Air France Flight 447 crash: Stall warnings?

I just have a question about the AF 447 crash. It say that the two (co)-pilots in control of the aircraft minutes before the crash attempted to gain altitude even though the STALL WARNING system activated. Would the correct procedure not be to point the nose down in this situation to gain airspeed? Why were they trying to gain altitude during a stall!? Is it possible that the IAS was reading higher to them and they ignored the stall warning?