How to and What to - Statements or Questions?

Hello, I'm new and I would like you guys (native speakers and ESL teachers with a big experience in grammar) to solve this doubt:

I've always seen in several places (web pages even Thesis!) this kind of question: "How to improve students' language skills? " .. as A QUESTION. But now, a teacher told us that kind of question, it's not actually a question since it doesn't have an auxiliary. Those structures are used as statements, but not as questions, according to my teacher. So, the only "grammatically" correct way to say it is: "How to improve students' language skills": NO QUESTION MARK.

However, I really think both are OK... as a statement and as a question... and it's the same with "What to"... i've heard "What to wear"... or with why: "Why use ICTs in class?" ... so... are all those questions incorrect? Or are just informal? or what is the correct way? the natural way?

I hope you can help me. Thanks :)

Welcome to the forum, David. :hi:

"How to improve students' language skills? " This is not a question. As it is not in itself a complete sentence, it is not even a statement. Such constructions are frequently, and acceptably, used as titles for articles and books, but not as direct questions. They are sometimes so used by native speakers, and are readily understood, but I recommend that you do not use them.

They are fine as part of such constructions as "I dont know how to ...." and "I asked him how to ...".

The natural, 'correct' questions are, "How do I/we/you ....?", "How can I/you/we ...?", "Can you tell me how I/we ...?" etc.

Got it. They are not questions according to grammar because they are incomplete.
However, we can use them sometimes and they would be taken as questions, right?
Thanks! :D