We love games in our house and so much painless learning happens while playing them. So I recently purchased Games for Math by Peggy Kaye. I figured it’d be a fun way to learn some math concepts while spending some fun, quality time with my five year old. I didn’t expect, however, that it would lead to my 11 year old and I colluding together to experiment on five-year-old Nadia. Yep, I’m a great homeschooling parent. Math games, psychological experimentation, and a child development lesson all rolled into one engaging, fun-filled morning.
I didn’t even get to the first math game, however, because as I was perusing the introduction, something caught my eye. The author was explaining the strange view that young children have of certain mathematical concepts. She told about Julie, a girl of five or six years of age. When having two identical rows of pennies before her, Julie was asked which row held more pennies, or if they were the same. Julie said they were the same. Indeed, she was right. Each row held five pennies. When the author “stretched” out one of the rows of pennies so that there was more space between each penny, (but without adding any additional pennies to the row) Julie decided that the stretched out row held more pennies. Even when she counted and each row still held five pennies, it didn’t matter. The stretched out row had more pennies. As I read, my eyes got wider as I thought of all the fun we could have doing this same experiment on our own five year old.
I quickly and quietly summoned 11-year-old Felicia. “Read this,” I said to her, sliding the book across the table to her as if I were some sort of spy giving an agent their secret assignment. She read the section and looked up at me. No words were exchanged but she knew her mission. She quickly went upstairs to get some pennies out of her piggy bank and placed them in two rows.
“Nadia!” We yelled into the living room. “Want to play a counting game?” Felicia asked her, “Which row has more pennies; or are they the same?” Nadia looked, “They’re the same.” Felicia stretched one row out. “Are they still the same?” Sure enough, Nadia thought the stretched out row had more. Even though we had her count each row, the one row still had more pennies in her mind.
We moved on to the next experiment involving two parallel strips of paper. “Which one is longer, or are they the same?” we asked. Nadia said that they were the same. Felicia moved one strip over a little. Nadia thought the one that had moved was longer. Felicia and I were fascinated.
The book explains that psychologists have a name for Julie’s and Nadia’s stage of mathematical thinking. They call it pre-operational and sometime between the ages of five and seven, children naturally and effortlessly move into the next stage of concrete operations. So I didn’t try to correct Nadia. I simply observed her normal (and funny) stage of development. I figure some time in the next couple of years, she’ll grow out of it on her own. In the meantime, it sure provided Felicia and me a morning’s entertainment.