Its not been easy for Iraqi troops to adapt. The Russian style made it easy to goof-off and just go through the motions. The American approach includes frequent testing. You have to remember what you learned, or the American trainers will make you go through the lessons again. But the Iraqi troops who stick with it, find themselves much more effective in combat than any previous Iraqi troops. Even Saddams elite Special Forces and commando units were not as good as these new SWAT teams and special infantry units. But the American approach holds out even more promise, because it assumes that every Iraqi infantryman is capable of operating like a SWAT team. The Iraqis see the American infantry doing this all the time.
The only downside is that the American approach is expensive. When Saddam was in charge, infantrymen would be lucky to fire two or three dozen bullets from his AK-47 each year. Other weapons training was equally meager. There were plenty of tactical drills, but not much in the way of tests and exercises like the American trainers insist on. The American also insist on lots of live firing exercises. Veterans of Saddams army find themselves firing more bullets in one month of this American style training, than they did during a decade of service for Saddam. Same with other weapons, from machine-gun to tank cannon.
The American training also makes big demands on NCOs and junior officers. This is something radically new for the Iraqi military. The younger troops eat it up, the more senior officers have a hard time adapting to all this initiative among their subordinates. But with so much terrorism going on, the government is telling the colonels and generals to let their troops do their job, and not try to micromanage (as the Russians taught.)
Many Iraqis, especially Sunni Arabs, still adhere to the old Iraqi style of warfare (whoop and holler, and charge forward shooting at everything in sight). That approach is proving consistently fatal when it goes up against Iraqis trained in the American style. The Iraqis operating like this have plenty of live examples to copy, and copy they do. Many Iraqi troops carefully watch U.S. troops they are operating with, and copy their moves and gestures. Iraq gets a lot of media coverage as the people try to adopt the American style or government. Unnoticed is how quickly Iraqis are adapting the American style of fighting as well.
The new Iraqi army is going through a generational shift, with a new package of tactics and techniques being taught to a new generation of recruits. Previously, the Iraqis had used what they learned from Russian advisors. The Russian techniques, derived from Russian traditions, and experience during World War II, were based on tight control from the top, and troops going through simple, and well rehearsed, drills and maneuvers. Improvisation and initiative were not encouraged. Naturally, Saddam, and many other Middle Easter despots, liked this Russian approach. However, these tactics proved ineffective, time after time, when they went up against troops, usually the Israelis, who were trained in the more flexible Western style. Arabs did not like to dwell on this string of defeats at the hands of the hated Israelis. But then the Americans did it to the Iraqis in 1991, and 2003, beliefs began to change. Russian military techniques are out, American techniques are in.