Ghiada abu Elaish's fingers twist in her lap and her eyes cloud over as she recalls the day an Israeli shell killed four of her cousins and left her in a coma for 22 days. She has had almost 12 months to reflect on the tragedy, a time in which hatred and anger might have consumed the 13-year-old. Remarkably, though, not only has she survived shocking injuries and a dozen operations, with many more to come, but she has retained both her sweet nature and faith in a bright future.

Which makes it all the harder for her to return each day after school, dressed in the ubiquitous Palestinian uniform of blue-and-white-striped smock over jeans and trainers, to the scene of the massacre – her family home.

It was Friday 16 January and Ghiada was studying for exams. Her father, a pharmacist, woke from a nap, demanding tea and shouting at the younger children to be quiet. "Suddenly I could hear my cousin downstairs, screaming 'Dead! Dead!'" A shell had hit the building – a block of five apartments, housing the extended Abu Elaish family – smashing windows and causing extensive damage to the flat below.

In the ensuing panic, Ghiada defied her father and followed him downstairs. "One room was completely black. I saw Aya [my cousin], she was on the ground with wood on top of her. There was a big hole in the wall."

Ghiada tried pulling Aya out from under the furniture. A second shell struck. "There was a big light for a second," she says. "I saw some windows smash and I heard screaming all around. A piece of shrapnel hit me. I started to scream for help and then fell down unconscious."

Ghiada's father, Atta Mohammed abu Elaish, rushed into the room. "I saw bodies without heads and legs. I saw my daughter. I saw her mother screaming." He ran outside to call an ambulance. "The Israelis stopped the ambulances 250 metres from the house. Some boys from the street came to start ferrying the bodies and the injured out of the building."

The attack was one of countless assaults during Israel's 23 days of war on Gaza – Operation Cast Lead – that began on 27 December. But it was also one of the most notorious because Ghiada's uncle – Aya's father – was a doctor who worked in Israeli hospitals and was well known to Israeli viewers for advocating peace and reconciliation. All through the conflict, Dr Izzeldin abu Elaish gave regular eyewitness accounts by phone in fluent Hebrew to Israeli television. Within minutes of the attack on his own family, he was back on the phone to a journalist in a Tel Aviv studio, weeping and begging for help as Israeli viewers listened: "My daughters have been killed."

Indeed, they had: Bissan, 20, Miar, 15, and Aya, 14, were dead, along with another cousin, 17-year-old Nour. Ghiada was in a critical condition; another of the doctor's daughters was also wounded.

The injured girls – thanks to that live TV broadcast – were unusually and swiftly evacuated to a hospital in Tel Aviv, where Ghiada was found to be suffering from multiple problems with her heart, kidneys, stomach and legs. She remained in hospital in Israel for four and a half months.

Now, Ghiada says, she thinks about that day "always", but tries not to let others see her pain. "When I am crying, I go to my room and cry alone," she says. Does she feel angry? No, she says, just sad. And she plans to stay put in Gaza: "Maybe others would like to emigrate, but that's not for me."

Toll of death and destruction

But if Ghiada expresses no bitterness, her father insists she is angry and so is the rest of the family. "It's very hard for us," he says. "That accident took Bissan, Nour, Miar, Aya – and my brother." Dr Abu Elaish has left Gaza for Canada. "He is the eldest brother, the father of the family, and now he's gone. How can we forgive?"

The shelling of the Abu Elaish family was unusual in that it caught the attention of the Israeli public, but what Ghiada continues to endure 12 months on is shared by many of Gaza's 750,000 children – half of its population.

More than 1,400 Gazans were killed in the 23 days of the Israeli assault, including several hundred children. The actual number is in dispute. The Palestinian Centre for Human Rights (PCHR) documented 313 deaths, almost 40% of them less than 10 years old. Other Palestinian groups say the toll was much higher. More than 1,600 children were injured.

But the 23-day war is only part of the story. The long history of Israeli assaults on Gaza, and the two-and-a-half-year-long blockade of the territory after Hamas took power, has exacted a toll on almost every aspect of children's lives: schooling, housing, leisure time, what they eat, what they wear, how they see the future.

A Gaza Community Mental Health Programme (GCMHP) survey earlier this year found that about 75% of children over the age of six were suffering from one or more symptom of post-traumatic stress disorder. Almost one in 10 ticked off every criteria.

"The majority of children suffer many psychological and social consequences," says Dr Hasan Zeyada, a psychologist with GCMHP. "Insecurity and feelings of helplessness and powerlessness are overwhelming. We observed children becoming more anxious – sleep disturbances, nightmares, night terror, regressive behaviour such as clinging to parents, bed wetting, becoming more restless and hyperactive, refusal to sleep alone, all the time wanting to be with their parents, overwhelmed by fears and worries. Some start to be more aggressive."

