Your child picks up lots of new reading and writing skills in kindergarten. The idea of communication used to mean verbal requests. Your child used communication mostly so that you could meet her needs or fulfill her curiosity. Now, your kindergartner will learn that standard linguistic patterns shape the ideas her mind can share.
Expect a kindergartner to understand the sounds of the alphabet, know the difference between capital and lower-case letters, write her full name and recognize sight words.
Addition skills come later, but your kindergartner will learn that numbers represent values. He will count to 20 and be able to tell you how many of something exist in a group.
The identification of shapes occurs during this period, too, as your kindergartner begins to understand the idea of form. For instance, a square has four equal sides, while a rectangle has two sets of equal sides. The ability to match shapes of different sizes becomes an important demonstration of understanding form, too.
Scientific understanding in kindergarten is a fun development to watch. Your child isn't so much learning new ideas as learning to identify ideas that are instinctual. Scent, touch, taste become more refined as awareness develops. Hearing and seeing become more observant. Your child may have bursts of curiosity as the sensory world opens up.
Your kindergartner also begins to understand time. The difference between today and tomorrow matter now and the concept of yesterday and its impact on today and tomorrow start to hold a place in linear thought.
The simplest aspect of new scientific ideas for kindergartners is color. Kindergartners who couldn't already will be able to identify the major colors with no problem.
Kindergarten is key for socialization. Ideas that simply cannot be demonstrated in the home take on dimension in school. The main idea is sharing. Not only in the sense of sharing objects, like toys or crayons or nap mats, but in the sense that sharing allows community, friendship and trust. Your kindergartner will not be able to identify this idea as such, but the emotional groundwork it lays is crucial.
Additionally, directions begin to mean something more than something that comes from an authority. Kindergartners begin to understand that directions have an end or a goal, even if that goal is just walking to the cafeteria in an agreeable fashion. As socialization develops, attention span will, too.