Sunday, November 1, 2009

Exposure vs. Mastery

A couple of years ago we were visiting my husband's parents. I overheard his grandmother (who also lives with them) asking my oldest son, five years old at the time, what he was learning "in school".

"Well, actually we homeschool," he patiently explained. Then he proceeded to tell her that he was learning about multiplication and division.

A little taken aback, she said, "Isn't that too hard for you?"

"No," he answered cheerfully, "it's fun!"

Now, although math does come easily to my son, he was not memorizing multiplication tables or doing long division at age five. The truth is, he was doing exactly what he said--learning about multiplication and division. The math curriculum we use does a fabulous job of introducing concepts in developmentally appropriate ways and coming back to them again and again to go a little deeper each time.

I love this system's emphasis on exposure, rather than expecting learners to master concepts the first time they are presented. My then five-year-old could readily understand, for example, that division means taking a certain number of items and sorting them into groups of equal size, while multiplication means adding up groups of equal size. He wasn't ready to tell me from memory that 10/2=5, but he could figure out that if he had to share his 10 M&M's with his sister, they would each get 5. He couldn't spout off multiplication facts like 4x3=12, but he could use drawings or manipulatives to discover that if 4 friends each brought 3 cookies to share, there would be 12 cookies altogether. He hadn't mastered multiplication and division, but he was certainly being exposed to the concepts in a meaningful way.

Now, as we are actually working on multiplication and division facts, the foundation has been laid. He comprehends the underlying idea of what these operations mean, so he can focus on practicing the actual facts until they come automatically to him. At this stage, he can see the benefit of knowing basic math facts by heart in order to solve more complex problems. (At age 5, it would have merely been a matter of me telling him it was useful!) His early exposure paved the way for this stage in his mastery.

My point, I guess, is that we should never refrain from teaching a child something because we think it is too difficult for them. They will not master everything (or even most things) the first time they are exposed to them, but they will also never master something they have not been exposed to. Take a chance, and they may just surprise you!

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