When you are a PTO your are an independent group governed by your bylaws, so you would have to check with what is stated in the bylaws. I would think you could sit in and listen to a board meeting. It would also be in the best interest of the executive board that they share the budget with the members, so that everyone can see where the money is going, and have a vote on how it should be spent.
You may want to ask to take a look at the bylaws and see what they say.
All the board meetings of our PTO are explicitly closed to members. Is that normal? This sounds like every board meeting is effectively an "executive session". Do other boards allow members at their board meetings, just to listen in?
Are the budgets of most PTOs private or public? Ours is shared only with members and only at the meeting where members vote on the budget. Requests to later view the budget, even by members, have been denied.
