I’m going somewhere with this; just hear me out.
Ian has been playing Little Big Planet for months now. After completing each level, the video game tells you what percent of the prizes you have collected from that particular level. He learned pretty quickly that we always aimed for 100%. If we didn’t get 100%, that means we missed something, and we would usually go back and try the level again to see if we could find what we missed. Sometimes there were twenty or thirty things in a level, but never 100 things. Ian figured out that 100% meant “all.” Yesterday, he was playing again. He found a level that he wanted to play and said, “Wow! I don’t even have half of the stuff for this level!” It kind of surprised me that he said that because we’ve never gone into percentages in detail (he’s only six). So, just to find out how much he knew, I said, “So what percent would it be if you had half of the stuff?” “50%,” he says. Hmmm. So I said, “If there were 8 things to get in a level, and you had 50% of them, how many would you have?” He thought for ten or fifteen seconds and said, “4.” Hmmmmmm! I was so impressed, I had to send an email to Jesse at work. Impressed, because I never taught him. He figured out how percentages work on his own, the same way babies learn to use language – by seeing it in action. When Jesse came home from work last night, we were all sitting in the same room, and I thought I’d dig a little deeper into Ian’s well of knowledge. So I said, “Ian do you know how many 25’s there are in 100?” He didn’t. “Remember talking about money? How many quarters are in a dollar?” “Oh, yeah,” he says, “4!” “Okay, so if there were 4 things to get, and you had 25%, how many would you have?” Brief pause. “1!” Explosion of amazement and pride from me and Jesse. “What if there were 8 things to get? How many would you have if you had 25%?” Slightly longer pause. “2!” Yay! I’m so proud of him! Can you tell? So, thanks to Little Big Planet, and a little scaffolding from me (by using Vygotsky’s zone of proximal development), Ian understands percentages. We have another video game called Boom Blox that has made him an expert when it comes to negative numbers. It doesn’t set out to teach you the concept; that’s not the purpose of the game. However, if you lose enough points, your score drops below zero, and since it took Ian a while to get good at the game, he has LOTS of experience with negative numbers 🙂
I said all of that to say this: when teaching math, take time to make sure your child understands each concept. Start with the why, see if they can understand it and figure a few easy problems based on what they know, and then teach them how to work the problem. You’ll be amazed at what they can do.