There 2 similar words: НАДЕВАТЬ - to wear, and ОДЕВАТЬ - to dress. Many native speakers of Russian, would even say that most of native speakers use them grammatically incorrect, and I have to admit that I do it too. НАДЕВАТЬ is used as "to dress" and ОДЕВАТЬ is used as "to wear". In English these words are different, but in Russian are quite similar.

So, what is correct and what is incorrect? Let's see the examples:

НАДЕНЬ ШАПКУ - wear a cap!  - grammatically correct

ОДЕНЬ ШАПКУ - dress a cap! - grammatically incorrect

However, НАДЕНЬ ШАПКУ and ОДЕНЬ ШАПКУ always have the same sense - wear a cap!

And this tiny grammatical trick often causes a butt-hurt from radical linguists and gramatic scholars. One can meet agressive callings to ban and punish everybody who use these words incorrect (but I suppose they do it too and don't notice). However many people say as they want and don't think about it at all, and to be honest, it doesn't discredit. Anyway, it will not change anything, the grammar rules will rather be changed to actual condition of the languge than "illiterate speech" will be restricted!

Well, not all "grammatically incorrect" things are "colloquially incorrect" too. Language is being changed every year and every day. Hundred years ago there were words that one doesn't use anymore. Accept it or not - a ersonal decidion.

odet and nadet in russian language