Dr Abdel Aziz Mousa Thabet, professor of psychiatry at al-Quds university in Gaza, says the conflict has a different impact on boys and girls. "Girls have more anxiety and depression, boys are more hyperactive."

Some children no longer look on their homes as a place of safety, security and comfort. Others don't even have a home to go to. The Israeli bombardment damaged or destroyed more than 20,000 houses, forcing some families into tents and others into crowding in with relatives. Hamas distributed money to displaced families to rebuild their homes but the Israeli blockade has created a desperate shortage of materials. Almost one year later, some children still have no roof over their head.

Hanan Attar, a slight 10-year-old wearing flip-flops several sizes too big for her small feet, is wistful as she recalls the house destroyed by an Israeli tank shell. "We had land, my father is a farmer," she says. "We used to grow watermelons, but the land was too close to the border and we can't get there now."

Home is now a tent on a patch of scrubby sand, shared by 10 members of her family, including a 50-day-old baby sister with a pinched face and a tin of formula milk perched on her rusting iron crib. The baby, Haneen, is seriously underweight at only 3kg, and is not growing. Her mother, Arfa, 40, cannot breastfeed because she is taking medication for back problems; the formula costs 45 shekels (£7.50) a tin, money that the family has to borrow. The father, too, is sick as well as unemployed. He reaches on top of a tall fridge that dominates the tent to pull down a sheaf of x-rays showing how his leg, broken in the conflict, is pinned together with metal.

"We are civilians, we don't belong to any faction," he says. "What are we guilty of so that we have to live like this? I spent my entire life building up my home. In one hour everything was gone."

Hanan doesn't complain about the tent, but says "the house was better". She adds: "A snake came one night and bit my mother. I can't sleep at night; I'm scared of the snakes and the dogs."

Meals are cooked on a Calor gas stove; the toilets – a hut donated by an Arab charity – are shared by all the families in the compound of tents. "There are big queues," says Hanan. Winter is coming; the tent is "freezing", she says.

There is a community of tent families, circled round the shared lavatories. The children play as all children do, kicking a football, wrestling, dragging sticks through the sand. The families are doing their best in near-impossible circumstances. Some families have even planted small gardens in the scrub: corn and a few flowers.

But Hanan – who wants to be a doctor so she can treat the sick – says she spends most of her time in the tent with her seven brothers and sisters. Do they think they will ever go back to a proper home? "God knows," says Arfa.

Overcrowding, lack of privacy and poverty are contributing to what some in Gaza call the "mental siege" . Tensions within families are increasing, say Gaza's mental health experts. "Some parents themselves have depression and anxiety. Some become more aggressive towards their children," says Zeyada.

John Ging, director of UN operations in Gaza, puts it like this: "Parents are sitting there in their homes, very upset and very frustrated at the their situation, and that is of course having ramifications for the home environment." Has there been an increase in domestic violence? "Of course . . . children are losing respect because of the breakdown of the role-model structure. They see their parents as incapable of providing for them, they're seeing their parents as a failure."

Lost childhoods

Part of the problem is the lack of release and entertainment for children. There are few gardens or parks, no cinemas or theatres, many sports facilities have been damaged or destroyed by Israeli bombing, and one of Gaza's great natural advantages – a 25-mile stretch of sandy beach facing the Mediterranean – is hiding a fresh danger.

In the summer months, families flock to the beach on Fridays and Saturdays. The sight of children splashing in the waves is cheering until one remembers that every day 20m gallons of raw sewage is pumped into the water. Since Gaza's sewage processing plant was bombed after the kidnap of Israeli soldier Gilad Shalit in July 2006, there has been no alternative means of disposal. Now, according to Save the Children, children are developing skin diseases as well as bacterial infections from swimming in polluted water.

"There are not enough safe places for children to play," says Mona al-Shawa, head of the women's unit at the PCHR. To counter this, the UN organised a hugely popular "Summer Games" during the long school break, despite objections from Hamas about boys and girls mixing together. "There were those on the political side saying kids should be going to summer camps, not doing sport and recreation, but preparing for a future life of militancy," says Ging.

Ging says schooling has also suffered. Thirty-two of the UN's 221 schools were damaged in the Israeli assault, plus scores more government ones. None have been repaired because Israel does not allow construction materials into Gaza, saying they could be used to make weapons.

"So the schools, where the windows were blown out or other damage was done, have been cleaned up, made safe, and continue in operation today without the physical repairs because we haven't been allowed to bring in one pane of glass or one bag of cement since last January," says Ging.

