La maestra ci dice di imparare a memoria la coniugazione del verbo.

Ci means to us or us here.

So:

• La maestra ci dice... = The teacher tells us...

With dire, Italian often uses an indirect object pronoun:

• mi dice = tells me
• ti dice = tells you
• ci dice = tells us
• gli dice = tells him / to him

So ci is not the subject. The subject is la maestra.

Because after dire a qualcuno when you mean to tell someone to do something, Italian normally uses:

dire a qualcuno di + infinitive

So:

• La maestra ci dice di imparare...
• literally: The teacher tells us to learn...

This is a very common pattern:

• Mi dice di aspettare = She tells me to wait.
• Ci dicono di entrare = They tell us to come in.

English uses to + verb after tell someone, but Italian uses di + infinitive.

Good question. The full pattern is:

dire a qualcuno

But when qualcuno is replaced by an indirect object pronoun like mi, ti, gli, le, ci, vi, gli, the preposition a is no longer said separately.

So:

• La maestra dice a noi di imparare...
• becomes
• La maestra ci dice di imparare...

Both mean the same thing, but the pronoun version is much more natural.

Yes. That is also correct, but the structure is a little different.

• La maestra ci dice di imparare... = The teacher tells us to learn...
• La maestra ci dice che dobbiamo imparare... = The teacher tells us that we must learn...

The first one is more direct and compact.
The second one uses a full clause with che + a conjugated verb.

In many situations, the di + infinitive version is the most natural when the subject of the second action is the same person being told.

It means to learn by heart or to memorize.

Literally, a memoria is something like from memory / by memory, but idiomatically it means learning something so well that you can repeat it without looking.

Examples:

• imparare una poesia a memoria = to learn a poem by heart
• so la tabellina a memoria = I know the multiplication table by heart

So in this sentence, the teacher is telling the students to memorize the verb conjugation.

Italian uses articles more often than English.

Here:

• la coniugazione = the conjugation
• del verbo = of the verb

So la coniugazione del verbo is a very normal Italian way to say the conjugation of the verb or simply the verb conjugation.

English often drops articles in more general phrases, but Italian usually keeps them.

Del = di + il

So:

• di = of
• il verbo = the verb
• di + il = del

This is called an articulated preposition.

Other common combinations are:

• dello = di + lo
• della = di + la
• dei = di + i
• degli = di + gli
• delle = di + le

So la coniugazione del verbo literally means the conjugation of the verb.

Because the sentence is referring to the conjugation of one specific verb.

• la coniugazione del verbo = the conjugation of the verb
• la coniugazione dei verbi = the conjugation of verbs

If the teacher had assigned multiple verbs, Italian might say:

• le coniugazioni dei verbi
• or
• la coniugazione dei verbi, depending on the intended meaning

But in your sentence, it sounds like one particular verb.

Both can mean teacher, but they are used a bit differently.

• maestra usually refers to a female primary-school teacher
• insegnante is a more general word for teacher

So la maestra gives a slightly more specific image, often an elementary-school teacher.

Also:

• maestro = male primary-school teacher / master
• maestra = female primary-school teacher
• insegnante can be masculine or feminine depending on context

Yes. Dice is the present tense of dire and can mean either:

• says
• is telling

depending on context.

Italian simple present often covers both the English simple present and present continuous.

So:

• La maestra ci dice... can be understood as
  • The teacher tells us...
  • or The teacher is telling us...

If you really want to emphasize the ongoing action, Italian can also use sta dicendo, but that is not necessary here.

The sentence breaks down like this:

• La maestra = the teacher
• ci = to us
• dice = tells / says
• di imparare = to learn
• a memoria = by heart
• la coniugazione del verbo = the conjugation of the verb

So the pattern is:

subject + indirect object pronoun + dire + di + infinitive + object

In a more formula-like way:

La maestra ci dice di + verb

This is a very useful structure to learn because it appears all the time in Italian.

A little, yes, but the original order is the most neutral and natural.

Standard order:

• La maestra ci dice di imparare a memoria la coniugazione del verbo.

You might also hear emphasis in spoken Italian, but pronouns like ci normally stay before the conjugated verb:

• La maestra ci dice...

You would not normally say:

• La maestra dice ci... ❌

So the position of ci is important: it comes before dice.

They are close, but not always identical in tone.

• imparare a memoria = to learn by heart
• memorizzare = to memorize

Imparare a memoria is very common in school contexts and often sounds more natural in everyday speech.

For example:

• Dovete imparare a memoria la poesia.
• Dovete memorizzare la poesia.

Both are understandable, but the first often sounds more idiomatic in traditional classroom language.

Yes, absolutely. It sounds natural.

A teacher might say:

• La maestra ci dice di imparare a memoria la coniugazione del verbo.

In direct speech, you could also hear:

• La maestra ci dice: imparate a memoria la coniugazione del verbo.
• La maestra ci chiede di imparare a memoria la coniugazione del verbo.

The version with dice di is a normal reported-speech sentence describing what the teacher tells the students to do.