When a board member gets a written or electronic note about a board issue, how should it be shared with the full board?
Your board should have an established agreement in place among board members on how they will deal with communications that come to them individually. I suggest that any mail or electronic communication directed to them individually because he/she is a board member should be shared with the full board.
First, if a communication to an individual board member is a complaint, ensure that you follow your district's complaint policy.
The method typically used for dealing with communications to the board or individual board members is a board communications (or "Read") file. It's a physical or electronic file into which the board secretary puts copies of communications received by the board or board members. That file is made available for board members to read at their convenience, and, typically, new items will be in the file for board members to read before or after a meeting. As items are received, they may be noted in a memo to the board or even under "Board Member Communications" on the agenda, but they are NOT there for discussion. The communications, once received, become public records.
If a board member wishes to discuss something in the communications file, he or she must request that the topic be added to the agenda for the next meeting as a discussion item, following the board policy on adding agenda items. The board may discuss the issue raised by the communication, but the board should not discuss the individual who sent the communication unless relevant to the communicator's credibility/reliability.
If there is something confidential in the communication, it should go into a "confidential communications" file, and it should not be discussed in public session. Usually, communications that are classified as confidential are those containing complaints about individuals, so you will follow the district's complaint policy and applicable bargaining agreement. In most of those cases, the complaint should be sent back through the chain of command to be resolved at the lowest level possible in the organization.
The board also needs to agree on how it will respond to these communications. A good way to do this is to respond back saying "Thank you for your communication. It has been shared with the full board."