In East Legon, a smart suburb of Ghana's capital, Accra, two men and a woman in their 20s stand in front of a slick ad featuring a large plane in mid-flight. They are pitching a business idea for a website that would allow travellers to compare ticket prices, then book and pay for airline tickets on domestic flights.

The pitch has sparked a lively debate among the pupils who sit in a darkened classroom, with the words "generosity, positivity, standards" emblazoned on the wall. The students, who nod seriously at the feedback, are on the first year of an intensive training programme at the Meltwater Entrepreneurial School of Technology (Mest), a postgraduate school that offers university graduates – some with no prior experience at all – a two-year course in software programming and business development.

Mest provides its students with housing, pocket money, meals, transport and a laptop – free of cost – and, in return, it expects full concentration for two years of full-time study. Its teaching staff say that the transformation after students have been through the process is extreme. "When they join, they probably haven't written two lines of code before. Next year they are creating apps left and right," says Unni Krishnan, senior faculty member at Mest.

It is widely acknowledged that intensive training of this kind – which Mest says is producing world-class software engineers and businesses – is exactly what is needed in West Africa. But, like many of its neighbours, Ghana is still a country of contradictions, with pockets of world-class innovation coexisting alongside chronic poverty.

The mobile penetration rate in Ghana, which is now a lower-middle income country, exceeds 100%. Of a population of 24 million, 17 million people own a total of 27 million mobile phones. The six telecommunication companies operating in the country earn an average daily income of about $10m (£6.2m).

The Ghanaian company RLG is increasingly popular in West Africa with its locally manufactured laptops, smartphones and tablets. Last month it added a Ghanaian tablet, the "G slab", invented by a 28-year old as a rival to Apple's iPad and Samsung's Galaxy tablet.

Yet the Ghanaian education system still teaches through a Victorian English-inspired system of rote learning. In many schools, IT is taught in classrooms with no electricity, let alone access to computers, and pupils are asked to copy out pictures of a desk monitor and keyboard into their notebooks.

"The Ghanaian education system is not generally producing people who are innovative," says Mac-Jordan Degadjor, a tech blogger and entrepreneur who has raised the profile of tech startups in Ghana. "We need to start focusing on entrepreneurial skills as a topic within schools, and make sure that by the time you get to university, you are not just thinking about applying for jobs, but starting something for yourself."

But, like those of many African countries, Ghana's tech entrepreneurs are thriving in spite of what is often perceived as a far from ideal environment.

Mobile applications for money transfers, bypassing the lack of access to formal banking for many rural dwellers, and for farmers who need real-time updates about prices and help accessing marketplaces, are examples of how developing country problems have only created opportunities for local entrepreneurs to come up with innovative problem-solving.

"The exciting thing is that there's a new generation of technology entrepreneurs in Ghana who are starting to transform the country," says Dr Sipho Moyo, Africa director for anti-poverty charity One, which is supporting tech innovation in Ghana. "I have high hopes that their innovation can accelerate progress right across the continent, thus shaping its future."

"Could the next Google come from Africa? Why not?" says Richard Tanksley, entrepreneur and senior faculty member at Mest. "Our whole business model is to produce a globally successful software company in the next five years, and we have every reason to think it will happen.

"There is so much focus on Africa as a place to invest, to build businesses, there is no reason why you couldn't have multimillion dollar software companies coming out of here."

Eyram Tawia, Leti Arts

Walking into the office of Leti Arts is a bit like walking into a teenager's bedroom. Behind a closed door, on the ground floor of what is still a partly residential building, a room opens up, the walls plastered with giant comic figures of superheroes, dressed in bright Lycra with clenched fists and coloured lights emanating from their eyes.

But the half-dozen people sitting in this office are not playing games. They are working on a project they believe will revolutionise the way Africans relate to their folklore and history, by modernising ancient stories for a younger audience through games and comic strips on mobile phones.

"We are not even good at preserving our history and folklore – we watch Thor, the Nordic god of thunder, or Superman, Spiderman, Captain America, Batman," says Eyram Tawia, 29, co-founder of Leti Arts.

