Learn Turkish: Çocuk öğretmeni duymazlıktan geldi. - The child pretended not to hear the teacher.

This is a set grammatical structure for feigning ignorance. Let's break it down: duy (hear) + maz (negative aorist suffix meaning "does not") + lık (creates an abstract noun, "the state of") + tan (ablative case, "from") + geldi (came). Literally, it translates to "came from the state of not hearing." In Turkish, this formula (-mAzlıktan gelmek) is the standard way to say you are ignoring something or turning a blind eye or deaf ear to it.

Why is there an -i at the end of öğretmeni?

Even though the main conjugated verb of the sentence is geldi (which doesn't normally take a direct object), the object here belongs to the root verb duymak (to hear) hidden inside the pretense structure. Since the child is ignoring a specific, known person ("the teacher"), öğretmen requires the definite accusative case ending -i.

Why does the ablative case suffix take the form -tan here instead of -dan?

The preceding suffix -lık ends in k, which is an unvoiced (hard) consonant. Because of Turkish consonant harmony rules, any suffix starting with d changes to t when it attaches to a hard consonant. Therefore, -dan becomes -tan.

Could I just use gibi yapmak (to act like / to pretend) instead of this complex structure?