I think that Peter didn't have enough time to fully reach the fourth level, so I would say he belongs in the third level because he isn't able to subconsciously act like the people around him, he still needs to put in effort in order to act culturally appropriate. .
Since Peter is at level three, I believe that he was getting close to cultural competence in several ways, such as trying to learn the language. It's important for anyone trying to reach cultural competence to learn the language because then they are able to speak with the locals, read signs, communicate efficiently, and learn about the differences in cultures. When Peter got to Fuling, he quickly discovered that almost nobody spoke English there except for his students and Adam. Both of them tried to find tutors as soon as they could, but they weren't able to get English speaking teachers, so they had to do with teachers that only spoke Chinese. Many people would find this frustrating and too difficult to continue on with, but both of them knew they were going to be there for two years and needed to learn the language. Their determination is really what helped them learn the language because without determination, they would have given up quickly and also would have never been able to speak to anyone in the city fluently.
I think Peter showed some sign of cultural competence because he made attempts to talk to the people that were from Fuling. This could be a sign of cultural competence because Peter is trying to learn more about the culture that he is immersed in and understand the cultural norms. In River Town, Peter would travel to the city and instead of wandering around he would often stop to talk to a photographer named Ke Xianlong and he would also go to a teahouse and talk to people that stopped out of curiosity (Hessler, pg. 140). He would usually stay there for hours reading his textbook and talk to people that wanted to learn more about him because he was a foreigner to Fuling.
