Htydjtk

Part of this answer made me think about my own situation:

It's entirely possible that the ranger is the only one that has a chance at succeeding at the check and thus it would be inappropriate to ask other players to roll.

I think I have a problem in my DnD group. We're fairly new players - the DM and 1 party member having played a lot before, but the other 2 of us have never played at all.

The first few sessions went great, with the DM guiding us through our first battle, helping us figure out abilities, and doing various checks (spell saves, strength checks, etc.). We all pretty much had it figured out at that point. But then we did our first dungeon.

Immediately upon entering, the seasoned member decided to "take the lead" and start rolling perception checks (without any prompting), even though their character is an extremely low WIS barbarian. They fail practically every check because of their modifier, but they are always the one to start the roll. This continued further, including during conversations with NPCs and investigating piles of bones, etc. The DM would say "in this room you see a pile of bloody skulls, but you don't know what they're for." The barbarian would then immediately say "I'll roll investigation and look through the pile of skulls for clues".

This "preemptive rolling" has now become a habit of the new player to the group (the one that is not me), wherein they say "I'll roll strength to see if I can jump over this gap", when in actuality if they had said what they wanted to do (normal RP) and waited for the DM, they would know they need to roll acrobatics.

It's an issue of presumptuous/preemptive rolling, and our group becoming stuck on the mechanics of dice rolls and skill checks rather than role-playing and finding out if they succeed or fail.

Even if players know what they should roll to do a certain action, isn't the DM supposed to be the one prompting it? If this really is problematic behavior (personally I think it is), how can I go about changing it if 2 of the 3 members of the actual party are doing it?

In gaming, nothing is "wrong" if the group agrees on it.

Having said that, I would venture to say this approach is somewhat against custom and wouldn't be received well in the average table. If I had a player show up who just started to declare "I roll X", I'd respond, regardless of the result, "You fail. I call for rolls at this table." There are many reasons known only to the GM what roll is appropriate, if one is appropriate, if one of those skills is going to bite you the second you start rummaging, etc.

However, if your GM is unwilling or unable to do that, there's very little you can do to affect what the group does short of:

a) spurring a discussion on it with your group, "Hey guys, shouldn't we wait for the GM to tell us what to roll?" (which you seem oddly reticent to do as you are coming here instead), or

b) leading by example, and declaring what you want to do and explicitly deferring to the DM on "What would you like me to roll?" or "Can I roll an Investigation check?" to set the tone.

I've done this kind of "managing up" to GMs before I thought were being taken advantage of in some way by somewhat ostentatiously insisting on the proper protocol, and often they do tweak to it. "Hey yeah I'm the one who gets to say. Joe, stop rolling till I say!" This does run the risk of them saying "Stop asking me, I'm not your mother, just roll something!" if they strongly agree with the other camp here, though, so really a) is the most effective strategy, I'd only use b) to reinforce it.

In the situation you describe if a player were to say "I roll," at our table, as GM I would say, "Your dice clatter to the ground and rattle amongst the old bones. Riznar, (the druid with high WIS) you perceive that this is an ancient ritual of this barbarian's tribe to honor the remains of the dead and judge that it is best to be silent in this moment of reverance."

It only takes one or two responses like this from the GM to completely correct this type of behavior and bring more RP into the G for the rest of the campaign.

So what can you do as a player?
Sounds like you need to initiate a table conversation about what the expectations of the group are. Whether you do this by speaking with the GM first or bringing it up with everyone depends on the social dynamics of your table. In general, though, part of the GM's role is resolving issues like this, so bringing it up with the GM first is always a good idea. Ultimately the GM is best positioned to address this situation.

At my current table, with a couple very excited and new-to-D&D kids, I advise:

You tell me what you want to do

I'll tell you if you need to roll

Don't roll dice unless I ask you to

In combat I'm fine with pre-emptive rolling (I encourage it to move things along) but when we're not in a combat situation I'd like to have them narrate. If a roll is required I'll request it, sometimes of one player, sometimes of them all.

Most of the time they will succeed at actions without a roll, especially if it's a thing they are logically good at.

As a player I'd recommend you have a 1:1 conversation with your DM about your concerns with this behavior, and suggest that the DM be the one to say what the expected behavior should be at the table.

Every table is a little different. In general any dice rolls done without the DM's say-so are invalid. You declare your action, and the DM might say you just succeed or fail, or might ask for a specific skill roll, and only then do you roll it.

But, as you're not the DM, you should lay out and let the DM handle it if he thinks it's actually an issue. You say the DM and this player are experienced with the game, and if they've played together a lot, it's entirely possible the player knows how the DM tends to operate and is okay with being corrected if necessary.

They may not be strictly adhering to the "official" way to run the game, but it isn't really your problem.

Roll as many dice as you like

Just be aware that, as DM, I will totally ignore any that I didn’t ask for.