Here is the e mail I wrote when Kelsey “discovered” the concept of multiplication in her room while playing with her many beanie babies:
I believe and have observed that there is a direct link between children's play and the development of common sense. A common sense intuition about how the world works. It is through play that children learn and internalize scientific or mathematical concepts that they won't be formally taught or required to put a name to until jr high, high school, or maybe even college. Without this experience - this internalization, the book knowledge is empty. (No one ever said that books were better than experience, I know.)
Children are naturals at the scientific process and experimentation; they are wired to learn about the world they live in - by playing. Watch them on a slide; they are gaining experience and living "object in motion stays in motion" until they hit the ground. They learn about friction when they realize that if they take off their socks they can slide much faster or that the baby doesn't go down the slide very fast if he is naked. Rub your socks on the carpet and shock your friends and family members, literally. Then try it in the dark and see the spark! How many times did it take the cat to run when he saw you rub your feet on the carpet? Hmmmm association and conditioning?
You know, the more children are seated on a merry-go-round, the harder it is to stop? The children seated on the inside of the merry-go-round aren't actually spinning as fast as the children on the outside? A child in a bathtub causes displacement, experiences some buoyancy, and learns about what type of toys float and what types sink. Some of the toys that usually float will sink when filled with water. What about those bubbles? Children might notice that when they get out of the bathtub, the water level seems to drop. (When mom gets out it REALLY DROPS!) After playing in the mud, there might be a ring around the tub! A washcloth appears darker when it is wet. The wet cloth can actually stick to the side of the tub, but a dry one can't. The wet cloth, after a few days falls off of the tile and hardens - molds if left in the hamper... (great time to talk about seeds, spores, and buds)
I've observed my children's discovery of mathematical concepts through play! And not just with the abacus and Math Blaster at the computer. When my daughter ran out of fingers and toes to count on, she found that beanie babies were great for counting. She learned that she could divide her 25 favorite beanie babies into equal groups of five's, but she couldn't divide them up into equal groups of 3's or 4's, however, if she tossed ONE beanie baby and only played with 24 beanie babies she would divide them up into equal groups of 3's or 4's!!! This discovery thrilled her and she explained it all to me. When I realized that she had discovered the concept of division and multiplication on her own, I knew that she would be able to understand these concepts if I explained them to her. It was her hint to me that she was ready. I just participated in her play and showed her many other ways to divide up beanie babies. "By the way, you know how to divide and multiply, Kelsey." My daughter also discovered, on her own that, "If ten plus ten is twenty, then ten plus eleven is twenty-one!" She announced this to me before she ever heard of place value or had any type of lesson on adding two digit numbers.
These simple concepts that children discover or experience while playing have scientific explanations that they won't have to learn until later, but they have internalized examples of these concepts. What if instead of letting my daughter play with her 25, then 24 beanie babies, I had made her sit down to do seat-work for math? I could have filled up her busy play days by teaching these concepts in a very organized and structured way. Maybe she would have learned these concepts earlier. Maybe I could have bragged to my homeschool friends or family members. Would the lessons have been as important to her? Would these same concepts that she learned on her own, been as important to her if I had sat her down and taught them to her?
My daughter learned many similar mathematical concepts by playing with her many beanie babies! Not only did she learn these concepts on her own while playing, but she OWNS these concepts. They weren't mom's ideas or some concepts dictated by a scope and sequence, they were HER discoveries. She is learning to learn from life! Unfettered play is soooo important to learning and common sense.