Ég tók eftir því að dóttir mín hlustaði betur á þjálfarann eftir fyrsta markið.

No. taka eftir is an idiomatic expression meaning to notice, to observe, or to become aware of.

So Ég tók eftir... means I noticed...

It is not related to English take after, which means to resemble someone.

When taka eftir is followed by a whole clause, Icelandic very often uses því before að.

That því is a neuter pronoun, and it works like a placeholder for the thing/the fact that was noticed. So the structure is roughly:

• Ég tók eftir því að...
• I noticed that...

A very literal gloss would be something like I noticed it, that..., but natural English just says I noticed that...

No.

In this sentence, því belongs with tók eftir því, and að simply introduces the following clause.

So this is not the conjunction því að meaning because. Here the whole pattern means noticed that.

Because this is a subordinate clause.

In main clauses, Icelandic usually follows the V2 pattern, where the finite verb tends to come early in the clause. But after að, the clause is subordinate, and the normal order is more like:

• að dóttir mín hlustaði...
• that my daughter listened...

So subject + verb is the expected order here.

Because the main verb is already in the past:

• Ég tók eftir... = I noticed...

The listening is being described as something happening at that same past time, so Icelandic uses past tense there too:

• hlustaði = listened / was listening

Also, Icelandic simple past often covers meanings that English might express with either listened or was listening, depending on context.

Betur is the comparative adverb better.

Its forms are:

• vel = well
• betur = better
• best = best

So hlustaði betur means listened better, often with the sense paid better attention or listened more carefully.

In neutral everyday Icelandic, possessives often come after the noun:

• dóttir mín = my daughter

You can say mín dóttir, but that usually sounds more emphatic, contrastive, or literary.

Also, Icelandic normally does not use the definite article when a possessive already makes the noun definite. So:

• dóttir mín already means my daughter

You do not need the equivalent of the here.

Because possessives in Icelandic agree with the noun in gender, number, and case.

Dóttir is feminine singular, so the matching possessive form is mín.

Compare:

• minn sonur = my son
• mín dóttir = my daughter
• mitt barn = my child

The verb hlusta normally takes the preposition á when you say who or what someone is listening to:

• hlusta á einhvern/eitthvað = listen to someone/something

Here, á takes the accusative, so þjálfarann is accusative singular definite, meaning the coach.

The dictionary form is þjálfari.

It means the first goal.

Breakdown:

• mark = goal
• markið = the goal
• fyrsta markið = the first goal

The article is attached to the noun as a suffix:

• -ið = the on a neuter singular noun

The adjective fyrsta is in the weak form, which is what Icelandic normally uses with a definite noun.

Here eftir means after in a time sense, and it takes the accusative.

So fyrsta markið is accusative singular.

Because mark is a neuter noun, its nominative and accusative singular look the same, so you do not see a visible change in the noun’s form here.