Israel did permit a consignment of wood into Gaza to make school desks for 8,000 children, but then blocked delivery of the steel necessary to complete them. "Now you see three kids squashed on to a desk," says Ging. "How are teachers supposed to give each child the attention they need?"

There is also a shortage of school books and pens, and what does arrive mostly has to be smuggled through underground tunnels from Egypt.

The result is children attending overcrowded schools on a double or even triple shift system that has contributed to a continuing decline in education levels. One in five of the 200,000 pupils at the UN's 221 schools in Gaza failed basic Arabic and maths exams this year.

Engendering extremism

"It's shocking for them but it's also alarming for us in terms of the future," says Ging. "The objective of the [Israeli] policy is to counter extremism. Education is probably the most effective tool through which you will counter extremism, by developing a positive and well-educated mindset. And yet we are being prevented by the policy from educating these children."

It is, he says, "facilitating the destruction of a civilised society and, worse than that, the development of an extreme society".

One of the starkest examples of school destruction is the American International school, Gaza's elite fee-paying institution in Beit Lahiya, which was bombed in the early hours of the morning of 3 January. The Israeli military claimed it was being used as a rocket-launching site. Now, where once stood science laboratories, computer rooms, a music centre and sports fields, there is a mountain of crushed masonry, twisted metal girders, broken glass and droppings from the sheep that roam the deserted site. To the side of what was once the main building lies a row of burned-out schoolbuses. The odd fragment of textbook can be seen amid the rubble.

Then there is the difficulty of trying to concentrate in class when children are clawed by hunger. Three-quarters of Gazans rely on food handouts, according to the UN. Save the Children says it is seeing newborn babies suffering from malnutrition. Anaemia, especially among girls, is common.

The UN has started feeding children in its schools because, says Ging, "they're coming to school without breakfast and therefore their attention span is very short and the academic results will then reflect that".

Food, at least, is something that is relatively easy to fix. There are many less tangible issues that concern child experts, such as a lack of healthy role models. "During the war, children could see that their parents could not fulfil their needs," says Zeyada. "They see their fathers as weak, powerless. They see parents can't give them feelings of security, can't protect them. So they look towards other figures. That might be God as an absolute power – so children might go towards religion, become more fanatic. Some identify with fighters from Hamas and other groups.

"Without hope, we are moving fast towards more aggressive children, more fanatics. If the siege ended you would see positive changes among children. They [Israel] are creating their enemies. They are pushing a new generation of children to believe in violence as a way of solving their difficulties. They are creating their own enemies of the future."

In September 2007 Israel declared Gaza a "hostile entity". "I said at that time, and I continue to say it, that's a self-fulfilling prophecy," says Ging. "You designate it as a hostile entity, you treat it as a hostile entity and in fact what happens is you generate hostility. And that's precisely what we have been witnessing here at the grassroots level for the last two and a half years under this illegal siege . . . We have more extremism in Gaza every single day."

Yet through it all, it is striking how many Palestinians cling to a belief in a better future. For all her traumas, Ghiada hasn't given up. She attends a thrice-weekly English lesson after school to improve her chances of fulfilling her dreams.

The teacher hands Ghiada a question to answer to the class in English: If you were a colour, what colour would you choose? The girl doesn't hesitate. "Red," she tells the class.

The teacher asks the students what the colour red means to them. Blood, suggests one; danger, says another, both witnesses to last year's carnage. Ghiada considers for a moment, then replies: "It makes me happy. It's the colour of love."

And what will Ghiada do with her English? She wants to be an airline pilot, she says.

Ironically that's one career choice that will certainly require emigration: Gaza has no aeroplanes and the runway of its only airport was bulldozed to rubble by the Israeli army years ago.

The 23-day war in numbers

Statistics from the Gaza Community Mental Health Programme

• 1,420 Palestinians killed, 446 of them children

• 5,320 injured, 1,855 of them children

• 4,000 houses destroyed

• 16,000 houses damaged

• 94.6% of children aged six-17 heard the sound of sonic jetfighters

• 91.7% of them heard shelling by artillery

• 92% saw mutilated bodies on TV

• 80% were deprived of water or electricity

• 50.7% left home for a safer place

• 25.9% report one symptom of PTSD

• 39.3% report more than one symptom

• 9.8% report full criteria of PTSD

Statistics from the Palestinian Centre for Human Rights

• 1,414 Palestinians killed during the conflict, including 313 children, of which: – 31% girls, 69% boys

– 15% under 5; 23.3% 5-10; 62% 11-17

– 73% died from bombs; 19.8% from artillery shells; 5.4% shot; 1.5% from white phosphorous

• 5,300 Palestinians injured, including 1,606 children

• 36 UN schools damaged

• Approximately 20,000 homes completely or partially destroyed