Children are born curious. Even babies, they are fascinated by the world around them. When I was pregnant, the midwife that led to prenatal classes a story a baby she helped deliver. The moment the baby's head popped out of the body of his mother, the child looked around the room with eyes wide open, eager to take in its new environment. She was not yet officially born, not until the next push anyway.
Babies are eager to learn, as are the preschoolers. It's time to teach them to think. To analyze and deduce things for themselves. Do not keep spoonfeeding. Challenge with puzzles they must understand their own.
As soon as the child can sit, get him or her stacking rings and let her play with them. A favorite toy I had as a child was a box with holes to fit different shapes around him. Shape sorting is a skill related mathematics that helps children develop analytical abilities.
Then there are television programs. Some are actually very educational. As a child, my favorite was Sesame Street. When my children arrived, they were hooked too. We would watch Elmo and the gang as they learn the letters and numbers in the show. This is a great show for literacy. Especially with the emphasis on phonetics.
Yet when it comes to analytical, Blues Clues I think is the best. My kids love guessing what Blue is up. Although meant for preschoolers, even my older kids enjoyed the show. Basically, riddles and treasure hunts with one clue to another and puzzles are great ways to develop their analytical skills of a child. Children with more exposure to those games have an advantage over their peers when it comes to math and science subjects at school.
