Can players declare that they are making a specific ability check?

A player in my game has a habit of making statements like:

“I make a Religion check to see if I recognize that symbol.”

“I want to use my Persuasion skill to talk past the guard.”

“Can I use Insight to try to…”

All of these sound wrong to me, as I’m expecting them to just say what they want to do without reference to a skill. Sometimes there wouldn’t even be an ability check required, or what they’re describing is covered by a different skill.

I don’t find much support in the core rules for players describing actions like this, though the books don’t spend a lot of time on how players describe actions. Are players allowed to declare outright that they are making a specific ability check?

I’m not necessarily looking for how to handle this particular player. The problem I’m seeing at my table is that less experienced players have started to adopt the same mannerism. I want to tell them “this isn’t how you play the game”, and my question here is really “This isn’t how you play the game, right?” or “Should I be discouraging new players from playing this way?” I think the example of play and the How to Play on pages 5 & 6 of the PHB support this. I want to know if there are other sources that might strengthen or weaken that argument.

Note: I’m concerned only with the general rules. There might be specific cases where this is okay, e.g. if a monster had turned invisible and a player, knowing the rules about hiding said, “I make an active Perception check to find them”, I’d allow it (though even here the player could just say “I try to find them” without needing to reference the skill).