"But Africa has a lot of stories, voodoo and tradition that have been almost lost and can be brought back. Why not bring back a pharaoh from Egypt and turn him into a fantasy character? Why not bring back Yaa Asantewaa, the famous Ghanaian female warrior?"

Yaa Asantewaa – who led Ghana's Ashanti people into battle, famously defeating the imperial British army – has until now only been accessible through oral history and dense academic tracts. But, reinvented, she looms large on the wall of the Leti Arts office, appearing as never seen before with a tiny waist, ample cleavage, six-pack and bulging biceps in the unmistakable guise of a female superheroine.

"History in school is so boring," says Tawia. "You have to read through 1,000 pages of textbook to learn about Yaa Asantewaa. You have to listen to about 15 cassettes to learn about Shaka Zulu. Modernising culture is very necessary to preserve the story for the new generation."

The Leti team designs games, which Tawia codes himself, and has produced "Africa's Legends" comic editions – described as an "African Avengers" – available on mobile devices through a free app, with some comics free and some paid-for.

The company is already generating its own revenue by building technology which it licenses to other companies, including a game for training health professionals on childbirth and a greeting card app made from a customised version of its server.

Leti Arts is already a viable business but Tawia says he hopes it will be much more than that. "We are getting exceptional people to do really innovative things," he says. "We are not just creating a company, we are building a whole new industry. Nobody has had job titles like 'lead illustrator' or 'game developer' in Ghana before. Now when I go to conferences, I meet lawyers, doctors, I say I'm a 'game developer' – it feels good."

Mac-Jordan Degadjor, tech blogger

For tech people anywhere in Africa, this is a familiar sight. A dapper, 6ft 4in young Ghanaian, wearing Ray-Bans, a smart navy blue suit and brown beads around his wrist, sits engrossed in a laptop emblazoned with "Make Fufu not War!" and a sticker marked "I do not consent to the search of this laptop".

"They tried to search it once!" exclaims Mac-Jordan Degadjor, referring to when Dutch authorities insisted on gaining access to his laptop at Schipol airport. His beloved machine now bears the sticker as a form of protest.

Degadjor is no stranger to run-ins with the authorities. The 28-year old first began his blog, macjordangh.com – now renowned as one of the best tech blogs in Africa – as a young student in Ukraine, frustrated with persistent racism and unwanted attention from the authorities.

"I started blogging because of the way the Ukraine police were targeting African students – harassing them and extorting money from them if they were not carrying their passport," he says. When he returned to Ghana, he realised that there was very little blogging going on back home, and what there was was not engaged with tech and innovation.

"In Ghana we are still talking about political parties, about corruption," he says. "We are behind other countries. Kenya has a goal to achieve broadband penetration of 100% by 2015. We are still below 20%."

Degadjor's blog is now at the forefront of a change in Ghana. Despite the undoubted challenges in a country where basic infrastructure is still lacking – with erratic water and electricity supply even in major cities and poor roads – the Mac-Jordan Degadjor blog is a hub of startup tours, hackathons, tech ideas, and good news for those who care about Africa's place in a tech-driven world.

"There are challenges, but the tech revolution is happening all over Africa," says Degadjor. "Day in, day out people are getting together at hacker spaces or innovation centres, and gradually ideas are coming up from these hubs."

Now Degadjor is working on a project called AfroPreneus Web-series: How We Made It – a web series of 30-minute interviews with up-and-coming entrepreneurs across tech, fashion and social ventures, with a particular emphasis on featuring female-led businesses.

"This is about celebrating African entrepreneurs," he says. "So our target is to share these stories across the blogosphere, so that other young people coming up in Africa can know that when they finish school, they don't have to struggle to get a job, when there is so much unemployment – they can start their own company."

Nicole Amarteifio, social media strategist and online TV creator

In 2010, Nicole Amarteifio was sitting in a class for her masters degree at Georgetown university in Washington DC, feeling upset. She was studying corporate communications, and a guest lecturer had come to discuss development.

"This American woman did a presentation on development communications, and every African woman in it had a pot on her head and was half naked except for strings of beads" says Amarteifio. "I was very upset. Afterwards I told my professor; this is not the story of the African woman. It is only part of it."

