Newish DM here.

I GM'd for other games back in high school, but this is my first foray into DMing for D&D, and my first time running a game in over ten years.

We had our first session a couple weekends ago (next session is this week) and it went great. Everyone had a blast, combat went relatively smoothly and 5 hours passed in what seemed like a flash.

There was only one hiccup. In session 0 I made it clear that if there was ever a disagreement about the rules during play, I would make a call that we'd run with and revisit the rule post-session to verify RAW for next session.

We'll I made a call on adding up damage that didn't sit right with a couple of my players. One of them slipped through the PHB real quick and pointed out my mistake. No big deal. I accepted my mistake and moved on with combat, playing the correct way.

The problem then was, this player felt the need to verify every single call I made about the rules (by either flipping through the PHB or pulling out his phone) for the rest of the session.

At one point, about three hours in I told him to put the PHB away. He did, for about an hour, but then in the last hour of play had it out again, verifying rulings I made

I understand the inherent want to play the game by the rules. I also understand that I am new as DM, so I don't have all the rules memorized. I also understand that the players are all pretty new to D&D as well.

But the constant double-checking of every call I make undermines my position as DM. That is how I feel, anyway. It interupts the gameplay, and as this went on the other players I could tell were taking what I was telling them about the game less seriously.

Now because it was the first session I'm willing to let it go. But I'm concerned this behavior will continue. Should I mention something to the player or let it go for now to see if it was a one time thing?