To dream of a chalkboard represents an open or receptive attitude to new ideas, brainstorming, or figuring something out. You may be considering options, theorizing, experimenting, or trying to come up with creative solutions to problems.
A chalkboard is a sign that you're working towards an answer, or that you're open to a number of possibilities.
To dream of a teacher that asks you to read something off a chalkboard may represent your interest in solving a problem or your sense of intuition that wants to you consider or reconsider options.
To dream of a teacher that asks you write on a chalkboard represents your interest in solving a problem or your sense of intuition that wants to you begin brainstorming or working on solving a problem.
To dream of a doctor writing on a chalkboard may represent an interest or your sense of intuition that is focused on figuring out a method of healing.
To dream of an chalkboard menu in a restaurant represents an experimental attitude or open-minded approach to see how something makes you feel. You may be trying something new, or seeing if something fits with your lifestyle.
To dream of green chalkboard represents your attempts to brainstorm, or experiment with problems that are less embarrassing, and easier to accept.
To dream of a black chalkboard represents your attempts to brainstorm, or experiment with problems that are more personal, embarrassing, and difficult to accept.