Kids like to learn, but they sometimes resist others teaching them. Since they like to learn on their own, it can help to introduce them to activities that will guide them toward the things you want them to learn.
For example, kids are supposed to be able to write their names, count to ten and know their colors a year before kindergarten. Those things are not things they can learn on their own, at least not in the first few years of their lives.
Choose the activities that suit your child’s level of understanding, but remember that even very young children can enjoy playing a learning game.
Kids like to be active, so use that to the fullest. Try a treasure hunt for a young child. Hide three or four identical objects and ask him to find and bring them to you. As he brings each one, count them, then let him count them.
He will probably want to do it again and again and he will be counting again and again. Increase the number of objects when you think he is ready.
A treasure hunt works for letters, too. Cut out individual letters of his name and hide them. As he brings them to you, arrange them to spell his name. An older child can do the arranging himself.
If your child is just learning the shapes of letters or numbers, just hide one, then ask him to find the “J” or the “2.” Use a couple of different letters or numbers and alternate them. Be sure to pronounce the name of the number or letter so that he will associate it with the shape he finds.
Make “connect the dots” pages for numbers and letters so they can play by drawing from dot to dot to see what it turns out to be. Put only one letter or number on each page to avoid confusion.
You can give them crayons for drawing the shapes. For instance, give them a red one for numbers and a blue one for letters. Only do letters or numbers at one time because it can be confusing, but the different colors can help them understand that numbers and letters are different.
Dump a package of multicolored buttons or shapes and help your child sort them according to color. Stick with primary colors to begin with. When they are sorted, you can work on naming the colors by asking your child to hand you the yellow ones or the red ones.
Once you get started on these ideas, others will probably occur to you. Use the ones your child enjoys the most and make variations to teach them what they need to know. They might not even realize they are learning.