For Amarteifio, whose Ghanaian parents raised her in London and the US from infancy, the sense that what was really happening in Africa was not being communicated was the catalyst she needed. After graduating, she went on to become a social media strategist on Africa at the World Bank.

"Social media has really changed the discourse for young people in Africa," she says. "The Africa region of the World Bank has been there – we had the first Facebook page, the first Twitter page – we are online, talking to young people on the continent, we are in their space. Africans are excited about it. Now you can tweet your president. The gap was so big before."

Using social media to involve Africans in a global discourse about their own future – which Amarteifio continues to do as a consultant – was part of her project to bridge the gap between the Africa she knows and the one the rest of the world sees.

But there was another side to life as an African woman Amarteifio felt was still not being communicated – life as a single, young woman living in the Ghanaian capital Accra – or what Amarteifio describes as a kind of African Sex And the City.

"When I first saw Sex And The City, I just thought these women were so authentic – they are discovering their sexuality and talking in such an open way. But the gap between their experiences and my experience discovering the same things in Africa was so big."

In 2009, Amarteifio began writing her own series, An African City, set in Accra with characters from all over sub-Saharan Africa. But despite interest from TV channels, she is deliberately broadcasting the first series entirely online.

"By going online, I don't have to be dictated by TV networks about what they do or don't want to see," she says. "My show certainly pushes the boundaries – it is about five women who talk authentically about love and life, and that includes sensuality.

"People will be shocked, and some people will be angry – especially some African men. But by putting my show online I have the creative freedom to talk about these sexual politics. It is all about the conversation."

Ben Nortey, robotics innovator

Ben Nortey's sixth-floor office is one of the last places you would expect to find robots. Next to Makola market, the chaotic, pulsing centre of urban Accra, the Metro Institute of Innovation and Technology (Mint) is just one, neat room in a tower block which is surrounded by the commotion of traders, hawkers and shoppers on one side, the vast, misty Atlantic ocean to the other, and Accra's slow-trawling traffic all around.

But inside is a rare oasis of scientific order. Bookshelves lined with titles such as Algorithms from P to NP and Programming Language: Concepts and Constructs sit side-by-side with a neat array of robots – most made from scrap materials such as plastic bottles, colourfully painted, alongside electronics equipment, tools and robotics kits.

Nortey, an energetic 27-year old Ghanaian computer science graduate with an infectious smile, loves robots. "As a child I had a lot of interest in these kinds of creatures – I loved movies like Transformers," he says.

Since there is virtually no robotics teaching in Ghana, Nortey taught himself. "I worked out how to build robots by reading books, and by looking at what other people are doing on the internet and experimenting," he says. "I spent hours on the internet – it has been a serious resource for me. And I have taken online courses on open platforms, like one from MIT and one from Stanford."

Nortey's vision is that in 20 years' time he will be building sophisticated robots in Ghana: "In this part of the world, we start everything too late. In Ghana, many computer science students write their first computer program code during their first year in university. But I read stories of 12-year- olds in other countries who have built apps, put them in a store online and made loads of money. I want to transfer this knowledge."

Nortey's company runs private classes for young people with a natural passion and interest in robotics, as well as other computer programming areas such as creating apps and gaming. One of his proudest achievements is teaching a five-year-old how to write code.

"This five-year old learned how to program motors and micro-controllers. He could understand concepts like loops which some people find quite complex," Nortey explains. "He is exactly the kind of child I want to work with!"

Nortey is going to present a new TV programme called Scrapbot which will be a kind of Blue Peter-style "how to" show about building robots from scrap for children. So far Mint has trained around 2,500 people in Ghana, and Nortey hopes that through Scrapbot, they will reach many thousands more.

"I'm currently looking at an intelligent system to help deal with the traffic situation," he says, gesturing towards the gridlocked roads outside.

"And we have oil and gas in Ghana, but we have not harnessed the potential of technology to monitor the environmental effects – we could be embedding sensors into microcontrollers and collecting real-time data.

"It is possible for Ghana to produce this kind of technology – we just have to take it seriously."