In 2001, I hosted an event for reconciliation between Indigenous and non-Indigenous Australians. In the room were a former prime minister, a then opposition leader, assorted other politicians and leaders of business, media, academia, sport and culture. All had paid handsomely to eat good food, drink nice wine and listen to heartfelt speeches about the need for healing in our country.

As I welcomed the guests, I asked all the non-Indigenous people in the room to stand and for all the Indigenous people to thank them. Then I asked them all to remain standing.

"If anyone here has a close friend or family member who is Indigenous please sit down", I asked.

A few took their seats.

"If anyone here has shared Christmas dinner with an Indigenous person please sit", I continued.

Again a handful sat.

"If anyone has had one of their children’s Indigenous school friends over to stay please take your seat".

And so it went on, until it became embarrassingly obvious that even in a room of great goodwill, we were such strangers to each other.

I'm sure if I asked those same questions of a similar room today I'd get the same response. And it isn't at all surprising. There are great numbers of Australians who in the regular course of their lives have no contact with Indigenous people, and it is not just because we are roughly only 3% of the population.

Even in 2014, we are largely invisible. We simply don't figure in the broad spectrum of Australian life.

Yes, Australians marvel at the athletic talents of Indigenous stars like AFL's Buddy Franklin or NRL's Greg Inglis. Footballer Adam Goodes is even our current Australian of the Year. We can dance along to songs from Jessica Mauboy and watch feel good movies like The Sapphires and sometimes enter the world of television drama like ABC's Redfern Now.

Facebook Twitter Pinterest Adam Goodes, Australian of the Year. Photograph: Mark Metcalfe/Getty Images

But beyond these popular and talented examples, I'd argue an acceptable face of Indigenous Australia, there is a far deeper and painful malaise.

Consider this: in over a hundred years of federation, we have never had an Indigenous federal cabinet minister. Only now has the ALP even managed to get an Indigenous person into Canberra, Olympian and now senator Nova Peris. The Liberal party has MP Ken Wyatt. Together Peris and Wyatt represent the total of Indigenous representation in our nation's parliament.

Before parliament opens, Indigenous dancers are trotted out, there's a smoking ceremony and an elder performs a Welcome to Country and then we are ushered off the stage while Armenian-Australians, Asian-Australians, Greek-Australians, Lebanese-Australians, Italian-Australians, Anglo-Australians make decisions that will determine our lives. Our federal finance minister, Mathias Corman, is a Belgian-Australian who migrated to Australia less than 20 years ago (and full credit to him). Are we entitled to ask "when will the treasurer, or finance minister or heaven forbid prime minister be Indigenous?"

And it isn't just politics. Where is our high court justice? Where is our federal government department head? Where is the Indigenous person running one of our four major banks? Heading one of our leading hospitals? Damien Miller, recently appointed as Australia's ambassador to Denmark, is the first Indigenous person ever to represent this country at that level at a foreign mission.

An example I'm very familiar with is the media. For near three decades, our national broadcaster has been training young Indigenous cadet journalists – but look around. Is there an Indigenous person reporting on Four Corners, or as a foreign correspondent? Are they reporting from Canberra? Or Washington, London? Moscow? Beijing? Jerusalem? Yes there are a few scattered through the organisation, but this situation is pitiful and for the ABC frankly embarrassing.

Of course people may point to me and a career that has spanned the globe as a correspondent and news anchor for CNN. Yes, I have been fortunate and I have made the most of my opportunities. But I spent much of my early career here assiduously avoiding covering Indigenous issues for fear of being typecast and marginalised (ironically the more successful I became, the more some people questioned if I was even truly Aboriginal!). It wasn't until I moved overseas that I felt liberated from the weight of history and low expectations.

Facebook Twitter Pinterest Senator Nova Peris with Julia Gillard. Photograph: Lukas Coch/EPA

Sadly, still, for most Indigenous people, meaningful, mainstream achievement and recognition remains elusive. This doesn't happen by accident. It happens by exclusion. It happens when after two hundred plus years since settlement, Indigenous peoples are still the most disadvantaged in the community. We still die too young, are over represented in prisons, have the worst health, employment and educational outcomes.

It happens, when added to the neglect and suffering, is a lack of imagination of a country that still struggles to see us as an integral part of the nation. We remain a people apart, still marginalised, still the other; sometimes exotic, sometimes pitied, sometimes repulsive.

But why shouldn't Australia lack imagination? Look at our constitution, like other aspects of life there too we are invisible. There is no mention of Australia's Indigenous people. In fact, jurists have argued that the constitution actively disadvantages Indigenous people.

As it stands, the constitution contains what are referred to as race powers, Section 25 allows the disqualifications of persons of a particular race from voting. Section 51 provides for the enactment of racially discriminatory laws. We saw that with the 2007 Northern Territory intervention argued on the grounds of protecting Indigenous people.

Now all of this is up for debate with a proposed referendum to constitutionally acknowledge Indigenous peoples. In 2010, all major political parties committed to holding a referendum. Despite such multi-partisanship, the date for the vote has been pushed back as consultation and education continues.

It is no easy process. For a start, Australia lags other countries where Indigenous peoples have established new constitutional arrangements. Indeed, nations like the US, Canada and New Zealand have negotiated treaties, whereas here, the concept has never gained political traction and is right now barely imaginable.

Referenda are difficult to pass. Of 44 put to the Australian people, only eight have garnered the requisite majority of people in a majority of states. Crucial to success is the clarity and wording of the question.

A question of acknowledging Indigenous peoples in our constitution immediately raises hoary old fears of a nation divided; the creation of two peoples. There are crucial issues of how to represent the multiplicity of Indigenous nations within Australia, each distinct and proud of uniqueness. What of the incorporation of customary law practices? What does it mean for questions of Indigenous sovereignty?

NITV hosts an Awaken special this evening, which grapples with these questions. It is passionate and at times emotional. Some Indigenous people still see European settlement as an invasion and the current Australians illegal occupiers.

Darlene Hoskins-McKenzie, an activist and PhD candidate, defiantly says she has never ceded her sovereignty as an Eora woman. Others see constitutional recognition as yet another white man's trick, a fig leaf to cover the real questions of recognising Indigenous ownership and sovereignty of this country. To others, it is a chance for healing, to redress injustice, ignorance and neglect. To right the wrongs of history and tell ourselves and the world that Indigenous people in Australia are the original people of the land and valued as central to the nation's very being.

For me, it is not a panacea for disadvantage or an act that will remove all that still divides us. But it does go to removing the cloak of invisibility. It is about firing this nation's imagination, and helping to tap our potential.

I'm tired of seeing us as an anthropological curiosity to be wrapped in possum skin and welcome you to our country. I'm tired of seeing us daubed in paint and dancing in lap laps. Yes, ceremony has its place but in modern Australia I want us in our boardrooms, our operating theatres, in our highest courts and our highest parliaments.

I want outstanding people like Linda Burney not just NSW opposition leader, but as premier. I want actors like Deborah Mailman or Aaron Pedersen on stage at the Oscars. I want to see an Indigenous person as treasurer of Australia deliver a federal budget, and have it reported on television by a senior reporter who also happens to be Indigenous. Rather than play football, I want the chief executive of the AFL and NRL to be Indigenous.

I don't want us on the margins. I don't want us to achieve in designated Indigenous endeavours. For this to happen, we can't be strangers. You have to see us. You have to recognise us, and it starts with our constitution.

• Awaken: constitutional recognition special, 28 May at 8.30pm on NITV