how could Anne prove her point that talking was surely a student trait
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Answer:
In her essay, Anne wanted to come up with convincing arguments to prove the necessity of talking. She argued that talking was a student's trait and that she would do her best to keep it under control. This was how she justified her being a chatterbox in the essay.
Anne Frank supports her nantte by stating that talking is a student's trait and she will try to control it. But she also says that she has got it from her mother and such inherited traits cannot be curbed.
In her first essay Anne justified her talkativeness by explaining that it was in her genes, because her mother was also talkative. Although detail about second essay is not given but it can be assumed that it was a good essay, because Mr. Keesing didn't complain about Anne's habit for a long time.