A pedagógiai cél fontos.

In Hungarian, the verb to be is usually left out in the present tense when the sentence is in the third person.

So:

• A pedagógiai cél fontos. = The pedagogical goal is important.

But in other persons, Hungarian does use the verb:

• Fontos vagyok. = I am important.
• Fontos vagy. = You are important.

So the missing is here is completely normal.

A is the Hungarian definite article, meaning the.

Hungarian has two forms:

• a
• az

Which one you use depends on the sound at the beginning of the next word:

• a before a consonant
• az before a vowel

Here the next word is pedagógiai, which starts with p, a consonant, so it must be:

• a pedagógiai cél

If the next word started with a vowel, you would use az.

Pedagógiai means pedagogical or educational.

It is formed from the noun pedagógia = pedagogy / education theory plus the adjective-forming ending -i.

So:

• pedagógia = pedagogy
• pedagógiai = pedagogical

This -i ending is very common in Hungarian for making adjectives from nouns, especially in more formal vocabulary.

Because pedagógiai is an attributive adjective here: it directly describes the noun cél.

So:

• pedagógiai cél = pedagogical goal

In Hungarian, adjectives usually come before the noun when they are directly modifying it, just like in English:

• fontos cél = important goal
• pedagógiai cél = pedagogical goal

In this sentence, the whole subject is:

• A pedagógiai cél = The pedagogical goal

Because fontos is not directly attached to the noun inside the noun phrase. It is the predicate adjective: it tells you something about the subject.

Compare:

• a fontos cél = the important goal
  Here fontos comes before the noun because it directly modifies cél.

• A cél fontos. = The goal is important.
  Here fontos is the main description in the sentence, so it comes in the predicate.

So in A pedagógiai cél fontos, the structure is:

• A pedagógiai cél = subject
• fontos = predicate adjective

Cél is in the nominative case, which is the basic dictionary form of the noun. Hungarian often leaves the nominative unmarked, so there is no special ending.

Here cél is the head of the subject:

• A pedagógiai cél = The pedagogical goal

Many Hungarian cases do have endings, but the nominative usually does not.

Yes. Hungarian word order is quite flexible, and changing it often changes the focus or emphasis, not the basic meaning.

For example:

• A pedagógiai cél fontos.
  Neutral: The pedagogical goal is important.

• Fontos a pedagógiai cél.
  Emphasis on important: The pedagogical goal is important / What matters is that the pedagogical goal is important.

Both are grammatical, but they are not always used in exactly the same context.

A rough pronunciation guide is:

• pedagógiai ≈ peh-dah-GOH-ghee-eye

A few useful points:

• g is always a hard g
• ó is a long o
• i is like ee
• the final ai is pronounced as two vowels, roughly a-i

Also remember that Hungarian stress is always on the first syllable of the word:

• PE-dagógiai
• CÉL
• FON-tos

Cél most often means goal, aim, or purpose, depending on context.

So pedagógiai cél can be translated in several natural ways:

• pedagogical goal
• educational aim
• educational objective

The best English choice depends on the situation, but the Hungarian word cél itself is broad and common.

No. Hungarian does not have grammatical gender, and adjectives do not change the way they do in many Indo-European languages.

So:

• fontos cél = important goal
• fontos célok = important goals

And:

• pedagógiai cél = pedagogical goal
• pedagógiai célok = pedagogical goals

The adjective stays the same. This is often easier for English speakers than languages with adjective agreement by gender.