I believe that this question is asking when was Kit expected to teach school. Kit and readers find out in chapter 8 that Kit is being encouraged to help Mercy teach school. She finds out when Mercy tells Kit that an offer has been extended to her to help Mercy teach the children at the dame school.
The most wonderful thing, Kit! Dr. Bulkeley has recommended to the selectmen that you help me with the school this summer.
Kit actually didn't know that Mercy taught such a school. And Kit is further surprised to find out that the school is right there in the kitchen. She is not sure that she is qualified, but Mercy insists that because Kit knows how to read that she is indeed qualified to teach.
Next, Mercy tells Kit that Mr. Elzazer Kimberley, the schoolmaster, is being sent to test Kit's abilities. If Kit passes, the school will begin the following week. Kit begins to warm to the idea once Mercy tells Kit that the teaching job would pay them wages. Kit is hopeful that if she is earning wages, she will not be expected to do as many of the house chores as she is currently doing.
Kit turns out to be a natural at teaching. While she is not as patient as Mercy, Kit is exceptionally good at teaching the kids to read. Kit makes use of various reading games and rhymes to help the children catch on more quickly, and Kit is surprised at how much she enjoys the teaching job.
Kit had no idea that her methods were novel and surprising. She only knew that the past ten days since the dame school had begun had been the pleasantest she had known in Connecticut.