Aroosa Khan's Grade 8 history class is studying the French Revolution, and her head is full of images of peasants storming the Bastille. She has been thinking about revolutions, about how even the most marginalized of people can stage them. Starving French peasants, for example. Or perhaps Pakistani girls.

"The peasants had a very difficult situation, but they didn't give up," Aroosa says in English. "They fought back, and got power. Girls can fight back and can get an education. A girl can bring a big change."

She says this with ironclad conviction – and just a tiny hint of the condescension employed by 13-year-old girls the world over when explaining things to adults – and she is convincing. Aroosa has not the slightest doubt that she can do whatever she sets her mind to, be whatever she dreams. Her certainty is both the great hope for her country's future and at painful odds with its uncertain present.

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A few weeks ago, Taliban gunmen boarded a school bus in Mingora in the Swat Valley, Aroosa's home, and shot another dark-browed, wide-eyed schoolgirl in the head. Fifteen-year-old Malala Yousufzai was targeted for her work championing the rights of girls to go to school. Pakistan's politicians then lined up to declare Malala the pride of the country and to extol the value of educated, empowered girls. In a nation often bitterly divided, this seemed to be a conviction everyone but the Taliban shared.

But the chorus of support for sending girls to school drowned out some hard questions: Just what can a smart girl do in Pakistan? How much space can she claim? In a country this battered, fractured, dysfunctional – how much can she really hope to achieve?

Aroosa and Mahrukh know Malala Yousufzai: their cousin goes to her school – although like most of the other students, she is staying home, too afraid to attend – and the sisters lived near her in Swat until five years ago.

Then the Pakistani Taliban took over the area and ordered girls' schools to close. Malala, who was 11, was shut up in her house and started the blog that turned her into a widely recognized campaigner for education. Aroosa and Mahrukh's school tried to keep operating quietly, and the girls found themselves in a weird limbo, some days finding it open, some days closed – and sometimes passing by bodies strung up in the town square, victims of the Taliban's swift justice for those who did not meet their standards of piety. The girls speak of it haltingly, like a bad dream they have mostly forgotten.

Their family decided, as did many others in Swat, that they had to flee after the Taliban takeover. They moved to a rented house here in the military headquarters town of Rawalpindi, which seemed secure and has good schools. They were part of a tide of Pakhtuns who have moved to cities in the south and east as the conflict has swelled in the border regions. The Khan family moved into a neighbourhood where the Punjabi locals looked at them suspiciously, as "uncivilized Pakhtuns," in Aroosa's scornful words – people from the frontier, with their guttural language and their women all wrapped up. They were homesick, Mahrukh says – they still are – for the sleepier life and the vivid colours in Swat.

But they went back to the valley often, for weddings and holidays like today's Eid al-Adha holiday. They participated in a few special events at Malala's school. They admired her renown but did not see anything startling in what she had to say. "I don't know what was the problem with her, that you need to shoot her," says Mahrukh, the younger, more hot-headed sister, who talks with her hands and brims with scorn for "stupid people," like, say, the Taliban.

Over the past couple of years the girls grew used to city life, to the noise and the high-ceilinged concrete house; they loved their new schools and the family decided to stay in Rawalpindi even after the army drove the Taliban back out of Swat again. Aroosa and her sister did not often think of the militants who had forced them to move – until a couple of weeks ago when their older brother picked them up after school and told them the news about Malala being shot. Now they can't stop thinking about that. They are safe, they think – the Taliban haven't carried out attacks here or in nearby Islamabad in a while. But then, where are the Taliban, actually? And what can they get away with?

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Mahrukh has watched the shooting coverage on the hyperkinetic news channels. "In all the interviews I've seen, no one asks, Where was the army?" she points out acidly. Swat today is full of military and police checkpoints, part of the occupation that has been there since the army drove the Taliban out in 2009. By most estimates, the gunmen who tried to kill Malala, near the centre of town, passed through six checkposts to reach her bus, and as many again when they fled. How is it, Mahrukh asks, that no one noticed or stopped them?

The Malala incident, as they call it here, revealed to the rest of the country what people in Swat were well aware of, that the Taliban continued to operate there, not very far at all into the shadows, after they were supposedly driven out. And that, in turn, reignited the perpetual debate in Pakistan about the relationship between the military and the militants, between the intelligence agencies and the Taliban they helped create and financed and, some are sure, still covertly support.

Pakistanis were united in their revulsion about the shooting and their conviction that the Taliban had gone too far. But that unity dissipated within days – into speculation about conspiracies, about Malala's relationship with the CIA, about why the rest of the world was giving this story so much attention.

There was, briefly, debate about a military operation against the Taliban in North Waziristan, along the border with Afghanistan – something the United States has been pushing Pakistan to do – but the army said it couldn't act until there was consensus in government, and the right-wing parties refused that. Soon the usual fault lines and factions were clearly visible here again.

Aroosa and Mahrukh find all that a bit mystifying: How can anyone be sympathetic to the Taliban? The girls are acutely aware of how lucky they are, to have a family that could afford to move them out of Swat and send them to an English-language private school, which their father, Bakht, pays for with money he earns working in the United States.

And they know what the other options look like. They know a lot of girls back in the village whose fathers still think they belong at home, not school. "They're living in the Stone Age," Mahrukh says, rolling her eyes. Aroosa shudders a bit. "They think girls should just get married and have a bundle of children." Mahrukh interrupts again: "My friend? Oh my god. She's just my age and she's getting married right now."

