Swiss child psychologist Jean Piaget identified four stages in a child's learning. Three-year-olds are in the second stage, the pre-operational period, which lasts from age 2 until 6 1/2 or 7. At this stage, children judge mostly by appearance. For this reason, arts and crafts can be especially stimulating for children in this age group. Several inexpensive projects can engage 3-year-olds.

Homemade Books
Children love stories, and they can easily create their own out of magazine photos. First, have your child tell a story (you might have to help him out with the details), then print or type it out, keeping in mind how much you want on each page and leaving space accordingly. Then make a bound book: Fold together a piece of construction paper cut to 8 1/2 by 11 inches and as many sheets of typing paper as you want, keeping the construction paper on the outside. With a needle and thread, stitch along the fold through all of the sheets. Glue a piece of non-stretch fabric to an 11-by-14-inch piece of cardboard for the book cover. Glue the construction paper onto the cover. Press under some heavy books until dry and flat. Finally, add the text and pictures to the pages.

Concentration
Cut out, in pairs, swatches of wallpaper, fabric and pieces of art paper in various colors. Make sure the cutouts are equal in size. With your child's help, glue the cutouts onto pieces of cardboard or index cards for easy handling. You can now use the individual cards for a game of Concentration, also known as Memory, where you simply mix them up and begin playing.

Necklaces
Stiffen the ends of some yarn with nail polish, glue, tape or melted wax. Use the yarn to string pieces of plastic straws, dry cereal with holes, or macaroni. Color the macaroni prior to stringing it by putting it in a jar of alcohol and food coloring for a few minutes and then letting it dry on a paper towel.

Hanging Mobile
Making a simple hanging mobile involves cutting a wire or a clothes hanger into two equal-length pieces and assembling the pieces in the form of a cross. Twist another piece of flexible wire around the point where the two pieces connect, keeping them perpendicular. Ask your child to look for objects, such as old stuffed animals, small action figures or toy parts, that can be suspended from the four ends. Attach a string from the middle to hang the mobile from a light fixture or the ceiling.