Every parent and child are different. Part of my experience home schooling my kids (for high school) was to let them pick subjects they were interested in. I didn't see any need to force the usual public school agenda on them. Instead, I helped them understand that for the long term, learning is really up to them -- and I was there to help answer questions or provide guidance if they got stuck.
It helped that my kids went to a private school for nursery to 8th, where they taught in a similar way.
Some key moments of insight for me in their education included things like: for most kids (not all), if they are exposed to books and other written words, they will learn to read pretty much on their own, with only minimal instruction. The same is true for many other areas of study. Also, when they're young, nurturing a desire to learn, an enjoyment of the process and the ability to ask questions when they get stuck -- along with appropriate social skills -- is, in many ways, more important than the subject matter being taught. I know it probably sounds counter-intuitive; I found most other parents at my kid's school had a hard time accepting this at first, but finally got it by about 7th grade.
Here's their general curriculum for kindergarten, in case it's helpful:
In kindergarten, the abilities to express oneself and to make personal decisions continue to be encouraged. Children have opportunities to express themselves through art, play, and selection of activities. Creating self-portraits, for example, incorporates both observing and defining oneself and observing how others define themselves. Children also take pride in beginning to share responsibility for tasks within the classroom, including cleaning up and caring for materials.
While play is still central to the curriculum, the children begin to join in more formal group processes. For the first time they participate in class meetings-telling their news, expressing their opinions on how to solve class problems, voting, and listening while others talk. There is greater emphasis on group activities, including art, science, music, clay, and physical education. Special teachers come to the classroom every week to lead exploration in these areas. Class projects, which often develop out of the interests of the particular group, are generally initiated and guided by teachers, but are shaped and modified by the children. Teachers work at engaging each child's interest in the project at hand, and children may pursue tasks in highly individual ways.
Kindergarten also includes opportunities to develop pre-reading and math skills through activities which include counting, measuring, building, and letter and word recognition. Finally, the first field trips are taken, offering opportunities to draw upon local resources as well as to broaden the range of activities in which children may participate.
