In Acts 5:34, a Pharisee, Gamaliel, seems to be somewhat sympathetic to the apostles. At least he is credited with saving their lives. Later on, however, in Acts 22:3, Paul states that he learned about the law of the fathers at "the feet of Gamaliel." It was this learning that led him to be "zealous toward God," which was the basis for his subsequent persecution of Christians. Are we talking about the same Gamaliel in both events? And does that also suggest that Gamaliel had a change of heart regarding Christianity?
Most scholars do think the stories refer to the same Gamaliel – at least those who give the stories any credibility at all. There are a few historical problems with the accounts in Acts. You will recall in 5:17ff that the apostles had been preaching in the temple about Jesus – despite having been commanded by the Sanhedrin not to do that very thing. Since this was their second offense, they were arrested and thrown in jail by the Sadducees. That night an angel led them out of prison and told them to preach again at the temple the next morning. When the Sanhedrin gathered the following day to determine their fate, they discovered the doors of the prison were intact, but the apostles were nowhere to be found. It says, "The chief priests were 'perplexed'."
Subsequently, the apostles were discovered preaching in the temple (just like the angel had instructed them to do). Embarrassed and angry, the Sadducees were so determined to put a stop to the work of the apostles that killing them seemed to be the only good option. That is when Gamaliel stood up and cautioned against acting too hastily. His argument was very theological. He basically reminded the members of the Sanhedrin that not too long ago two other men had appeared. One was Theudas; the other was Judas, the Galilean. Both had big followings, but shortly after their deaths, everything just fizzled out.
Maybe the same thing would happen with Jesus' followers. His advice was to "Leave these men alone. Let them go. For if their purpose or activity is of human origin, it will fail." In other words, if Jesus is a charlatan, then they wouldn't have to do anything. On the other hand, "If this is from God, you will not be able to stop these men; you will only find yourselves fighting against God." Basically what he was proposing was a "wait and see" policy. Time would be the arbiter on this one. Regardless of his position, Gamaliel had enough clout that the members listened to him. Of course, they could not let the apostles waltz out without some punishment for ignoring the commands of the Sanhedrin, so they ordered them to be flogged before being released.
All in all, it is one of the best stories in Acts. The problem is that Theudas was executed in 44 CE, roughly a dozen years after Gamaliel's speech. His rebellion hadn't even happened yet. That raises a lot of questions about the historicity of his speech. It could have been tweaked or actually inserted into the story by the author of Acts.
On the other hand, there really was a prominent Pharisee by the name of Gamaliel in the first century. Many scholars believe he was the grandson of Hillel. He died 18-20 years before the destruction of the Temple. The Talmund refers to him as "Gamaliel, the Elder." He was the first to be called "Rabban," which means "our teacher." This Aramaic word was given to certain distinguished teachers to set them apart from ordinary rabbis. His name is the Greek form of the Hebrew, which means "reward of God."
Since Paul was a very zealous young man, it is entirely possible that he would have tried to learn from one of the more prominent teachers of his day. Still, we know nothing about any relationship between them. Nor are scholars convinced that Gamaliel converted, as Paul would do later. Early Christian tradition fostered that viewpoint, even claiming that he had been baptized and martyred for his faith. Apparently, at one point, he was considered a saint, but events involving his latter days cannot be verified.