit forecast downward.
The reflexive form 'sich korrigieren' (to correct oneself) is used almost exclusively in spoken language. You say it when you realize that you have just said something wrong and immediately correct it.
Wir treffen uns am Montag – ach nein, ich korrigiere mich, am Dienstag.
We're meeting on Monday—oh no, I correct myself, on Tuesday.
to improve
Verbessern and korrigieren can both be used when editing a text. Korrigieren presupposes specific errors that are removed. Verbessern can also mean correcting errors, but it can additionally refer to a general improvement in quality, for example through clearer wording, even when the original text was not incorrect.

Lea korrigiert den Text, indem sie einen falsch geschriebenen Namen berichtigt.
Lea corrects the text by correcting a misspelled name.
Lea verbessert den Text, indem sie die Einleitung klarer formuliert.
Lea improves the text by making the introduction clearer.