Magistra dicit talem disciplinam utilem esse, quoniam sine ordine nemo bene discere potest.

Because after a verb like dicit (says), Latin often uses an indirect statement instead of a clause with that.

In English, we say:

The teacher says that this kind of training is useful.

In Latin, that becomes:

Magistra dicit talem disciplinam utilem esse.

In this construction, the thing being said becomes the subject of the infinitive and goes into the accusative. So disciplinam is accusative because it is the subject of esse in the indirect statement.

It is accusative because it agrees with disciplinam, which is accusative.

Here utilem is a predicate adjective with esse. It describes disciplinam, so it must match it in:

• gender: feminine
• number: singular
• case: accusative

So:

• disciplina = nominative
• disciplinam = accusative
• utilis = nominative feminine singular
• utilem = accusative feminine singular

Because the sentence uses an indirect statement, both the noun and the adjective appear in the accusative: talem disciplinam utilem esse.

Esse is the infinitive of sum, meaning to be.

After verbs of saying, thinking, knowing, hearing, and so on, Latin commonly uses the accusative + infinitive construction. So instead of saying that ... is useful, Latin says literally:

the teacher says such training to be useful

That is why esse appears. It is the normal way Latin expresses this kind of reported statement.

Because classical Latin usually does not use a conjunction equivalent to English that in this kind of sentence.

English: The teacher says that such training is useful.

Latin: Magistra dicit talem disciplinam utilem esse.

Instead of a that-clause, Latin uses an indirect statement:

• accusative noun as subject
• infinitive verb

So talem disciplinam utilem esse does the job that that such training is useful does in English.

Talem is the accusative feminine singular of talis, meaning such or of such a kind.

It agrees with disciplinam, so together they mean:

talem disciplinam = such training / this kind of training

Like utilem, it must be accusative because it modifies disciplinam in the indirect statement.

Talis disciplina would be nominative, and you would expect that in a direct statement, for example:

Talis disciplina utilis est.
Such training is useful.

But this sentence is not a direct statement. It is embedded after dicit, so Latin changes the structure into an indirect statement:

Magistra dicit talem disciplinam utilem esse.

Because of that:

• disciplina becomes disciplinam
• talis becomes talem
• utilis becomes utilem
• est becomes esse

Quoniam introduces a causal clause, meaning a clause that gives a reason. It usually means since, because, or inasmuch as.

So here:

quoniam sine ordine nemo bene discere potest

means something like:

because / since without order no one can learn well

Unlike the indirect statement before it, this is a normal finite clause with a finite verb: potest.

Because the preposition sine takes the ablative case.

So:

• sine ordine = without order
• sine disciplina = without discipline
• sine magistro = without a teacher

That is simply the case required by sine.

Nemo means no one or nobody.

It is the subject of potest:

nemo ... potest = no one can

Latin often uses nemo where English would use no one. It is a very common word and works like a singular subject, which is why the verb is singular: potest, not possunt.

This is a straightforward combination of:

• potest = is able / can
• discere = to learn
• bene = well

So literally:

nemo bene discere potest = no one is able to learn well

The infinitive discere depends on potest. This is just like English can learn.

Because it modifies the verb discere, not a noun.

• bonus, -a, -um = good (adjective)
• bene = well (adverb)

So:

• bonus discipulus = a good student
• bene discere = to learn well

Here the idea is not that the learning is good as a noun phrase, but that the action of learning happens well, so Latin uses the adverb bene.

Yes: the word order is natural Latin, but it is more flexible than English.

A few things to notice:

• Magistra comes first, which puts the teacher in focus as the speaker.
• talem disciplinam utilem esse stays together as the indirect statement after dicit.
• quoniam introduces the reason afterward.
• potest comes at the end of its clause, which is very common in Latin.

Latin word order often helps with emphasis and flow, but the grammatical endings are what really show how the sentence fits together.

Yes. The direct version would be:

Talis disciplina utilis est.
Such training is useful.

Then when you put it after Magistra dicit, Latin changes it into indirect statement form:

• talis → talem
• disciplina → disciplinam
• utilis → utilem
• est → esse

So:

Magistra dicit talem disciplinam utilem esse.

This is a very useful pattern to learn, because it appears constantly in Latin.