They race towards a rubbish truck as it empties its load at a vast landfill on the edge of the city, hauling away bin liners that overflow with household waste. Their hands are black with dirt and their faces are hidden by headscarves that protect them from the high sun.

An estimated 500 gancheros (recyclers) work at Cateura on the outskirts of Asunción, where 1.5 tonnes of rubbish are deposited daily, separating plastic and aluminium that they sell on for as little as 15p a bag.

Among the mounds of refuse, however, are used oven trays and paint pots. Cast aside by the 2 million residents of the capital of Paraguay, they are nonetheless highly valued by Nicolás Gómez, who picks them out to make violins, guitars and cellos.

Gómez, 48, was a carpenter and ganchero but now works for Favio Chávez, the conductor of Paraguay's one and only landfill orchestra.

Favio Chávez, director of the Cateura Orchestra of Recycled Instruments, sculpting the neck of a string instrument from an old strip of wood. Photograph: Jonathan Gilbert

The Cateura Orchestra of Recycled Instruments is made up of 30 schoolchildren – the sons and daughters of recyclers – whose instruments are forged from the city's rubbish. And while its members learned to play amid the flies and stench of Cateura, they are now receiving worldwide acclaim, culminating earlier this month with a concert in Amsterdam that included Pachelbel's Canon.

The project was born in 2006 when Chávez, 37, began work at the landfill as a technician, helping recyclers to classify refuse. But his passion for music took him home each weekend to the small town of Carapeguá, 50 miles from Asunción, to conduct a youth orchestra.

After he brought the group to Cateura to perform, the gancheros asked Chávez if he could teach music to their children, many of whom would spend afternoons playing in the rubbish as they waited for their parents to finish work.

But as the months passed, Chávez – a longtime fan of Les Luthiers, an Argentinian band that uses homemade instruments – realised the ever-growing number of children under his tutelage needed to practise at home if they were to progress.

"A violin is worth more than a recycler's house," says Chávez. "We couldn't give a child a formal instrument as it would have put him in a difficult position. The family may have looked to sell or trade it.

Nicolás Gómez, a former ganchero, makes a violin from an old oven tray. Photograph: Jonathan Gilbert

"So we experimented with making them from the rubbish. We discovered which materials were most comfortable, which projected the right sound and which withstood the tension of the strings. It was fine to hand these out as they had no monetary value."

Gómez travels three times a week to Cateura to dig out material. He shapes the metal oven trays with an electric saw to form the body of a violin and engineers cellos from oil barrels. The necks of his string instruments are sculpted from old strips of wood, called palé.

Now with the aid of colleagues, Chávez – who has been teaching music since he was 13 – uses the instruments to give classes to around 70 children and also directs weekly orchestra practice.

But he has a goal that goes beyond music. Chávez believes the mentality required to learn an instrument can be applied more widely to lift his pupils out of poverty.

Paraguay is the fastest-growing country in the Americas, but nearly a third of its population lives below the poverty line. The gancheros and their children live in slums, called bañados, which occupy the swamps between Asunción and the River Paraguay.

"The state does nothing," says Gladys Águilar, 61, from a shantytown next to the landfill. "Politicians put a sweet in our mouths with their promises. But when they are elected all they care about is power and the sweet turns bitter."

Chávez recognises the shortcomings of the government, but says families can improve their lives by considering the long term. "Poor people need to eat today," he says. "They don't think about tomorrow's problems. But learning music means you have to plan. It's very challenging to explain to a child who lives in adverse conditions that if his dream is to play the piano he needs to sit on a stool for five hours a day."

Many parents also struggle to see the advantages of such an attitude. "Most tell their kids that a violin can't feed you; that they need to work to eat," says Jorge Ríos, 35, a recycler whose two daughters play in the orchestra. "But thanks to that violin my kids have seen new countries. They have an opportunity for a better future."

Ada and Noélia Ríos started attending Chávez's classes in a chapel two years ago after their grandmother, also a recycler, signed them up. They enjoy Chávez's strict regime, practising for two hours a day at their home – a shack with earth floors in the San Cayetano slum – and have travelled around Latin America with the orchestra.

"My dream is to be a musician," says Noélia, 13, clutching her guitar, made by Gómez from two large tins that once contained a Paraguayan sweet potato dessert. Her 16-year-old aunt, María Ríos, also plays in the orchestra.

"Going to other countries has opened my mind so much," says Ada, 14, a violinist. Following the trip to Amsterdam – its first outside of South America – the orchestra will play this year in Argentina, the US, Canada, Palestine, Norway and Japan. Chávez has also received an invitation to play at June's Meltdown festival in London.

Like her sister, Ada hopes to become a musician and also dreams of owning a Stradivarius violin, worth millions of pounds. But for now she is more than content to play her current instrument, whose face was taken from an old paint tin. "I don't care that my violin is made out of recycled parts," she says. "To me, it's a treasure."