The "free-market" reforms being instituted at the time were the shedding of responsibilities of the Chinese state by "privatizing" state-constructed factories via the (often secret) sale of the factories to party members, in other words they went from statism to crony-nepotism. The workers were unaware that these sales were going on and that their state jobs were no longer guaranteed, nor were they part of the public pension system, but effectively serfs to regional power brokers of the party.
Transparency, end of state-party corruption, and the guarantees of political and economic freedom were pretty much what I remember being called for at the time during the news coverage. Tank man was right at the end just before everything went off the air, and has stuck in people's minds because he was just a dude coming back from shopping who decided he'd had enough.
These were the seven demands drafted by the students in Beijing (from Wikipedia):
1. Affirm as correct Hu Yaobang's views on democracy and freedom;
2. Admit that the campaigns against spiritual pollution and bourgeois liberalization had been wrong;
3. Publish information on the income of state leaders and their family members;
4. End the ban on privately run newspapers and stop press censorship;
5. Increase funding for education and raise intellectuals' pay;
6. End restrictions on demonstrations in Beijing
7. Provide objective coverage of students in official media.
Transparency, end of state-party corruption, and the guarantees of political and economic freedom were pretty much what I remember being called for at the time during the news coverage. Tank man was right at the end just before everything went off the air, and has stuck in people's minds because he was just a dude coming back from shopping who decided he'd had enough.