I’m not sure how much help I can offer, as you are describing two concerns that do not generally “go together”—short attention span and shyness—along with impressive academic skills. Your daughter is obviously bright if she can already read a few words and do some addition and subtraction. Children with attention problems often have difficulty in such learning even when considerably older than your daughter. And a social problem that accompanies attention problems is more likely to be impetuousness—joining groups without an invitation, interrupting on-going group activities, etc.—than shyness.
Could it be that your daughter isn’t sufficiently stimulated by the toys you have provided her and the activities you have arranged for her? Give that some thought. And pay careful attention to things she does that she will stay with for longer periods and arrange more of those for her. Perhaps she has a special interest in dogs, or cars, or dinosaurs, or whatever. Give her old magazines and let her find pictures and cut them out. Then help her make little scrapbooks about these, printing in whatever she might dictate to you. Take her to the library regularly and let her browse among the children’s books for as long as she might like. Watch a children’s TV or video with her and, if she gets restless, ask her questions about what is happening and say, “Let’s stay here and see how it ends.” And try to arrange play opportunities with one or two other children at a time.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.