Kennarinn skrifar athugasemd við aðra málsgrein og bætir við leiðréttingu.

Because Icelandic usually puts the definite article on the end of the noun instead of using a separate word like the.

• kennari = teacher
• kennarinn = the teacher

So Kennarinn is simply the teacher. In this sentence it is the subject, so it is in the nominative singular.

Skrifar is the present tense, 3rd person singular, of skrifa = to write.

So:

• ég skrifa = I write
• þú skrifar is not correct; it would be þú skrifar? Actually standard Icelandic is þú skrifar only in some verbs? No, for skrifa it is þú skrifar and hann/hún/það skrifar as well.
• hann/hún skrifar = he/she writes

Here the subject is Kennarinn, which is singular, so skrifar is the correct form.

Icelandic does not have an indefinite article like English a / an.

So a bare noun can mean:

• athugasemd = a comment / a note
• leiðréttingu = a correction

If Icelandic wants to say the comment or the correction, it usually adds the definite article to the noun:

• athugasemdin = the comment
• leiðréttingin = the correction

So in this sentence, the lack of a separate article is completely normal.

Here við is part of the expression athugasemd við eitthvað, which means a comment, note, or remark on something.

So skrifar athugasemd við aðra málsgrein means writing a comment on/regarding another or the second paragraph.

This is not something you can translate word-for-word very neatly from English; it is just the normal Icelandic pattern for this idea.

Because við in this construction takes the accusative, and aðra málsgrein is accusative singular.

A few things are happening:

• málsgrein is a feminine noun
• annar = other / another / second
• the accusative singular feminine form of annar is aðra

So:

• nominative: önnur málsgrein
• accusative: aðra málsgrein

The noun málsgrein itself does not change form here, but the adjective does, so aðra is the clearest signal of the case.

It can mean either, depending on context.

The word annar often covers meanings that English splits up:

• another
• other
• second

So við aðra málsgrein could mean:

• on another paragraph
• on the second paragraph

The wider context tells you which meaning is intended.

It is the same word, but not the same construction.

In athugasemd við aðra málsgrein, við is a preposition linked to athugasemd.

In bætir við leiðréttingu, bæta við is a verbal expression meaning to add.

So this second við is best learned as part of the verb phrase:

• bæta við = add

This is very common in Icelandic: the same small word can appear in different structures with different grammar.

After bæta við, the thing being added is normally in the dative.

So leiðréttingu is functioning as a dative singular form here.

The base noun is:

• leiðrétting = correction

Its oblique singular forms use -u, so you get leiðréttingu.

One slightly tricky point: for this noun, the accusative singular and dative singular look the same, so the form itself does not tell you the case by sight alone. The construction bæta við tells you that it is dative here.

Because both verbs have the same subject, and Icelandic does not need to repeat it.

So:

• Kennarinn skrifar ... og bætir ...

means:

• The teacher writes ... and adds ...

English works the same way here. Repeating the subject would be unnecessary unless you wanted special emphasis.

This sentence has very straightforward word order.

Basic structure:

• Kennarinn = subject
• skrifar = verb
• athugasemd = object
• við aðra málsgrein = prepositional phrase
• og bætir við leiðréttingu = second verb phrase with the same subject understood

So for a learner, this is a good example of a fairly natural, uncomplicated Icelandic sentence. The main things to notice are the case forms and the two different uses of við, not an unusual word order.