As we drove through Baghdad's neighbourhoods, essentially the only car on the road except for military and police, we came across entire families making their way on foot to polling stations. With a ban on vehicle traffic, people here were given no choice but to walk, in some cases, up to 10 kilometres some with canes, others in wheelchairs, to cast their vote in a referendum they believe will reshape their future.

We came across a heavily guarded school for girls, doubling as a polling station. Out front a small legion of little children welcomed us with shouts of "mister, mister"… there's no gender differentiation here if you're a Western woman -you are afforded the same greeting as a man - it's still a great novelty for them to see an uncovered woman, working side by side with a man. I say uncovered but in reality it is still imperative to wear long sleeves, which at 45 degrees Celsius gets a little warm.

Heavily armed Iraqi police, numbering in the dozens at this one school, tried to quiet the children but their smiles betrayed them. Our camera was a novelty for police also and they eventually worked up the nerve to ask for a photograph. Using cell phone cameras, about six officers positioned themselves one by one, beside me, huge grins, eager to be seen as a friend to a foreigner.

Inside the school, through the warren of classrooms, voters, most of whom hadn't even read the constitution were exuberant again over the second time in nine months, to dip their finger in blue ink and mark a ballot. All of the people in this polling station were Shia, oppressed during the Saddam era, and now highly supportive of the constitution.

They see it as one more door closing on their past. A sweet celebration, one man told me, adding that he wished they would also put Saddam's verdict to a National vote, confident the death penalty would result.

During the January elections, the sound of gunfire and mortar attacks was constant throughout voting day. This time was very different. Despite threats from insurgents to wreck the referendum, there were only 20 attacks in Baghdad - compared to 120 in January – and not one suicide bomber. A sign of progress or part of an insurgent strategy? The answer may become clearer when vehicle traffic is allowed back on the streets.

I walked in one classroom and there were two sisters, a brother and their mother, all working as election officers. I'd met the family in January and we immediately recognized each other. There were big hugs and kisses, not surprising given that this environment tends to create fast friendships considering the uncertainty of the future.

I was fascinated to see how strong and confident the women of this family were, very protective of their brother who was the only man in the family now. They wouldn't allow him to go on camera for fear insurgents would see his picture on the Internet and track him down.

The women, on the other hand, were so open with their concerns about the constitution and how it lacked the necessary elements to establish equal rights. Islamic law still controls their lives. They are forbidden to have a passport or travel without a family male escort, forbidden to divorce without permission from a husband (rarely granted), and are still beaten for wearing bare arms.

Unlike other established democracies the Iraq draft constitution doesn't act as the supreme law of the land. Even it is passed, the rule of Islam will still rank higher.

These Iraqis women hope for a day when Iraq will have a secular not religious government. Only then, they believe will women be equal.

I admired their bravery and honesty, and was struck by the very long journey that lies ahead for them, before Iraq can become a functioning democracy, if ever.