With a group of friends and family members acting as a backup chorus, Ms. Giffords has been mouthing the lyrics to “Twinkle, Twinkle, Little Star” and “I Can’t Give You Anything but Love, Baby.” And as a surprise for her husband, who is celebrating his birthday this month, a longtime friend who has been helping her through her rehabilitation videotaped her mouthing the words to “Happy Birthday to You.”…

It is not uncommon for patients with a similar injury to have trouble communicating or undergo personality changes, brain specialists say. Everything from ambition and concentration to short-term memory and social inhibitions can be affected, doctors say.

But relatives and friends who have been at Ms. Giffords’s side as she undergoes rehabilitation at a hospital in Houston said in interviews and e-mail exchanges that though her recovery was slow and exhausting, it was marked by significant progress…

With the help of therapists at TIRR Memorial Hermann in Houston, the congresswoman known for her active, outdoorsy ways now labors through the halls clutching a shopping cart and does squats and repetitive motions to build her muscles, her mother, Gloria, said in an enthusiastic e-mail she sent about a week ago to friends that recounted her daughter’s progress. Others who have visited Ms. Giffords recently have left similarly upbeat.