The speed was decreasing and alternate law mode is activated by the system

1. 
   To avoid turbulence, the first officer directed the plane a little bit left instead of move up because the captain suggested the altitude already maximal and the temperature was decreasing slowly. This action required the automatic pilot system off. In this situation the man in action should be the captain instead of assigned to first officer.
   
2. 
   The speed indicator went wrong by showing low speed level. First was showed by left PFD and then followed by ISIS. However, only the speeds displayed on the left PFD and the ISIS are recorded on the FDR; the speed displayed on the right side is not recorded. In addition, the altitude was falling as well.
   

3. 
   First officer try to nose up and thrust up the 447 to gain expected altitude level and speed level. This action made the stall warning activated.
   
4. 
   The speed was decreasing and alternate law mode is activated by the system.
   

Note 2 : In alternate or direct law, the angle-of-attack protections are no longer available but a stall warning is triggered when the greatest of the valid angle-of-attack values exceeds a certain threshold.

At this moment, the pilot seems did not realized that the plane has a protection against stall problem if the alternate law is operated in autopilot mode. As an action, the pilot nose down the plane.

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First, the pilots may have assumed that 447 could not stall, because the Airbus’s computers are designed to prevent this from happening. The crew may not have realized that most of the built-in protections were bypassed when the plane flipped out of autopilot.

Second, on most commercial airliners, the right and left seat controls are linked; on such a plane, Robert would have been able to detect Bonin’s mistaken decision to lift the plane’s nose and correct it. For unclear reasons, the Airbus designers delinked the 330’s controls, which made it possible for Robert, and later the pilot Dubois (who returned to the cockpit as the plane was falling), to remain unaware of Bonin’s error until it was too late to fix.

Third, the technological sophistication of modern aircraft means that new pilots are no longer well trained in flying without the assistance of modern gadgetry. When the computers break down, many young pilots are at a loss. “Some people have a messianic view of software, meaning that it will save us from all our problems,” aviation safety expert Michael Holloway told PBS’s NOVA. “And that’s not rational, or at least it’s not supported by existing evidence.” Many older commercial airline pilots first earned their wings in the military, where they gained experience in flying manually, sometimes without power or while dodging hazards like mountains and missiles. Bonin may have erred because he hadn’t received sufficient training to ensure the correct response.

Even these problems might not have been enough to allow an intact modern jetliner to fly into the ocean. The interaction between the two co-pilots during the moments of crisis demonstrates remarkably poor communication, despite their training in crew resource management. Moreover, there was a marked lack of situational awareness, with everyone focusing on a few small details while ignoring a blaring cockpit alarm, which repeated the word “stall” 75 times before the plane crashed.

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It is pretty easy to see how the accident can happen, without anyone making mistakes other than the copilot. First, the airspeed indicators become invalid due to icing. Copilot, already nervous and jumpy, provides a nose-up input. Stall alarm sounds, but the airspeed indicators are invalid, so they may have dismissed the stall alarm as a system malfunction. Eventually, the airplane ends up in a configuration where it is flying so slowly that the airspeed indicators (now clear of ice) are invalid due to low speed, and the copilot is still providing a nose-up input. To the other pilot, this looks pretty much like a normal cruise/climb configuration, except he does not know what the airspeed is.

At this point, they are slightly nose-up, but with full throttle (and no airspeed indications). It is clear the plane is descending, but why? The nose-up attitude is quite shallow, and the airplane should be climbing (and it would be, if it were not flying so slowly). The other pilot, unaware of what the copilot is doing, wonders if they are in a stall (despite the lack of the horn), and provides a nose-down input. Now the airspeed indicator becomes valid, and the stall horn sounds! He backs off, and the stall horn turns off. So, from his perspective, they are not in a stall, but they are right on the edge of one, except it occurs with decreasing attitude! This makes absolutely no sense.

All the while, there is moderate to severe turbulence. At this point, he doesn't know what's happening, because the stall horn behavior is totally backwards from what he expects, so he's confused, and he's probably starting to panic, so his chance of figuring things out gets even smaller. "Why does the stall horn sound when I lower the nose?" "Why are we descending even though we're at only a 10-degree nose-up attitude with full throttle?"

They had a discussion about whether they were climbing or descending because the situation, from their perspective, was so bizarre. And remember that they were flying through a thunderstorm, and had just observed rare electrical activity (St. Elmo's fire), smelled a funny smell, and just witnessed the airspeed indicator stop working. It is perfectly reasonable for them to not trust their remaining instruments. As I said, if not for the copilot's stick input and the low airspeed (both of which were unknown to them), everything else about the control settings in the cockpit corresponded to a climb.

http://www.flightglobal.com/blogs/learmount/2011/05/air-france-447-the-facts-and-w.html

http://www.economist.com/blogs/gulliver/2011/12/air-france-flight-447

http://spectrum.ieee.org/riskfactor/aerospace/aviation/air-france-flight-447s-final-minutes-reconstructed

file:///D:/British%20Activity/Study/2011-2012/CO886%20-%20Software%20Engineering/Project1/AirFrance447/The%20Benefits%20of%20Risk%20-%20IEEE%20Spectrum.htm

http://www.popularmechanics.com/technology/aviation/crashes/4338827

http://community.the-hospitalist.org/2011/12/31/the-crash-of-air-france-447-lessons-for-patient-safety/

http://boards.straightdope.com/sdmb/showthread.php?t=634445

http://cdn-www.airliners.net/aviation-photos/photos/1/0/9/1531901.jpg

http://www.ahrtp.com/RSS-JSfeeds/AF_447_weather_pitot_tail_hypercomplexity-1.html