The jurors almost unanimously vote guilty at the start of the play. While many of the jurors do simply believe the defendant is guilty of murder, other factors, such as the sweltering heat of the courthouse and the desire to get out of jury duty as soon as possible, sway them to vote as they do.
The main thing which causes most of the jurors to change their vote is Juror Eight's call for further examination of the evidence. Juror Nine changes his vote because he is impressed by Eight's courage in offering a contrarian view and wants to re-examine the evidence too.
Slowly, the other jurors start to question the evidence themselves. Five does not believe one of the witnesses, an elderly and feeble man, could so easily run out of bed to witness the crime, nor does he believe the defendant stabbed his father with a switchblade since, as a former slum-dweller himself, he knows how fights are conducted there. Nine does not believe the woman witness could see well since she was not wearing her glasses at the time of the crime. The jurors also come to re-examine their own prejudices against the defendant, particularly when Ten goes on a racist rant.
The jurors who do not take the trial seriously and just want to go home, such as Juror Twelve who is largely indifferent to the case and Juror Seven, who wants to leave so he won't miss a Broadway show (or in the movie, a baseball game), just agree with the majority so they can leave sooner. However, Juror Three is the last to hold out is Juror Three. In the play, he gives in when he sees everyone else is against him. In the movie, he realizes his insistence on voting "guilty" has more to do with his anger at his son than a genuine belief in the guilt of the defendant.
In some ways, all the jurors in "Twelve Angry Men" except Juror Eight change during the course of the play; they all change their votes from conviction to acquittal.
As Juror Eight goes over the evidence and presents plausible scenarios in favor of the defendant, the other jurors slowly change their votes to not guilty. Whether they change as people in the process of changing their votes is questionable. However, it seems likely that they—at least in this instance—are becoming more thoughtful and deliberate.
At the beginning of the play, they're all distracted with their own concerns and ready to find the boy guilty of murder. It's hot; they don't want to be sitting on the jury. Juror Eight shows them how important their jobs are, though, when he interrupts a game two jurors are playing to pass the time. He also demonstrates how to look at the situation more closely. By the end, every other person on the jury has changed their vote—and perhaps a bit of their thinking as well.
At the start of Twelve Angry Men
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Twelve Angry Men, the jury votes 11 to 1 in favor of conviction; everyone in the room but Juror 8 believes that the defendant is guilty. By the end of the play, nearly every juror votes in favor of the defendant being not guilty. While some of the characters don’t change but change their votes, like Juror 3 or Juror 10, other jurors change their opinions based off of new evidence or discussion that happens during the play.
The first one to change his vote is Juror 9, an older man who stands up to Juror 10 when he starts saying racist things at the start of the play. Juror 9 says he changes his vote so that Juror 8 can have his say; he says it is the courage to stand alone that helped change his mind.
Juror 5 is next to change his vote, questioning the mobility of the old man who was a witness for the prosecution. He says it seems farfetched that an old man could “run” to see the criminal fleeing, as he was very slow and had a hard time walking in court.
After an outburst by Juror 3, who says he will “kill” Juror 8 after he proves that it could take a long time to get up out of bed and walk from the bed to the front door, the jury is split evenly 6 to 6.
A few of the jurors change their opinions for selfish or unfocused reasons, like Juror 7 changing because he wants to go to a baseball game and Juror 2 changing because he sees that Juror 8 is calmly laying out his case.
After bringing up the direction of the knife wound and the inability of another witness to see without glasses, the case is 10 to 2 in favor of not guilty. Eventually, Juror 10 and Juror 3 give in after they see that no one else agrees with them.
Your term, "change", has some interesting inferences. If you mean change, as in which jurors changed their final vote--three jurors changed their minds. The final vote was 9 to 3 for acquittal. You can find the exact vote in the link I've provided.
The more in depth part of the question is which jurors were most changed because they participated in the trial. This requires deeper reading. Keep your characters' original opinions clear in your mind. I would suggest a T-chart where you can list the characters down one side and the ways they changed on the other. I would also keep track of the Acts where each character changed.
The link below should help you sort out both parts of your teacher's clever question.