"Each time one prematurely teaches a child something he could have discovered himself, that child is kept from inventing it and consequently from understanding it completely." Piaget
This year I decided to live or die by this Piaget quote. (Also known as Pea-ag- it to my favorite college niece.) I decided to bypass the direct instruction of addition and subtraction strategies in favor of letting the kids discover them for themselves. The first thing I did was purchase a Rekenrek.
We spent a good 5-10 minutes everyday on a number sense activity, either a counting circle, the Rekenrek or visual images. After about 8 weeks I decided to not just ask what they could see on the Rekenrek but to ask how they saw it. Sure enough someone used one of the traditional addition strategies that I normally would have taught. I try repeating the strategy in a little more concise language and asked if anyone thought they could solve another problem in the same way. So I slid over a different set to add and everyone tried to solve it in the same way. We gave it a name and moved on to another student's idea. After about 3 days of 10-15 minutes of this, we had come up with this chart.
All strategies I could have taught, but instead they were discovered by the students. The best part is that my students are still talking in terms of strategies when they problem solve. And the next best thing is that when I gave my first grade level common assessment in a worksheet format everyone passed, even though it was the first worksheet experience of the year. I know I learned all about Piaget in my college and graduate days but somehow I hadn't discovered for myself all of the wisdom in his ideas. Each time one prematurely teaches a preservice teacher something they will have to learn for themselves the time and effort are wasted. Is that too cynical? Maybe. If you haven't used the Rekenrek for mathematical discussions, you should give it a try.
Electronic Rekenrek available from the Math Learning Center. It is a free app that my students love to use on the iPad.
|Number Rack App|