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In fact, there is considerable research to show that most Pakistanis now support education for girls, and the country has achieved improved gender parity in recent years – about 80 per cent of its girls are, at least on paper, enrolled in school.

But while Pakistan has schools in most villages and teachers in most schools, the quality of education remains, in the estimation of Shahida Khattak, a veteran educator, "abysmal." Ms. Khattak is from Khyber-Pakhtunkwa – what used to be called "the tribal areas" in the northwest of Pakistan – and was hired in the 1980s to train a batch of teachers, to try to improve educational quality in both boys' and girls' schools. That project spread first across the province and later across much of the rest of the country until she was responsible for training thousands of teachers.

But there was no true government commitment to education, she said, only to doing the minimum needed to placate foreign donors and to use teaching jobs and school funds as political sweeteners. After more than 30 years in the trenches, Ms. Khattak despairs. "There is no shortage of teachers or schools now – but the schools are a very boring environment, the textbooks would be considered substandard in any country, there is no drinking water or toilets, children enroll on the first day and are counted but they don't come back."

Many Pakistani parents choose to send their boys to madrasas, Koranic schools, which are free. There are an estimated 22,000 madrasas registered with the government, and thousands more that are not official. The curriculum followed in most madrasas is about 800 years old – religious studies, with a sprinkling of history and science from the early days of the Islamic empire, and a large emphasis on jihad.

"Parents prefer it because it's controlled – the madrasas feed their boys and teach them," Ms. Khattak said. "Teach them what – that's a question mark."

Thinking about it, Aroosa flinches. She left school on Thursday, for the start of the Eid holiday, with instructions to read Ernest Hemingway's Islands in the Stream ("It's 402 pages!") by Monday, and prepare a Power Point presentation for the class. Her sister needs to build a model of the pyramids at Giza, complete with little mummies. They informed their father that they would not be participating in much of the celebration; they have too much homework.

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Bakht is a doctor, a specialist who currently practises in the United States and keeps his children (the girls have two brothers), his parents and his brother's family housed and all the kids in private school.

His family members were religious leaders but not educated, and far from wealthy or elite. His own father could read a little bit of Urdu; his mother, none at all. There were no schools for his sisters to go to in their village in Swat, so only Bakht and his brother were educated; he seems to find it hard to believe, looking back.

His wife, Zenat, faced the same problem: the doctor's wife, the mother of these cracklingly intelligent girls, has no education herself. "I wanted to go to school so much," she said. "Even now I'm dreaming of going." But there were no schools.

And today Zenat – careworn beyond her 34 years – looks at her bold, chattering daughters and they seem a bit like aliens. Aroosa is sympathetic: "I think sometimes our mother thinks that she can't tell us things because we know more than she does – but your mother is always your mother."

Yet Zenat confides – with Aroosa translating her Pakhto because she knows no English or Urdu – that she is essentially a bit terrified of the girls. "I don't tell them what to do, because I'm afraid they will disagree with me, and tell me they know better." The girls love her, but in an unthinking sort of way: Already, her ability to be a force in their lives is dwindling.

She settles for nagging them to study, and expressing her belief in their abilities. "Whatever they want, they should set that goal and achieve it."

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But what, in fact, can they do? Lost in the hysteria over Malala and her fight were some hard questions about the options that exist for young women with an education. Unemployment, officially estimated at 6 per cent, is in truth more like three times that, and particularly high among the bulge of new graduates. Pakistan's economy is in tatters, with manufacturing and industry hamstrung by a critical lack of power generation and investment scared off by the uncertain politics.

And young women face particular challenges – Nighat Khan, dean of the Institute of Women's Studies in Lahore, points out that women outnumber men in every professional graduate program at Pakistan's universities, and yet have a minimal presence in the workforce. Culturally they must take responsibility for domestic affairs, must stay home with children, and can't take any job – such as an emergency-room doctor – that involves the need to travel after dark. Wealthy women can buy their way out of some of these problems and restrictions – that's how Pakistan came to have a female prime minister, Benazir Bhutto, and its current Foreign Minister, the glamorous Hina Rabbani Khar – and urban women have some career choices. But rural women – that is to say, two-thirds of women – can be teachers, or "lady health workers" (primary-care aides) – and that concludes their options.

Aroosa and Mahrukh will not entertain this idea. But how far in the face of their culture can they fly? How much will it change in the next 10 years – and will it be change for the worse if the slow, shadowy rise of the extremists goes unchecked? These girls believe they can do anything. So did Malala.

Aroosa says that the change that comes with education starts at home, with changing a family's ideas. "It's good when you know about the entire world. You get a lesson, a picture of the world – you can see bigger things than just where you are in your head." If more people asked critical questions, there would be less space for the Taliban. "If I can think, I can oppose them and we can fight them."

Mahrukh says she wants to be a doctor, but then confesses she admires Benazir Bhutto, who was assassinated in 2007. "She played that game of politics very well." Mahrukh is entranced by the idea of being famous like that. "Everyone has to go from this world, why not be famous? Why not make a name and leave your name on people's lips?"

The Taliban, she says, shot Malala "because they think girls have no right to be the strongest. America is the strongest country because its women are the strongest and they don't want us to have that power."

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Aroosa, no less angry, nevertheless can manage a bit of magnanimity. "And we pray that they get some sense and realize it's not a bad thing to get your country developed."