Learn Hardcore Icelandic: Kennarinn leyfir nemendum að spyrja margar spurningar. - The teacher allows the students to ask many questions.

Icelandic usually adds the definite article as an ending on the noun (-inn, -an, -ið, etc.) instead of using a separate word like the.

Why is it nemendum and not nemendur?

Nemendur is nominative plural (students as the subject).
In this sentence, nemendum is in the dative plural, because it is the indirect object of leyfir.

The declension of nemandi (a student) in the plural is:

Nominative: nemendur (students – subject)
Accusative: nemendur
Dative: nemendum ← used here
Genitive: nemenda

So leyfir nemendum = allows (to) the students.

Why does leyfir take the dative case with nemendum?

Some Icelandic verbs always take a specific case for their objects, and you simply have to learn them with that case.

Leyfa (to allow, permit) normally takes a dative noun phrase for the person being allowed to do something:

Leyfa einhverjum eitthvað = to allow someone (dat.) something

So:

Kennarinn leyfir nemendum að spyrja…
literally: The teacher allows to-the-students to ask…

What form of the verb is leyfir, and how do I conjugate leyfa?

Leyfir is the 3rd person singular present tense of leyfa (to allow).

Present tense (indicative):

ég leyfi – I allow
þú leyfir – you allow (singular)
hann / hún / það leyfir – he / she / it allows
við leyfum – we allow
þið leyfið – you allow (plural)
þeir / þær / þau leyfa – they allow

Past tense (just for reference):

hann leyfði – he allowed

What is að spyrja grammatically? Why not just spyrja?

Að spyrja is the infinitive form of the verb spyrja (to ask), introduced by the infinitive marker að (roughly like English to).

After leyfa, when you say what someone is allowed to do, you use að + infinitive:

leyfir nemendum að spyrja = allows the students to ask

Using bare spyrja without að would be ungrammatical in this structure.

Why is there að before spyrja? Can it ever be left out?

In this construction, að is required as the infinitive marker (like to in to ask).

With verbs such as leyfa, reyna, ákveða, reyna að gera eitthvað, etc., when followed by an infinitive clause, you normally must include að:

Kennarinn leyfir nemendum að spyrja. ✅
*Kennarinn leyfir nemendum spyrja. ❌

It is not optional in this sentence.

Why is it margar spurningar? What is going on with the endings?

Spurning (a question) is feminine. In this sentence, many questions is the direct object of spyrja, so it is accusative plural feminine.

Feminine nominative singular: spurning
Feminine accusative plural: spurningar

The adjective margur (many) must agree in gender, number, and case with spurningar, so:

mörg svör (neuter, plural, nom/acc) – many answers
margir nemendur (masc., nom. pl.) – many students
margar spurningar (fem., acc. pl.) – many questions ← here

So margar spurningar is exactly the correct agreement pattern.

Could I make nemendur definite and say Kennarinn leyfir nemendunum að spyrja margar spurningar?

Yes, that is grammatically correct:

nemendum = students (dative plural, indefinite)
nemendunum = the students (dative plural, definite)

The choice is mainly about context and nuance:

nemendum can sound a bit more general: allows students (in general).
nemendunum points more clearly to a specific, known group: allows the students (e.g. his class).

Both are possible; the original sentence is just a bit more general.

Could I instead say something like Kennarinn leyfir að nemendur spyrji margar spurningar?

Yes, that is also possible, but the structure is different:

Kennarinn leyfir nemendum að spyrja…
→ dative object (nemendum) + infinitive að spyrja
Kennarinn leyfir að nemendur spyrji…
→ að
- full clause with verb in the subjunctive (spyrji)

The first version sounds more like directly allowing the students to do something.
The second is closer to The teacher allows that the students ask many questions and focuses more on the fact that this situation is permitted. For everyday use, the original infinitive construction is more common.

Is it necessary to say margar spurningar, or could I just say að spyrja?

You can shorten it, depending on what you want to express:

Kennarinn leyfir nemendum að spyrja.
→ The teacher allows the students to ask (questions). – questions is understood from context.

Adding margar spurningar makes it explicit that asking many questions is okay, not just asking in general.

How is spyrja pronounced, and why is it spelled that way?

Spyrja is typically pronounced close to [ˈspɪrja] (roughly SPEER-ya with a short i).

The spelling reflects historical development:

The verb is related to spyr (I ask) and the noun spurning (question).
-ja at the end is a common infinitive ending in verbs like spyrja, kafla – kafla etc.

So although the spelling may look unusual, spyrja just follows regular Icelandic patterns for verbs of this type.