Why did Kit go to speak with Mr. Kimberly?

This question pertains to Chapter Ten. Mr. Kimberley does appear in the chapters you've cited. Kit goes to visit Mr. Kimberley in order to ask him to give her another chance. He didn't like her style of teaching, so she promised to change it accordingly.

Kit kept her word to Mr. Kimberley and threw herself so diligently into the school work that the children were bewildered. There were no more stories, no games, even no small unorthodox poems.