Learn Turkish: Çocuklarımıza çağdaş bir eğitim vermeliyiz. - We must give our children a modern education.

The root is çağ, meaning "era," "age," or "epoch." The suffix -daş indicates fellowship, sharing, or association (similar to "co-" or "-mate" in English). So çağdaş literally means "sharing the same era" or "co-existing in time," which translates perfectly to "contemporary" or "modern."

Why is the word order çağdaş bir eğitim instead of bir çağdaş eğitim?

In Turkish, when a noun is modified by both a descriptive adjective (çağdaş) and the indefinite article bir (a/an), the standard word order is [Adjective] + bir + [Noun]. Placing bir before the adjective (bir çağdaş eğitim) sounds unnatural unless you want to emphasize the number "one" (as in, exactly one modern education).

Why does çocuklarımıza take the dative case suffix -a?

The verb vermek (to give) requires the dative case to indicate to whom the action is directed. Breaking the word down: çocuk (child) + -lar (plural) + -ımız (our) + -a (to). The literal translation is "to our children."

Could we use vermek zorundayız instead of vermeliyiz here?