What are some of the important cognitive skills my child should learn during preschool (or in my case, at home)?

Well, the best tip you can get regarding what cognitive skills your child should develop would be to check out the preschool programs in your local area, or to do a search for "preschool curriculum" online. Another way to find out what skills you should be teaching your child would be to contact the elementary school in your area to find out what the children need to know before enrolling in Kindergarten. Don’t be afraid to ask these people how you can help prepare your child for this experience. Educators are usually very happy to foster parent involvement in the student’s education.

Another article by Diana Townsend-Butterworth, entitled, “The Preschool Routine,” explains that some of the typical activities of preschool include circle time (where the teacher facilitates a discussion), free choice time (where children choose from a variety of activities), group activity (children learn a song or dance, or do a creative project together), snack time (children set the table and eat together), outdoor play, clean up time, and story time.