As you may know, in french, proposition can be devoid of a finite verb (it is named “elliptique”, and it is often associated to an independant proposition [see below]).
The first title corresponds to a proposition which is :

• Infinitive, it expresses an order, a defense, an exclamation, an interrogation or an affirmation;
• Independant, because it isn’t related to another proposition.

The second can be decomposed in two proposition :

• “Pouvoir” (main proposition) + “enseigner la vertu” (subordinate proposition).

Titles of books/articles/films (but especially news headlines) don’t always follow grammar “rules,” and the two titles you mention might be examples of this, with “[Peut-on] and/or [Comment]” ellipted:

“Peut-on/comment enseigner la vertu?”

“Comment pouvoir enseigner la vertu?”

In scholarly articles like these, however, ellipted notions are often supplied in a suitable “sub-title”

“[Pouvoir] Enseigner la vertu[?]: Est-ce vraiment possible?/[Comment
le faire ?]”

or (in another context)

“Pousser les enfants[?]: Doit-on le faire?”),

so the lack of a “sub-title” in your two cases could signal that there’s another explanation.

They could instead possibly be examples of where someone hears a statement and is so amazed (usually in disagreement or disgust) by it that they repeat the essential part of the statement in a questioning tone (like when I told my horse-loving sister that she should try horse meat):

(Me): “Il faut manger du cheval, c’est vachement bon!”

(Sis): “Quoi? Manger du cheval?”

Regardless (especially with the “ellipted title” explanation), not having read the articles and based solely on their titles, I would hazard a guess that Dr. Barnes is asking
“How to teach virtue”
(which might imply that he does believe that it is possible),

whereas the second article’s author is asking
“How is it possible to teach virtue”
(which might imply that he doesn’t think that it’s possible at all).