The congresswoman wears a helmet designed with colors of the Arizona flag when she goes to therapy. With it off, friends say, she looks like herself. Her hair is growing back; her head wounds are healing.

She listens, smiles and frowns at appropriate moments. She speaks single words but can’t yet carry on a conversation.

The friends who have visited Rep. Gabrielle Giffords at TIRR Memorial Hermann Hospital in Houston say she’s getting better every day. They can tell she recognizes them; her eyes brighten when they enter, and sometimes tear up when they leave.

Healing proceeds in steps — not just in the hospital room but also in Giffords’ Tucson office. Her staff tends to business while fitting in visits to therapists. The office of an aide slain in last month’s shootings sat vacant until recently, his colleagues too devastated to reassign it.

Giffords’ staff believes she will fully recover. Each visitor brings back news of familiar gestures and words of recognition.

“We are like a family, and this was uncharted territory,” said C.J. Karamargin, the congresswoman’s communications director. “In 200 years of representative government, no congressional staffer had ever been killed in the line of duty before. Never before had a female member of Congress been the target of an assassination attempt.”

Giffords hasn’t been told yet of her staff’s pain. Doctors advised shielding her from the larger trauma of the shootings, the deaths of six and all the injuries.

Inside Giffords’ hospital room this month, Rabbi Stephanie Aaron was stunned. Only weeks before, her friend had been shot through the head. Now, Giffords was singing Don McLean’s “American Pie” with her family.

Yet shortly afterward, Aaron noticed that Giffords struggled to say something.

Aaron took her friend’s hand: “I said, ‘Gabby, it’s OK. Breathe. Just breathe.’ I wanted to let her know that this too shall pass.”

Giffords’ ability to sing while still struggling to speak is one of the mysteries of traumatic brain injury. The brain function associated with singing centers on the right hemisphere; speaking comes largely from the left, where Giffords was shot.

Therapists are working intensely to help Giffords regain speech. Those who know her identify with her frustrations.

Rep. Adam Smith remembers how she introduced herself: “She said, ‘My name is Gabby, and there’s a reason for that.’ “

Smith, D-Wash., said Giffords used her gift of gab last year to help him become the ranking Democrat on the House Armed Services Committee, on which they both sit as members.

“I’ve been here 14 years, but she is a very social person who spoke to a lot of fellow members for me, and it made an enormous difference,” he said.

When he came to see her in Houston this month, he brought a flag from a group of Navy SEALs that she and Smith had visited last year. After she was shot, the SEALs dedicated a combat mission in Afghanistan to her and sent the flag they carried. It now hangs in her room.

During his visit, Smith related committee news and told her how much she was missed.

Giffords reached out and hugged Smith. “She teared up when I said that,” he said.

On the day after Giffords was shot, about 25 people, including staffers and their spouses, gathered at a Tucson home with Kristin Welsh-Simpson, a counselor from the House of Representatives who flew in to help. They were shell-shocked.

Giffords was fighting for her life. Her community outreach director, Gabriel Zimmerman, was dead. District director Ron Barber and community outreach coordinator Pamela Simon were in intensive care.

Questions loomed over the group: Why them? Why now?

Welsh-Simpson told them they might never get an answer. Over the next weeks, she said, they’d feel anger, confusion, sadness, but each would react differently.

The group decided that Giffords would want them to open their Tucson office at 8 a.m. the next day, but they were unprepared for what faced them.

“The crush of media was unprecedented,” Karamargin said. “One day we had 900 media requests come in.”

Days later, President Obama came to town, stopping by to see Giffords and her staffers. And then the funerals began.

Working amid the clamoring phones, the thousands of e-mails and an office full of people helped. “It was comforting to be together,” Karamargin said.

Three weeks after the shooting, a small group of Giffords’ staffers returned to the crime scene at the Safeway in Tucson for the first time since the killings.

On the morning of the shootings, Mark Kimble, a Giffords spokesman, had been 8 feet away from her when the shooter started firing. He saw Giffords and Zimmerman go down.

During the return visit, he walked with his colleagues, Barber and Karamargin, recounting who stood where as the horror unfolded.

“I’m still very fragile,” Kimble said later. “But it felt good to go back … not like last time, when people were lying all around, injured and worse.”

Karamargin hadn’t been there the day of the shootings, but he needed to see the crime scene.

“I needed to have Ron and Mark explain it to me. I needed to know the details,” he said.

Rep. Debbie Wasserman Schultz knew the healing power of friendship when she visited her friend Giffords in Houston.

In 2008, Wasserman Schultz, D-Fla., underwent seven surgeries for breast cancer. “Having been through a health care crisis myself,” she said, “I knew what I wanted — not to talk about what I was going through.”

So Wasserman Schultz avoided medical questions and briefed Giffords on proposed Republican budget cuts, her kids and “normal girlfriend stuff.”

Wasserman Schultz said Giffords “concentrated on what I was saying. But it was sometimes frustrating for her. I could see it in her face. She was looking at me like, ‘I want to respond but I can’t.’

“And I said, ‘Gabby, don’t worry about it. I know you can’t respond right now. You don’t have to worry about responding to me. I’ll just keep talking.’ “

On Thursday, six riderless horses, carrying large photos of each shooting victim, led the 86th annual Rodeo Parade in Tucson. In the stirrups, boots faced backward — one had children’s cowboy boots commemorating Christina Taylor Green, the 9-year-old girl who died.

Last week, Simon returned to work at Giffords’ Tucson office. (Barber, who has not returned to the office, has had a difficult recovery from his wounds.) The counselor from Washington had gone, but Simon and most of her colleagues continue to seek help from private therapists.

Friday would have been Zimmerman’s 31st birthday. At the office, other staffers are slowly beginning to use his desk.