Magister dicit ordinem in schola servandum esse.

Because dicit often introduces an indirect statement in Latin. In an indirect statement, the subject of the embedded idea goes into the accusative, and the verb appears as an infinitive.

So in:

Magister dicit ordinem in schola servandum esse

the core indirect statement is:

ordinem ... servandum esse
= that order must be preserved

Here ordinem is the thing being talked about in the reported statement, so it appears in the accusative.

Servandum esse is the verb part of the indirect statement.

It is made up of:

• servandum = the gerundive of servare
• esse = to be

Together they form a passive periphrastic, which usually expresses necessity, obligation, or what must be done.

So:

• servandum est = it must be preserved / must be kept
• servandum esse = to have to be preserved / that it must be preserved in indirect statement form

Because the whole clause depends on dicit, Latin uses esse instead of est.

It is servandum because the gerundive must agree with ordinem.

Ordo, ordinis is:

• masculine
• singular

And here ordinem is:

• accusative
• singular
• masculine

So the gerundive also becomes:

• accusative
• singular
• masculine

Hence servandum.

It is not servanda, because that would be feminine nominative/ablative singular or neuter plural nominative/accusative, and it would not match ordinem.

It is not servari, because servari is a passive infinitive meaning to be preserved, but this sentence does not just mean that order is preserved; it means that order must be preserved.

A gerundive is a verbal adjective. It usually conveys the idea of needing to be done.

For example:

• liber legendus = a book that must be read
• epistula scribenda = a letter that must be written

In your sentence, servandum comes from servare and means something like needing to be preserved.

So:

ordinem servandum esse
literally = order to-be-preserved to be

A more natural English rendering is:

that order must be preserved

Because Latin often expresses must not with a separate word, but with the passive periphrastic:

• gerundive + a form of esse

So instead of saying something like order must be preserved with a separate word for must, Latin says:

order is-to-be-preserved

That construction itself carries the meaning of necessity.

In direct statement:

• Ordo in schola servandus est = Order must be maintained in school

In indirect statement after dicit:

• Magister dicit ordinem in schola servandum esse = The teacher says that order must be maintained in school

Because after dicit, Latin uses an indirect statement, and the verb of an indirect statement goes into the infinitive.

So if the direct statement is:

Ordo in schola servandus est
= Order must be preserved in school

then after dicit it becomes:

ordinem in schola servandum esse
= that order must be preserved in school

The finite verb est changes to the infinitive esse.

In schola means in school or in the school.

Here in takes the ablative (schola) because it expresses location, not motion toward something.

Compare:

• in schola = in the school / at school
• in scholam = into the school

So in schola tells us where the order must be maintained.

Yes, in terms of meaning, it is the subject of the indirect statement.

This is one of the things that can feel strange to English speakers. In Latin indirect statement:

• the logical subject goes into the accusative
• the verb goes into the infinitive

So in:

Magister dicit ordinem in schola servandum esse

ordinem is not the subject of dicit.
The subject of dicit is magister.

But ordinem is the subject of the reported idea: order must be preserved.

So you can think of it as the accusative subject of the infinitive construction.

Not in the same way.

After a verb like dicit, Latin normally uses accusative + infinitive for reported statements:

• dicit ordinem servandum esse

An ut clause is more commonly used for:

• purpose
• result
• some kinds of command or noun clauses depending on the main verb

So with dicit, if the meaning is simply says that..., the normal construction is exactly what you see here.

The dictionary form is:

• ordo, ordinis (masculine)

It means order, arrangement, row, rank, or sometimes discipline/orderliness, depending on context.

In this sentence, it means order in the sense of proper discipline or orderly behavior.

Yes. Latin word order is much more flexible than English word order because the endings show each word’s grammatical role.

This sentence is:

Magister dicit ordinem in schola servandum esse

A very common pattern is:

• main verb first or early
• then the accusative subject of the indirect statement
• then modifiers
• then the infinitive or verbal ending near the end

But other arrangements are possible, such as:

• Magister ordinem in schola servandum esse dicit
• Ordinem in schola servandum esse magister dicit

These all mean essentially the same thing, though emphasis may shift slightly.

Latin often places esse at the end of the clause, which is very natural.

Yes. The direct statement behind it is:

Ordo in schola servandus est.
= Order must be preserved in school.

Then after Magister dicit it becomes indirect:

• Ordo → ordinem
• servandus est → servandum esse

So:

Magister dicit ordinem in schola servandum esse.
= The teacher says that order must be preserved in school.

Yes, but Latin does not name that person here.

The passive periphrastic often implies that someone has the duty to do something, but if no dative of agent is given, the sentence simply states the necessity without naming who is responsible.

For example:

• Ordo in schola discipulis servandus est
  = The students must preserve order in school

Here discipulis would be the dative of agent, showing who has the obligation.

But in your sentence, no such word appears, so the idea is more general:

order must be preserved in school

Because magister is the subject of the main verb dicit.

So the structure is:

• Magister = subject of the main clause
• dicit = main verb
• ordinem in schola servandum esse = indirect statement, object of dicit

In other words:

The teacher says [that order must be preserved in school].

Yes. A very literal translation would be something like:

to be needing to be preserved
or
to be to-be-preserved

But that is not natural English. The normal English translation is:

that order must be preserved in school

When learning Latin, it can help to remember both levels:

• literal structure: order to-be-preserved to be
• natural meaning: that order must be preserved