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I remember the first time I encounteredCuisenaire rods in a graduate workshop. “Be sure you allow time forkids to play with them,” began the instructor, looking around at aroom full of educators turning the tiny blocks into towers andpatterns of stripes. As we knocked over towers and tried to payattention to the instructions on how to use these colorful littlethings with students, we laughed. Even the adults were drawn toplaying with their math.
I've since learned that there are amillion ways to play with your math and hold it in your hands. It'snot a necessary step for absolutely every student, but for most, itmakes math more fun, more tactile, and easier to understand. Mathmanipulatives can be a lifeline for some math strugglers, a shortcutto understanding for some thinkers, and a means to get to a deeperunderstanding for others. There are dozens of different products outthere for both arithmetic and geometry and even an array of productsfor algebra. There are also ways to make math hands on by bringing itinto the real world in other ways.
The simplest math manipulatives areprobably counters. Nearly all of us were born with a nice set of tenof them attached directly to our hands. You can get fancy, of course,and buy a set or you can use what you have around the house. For thesmallest math learners, going from the symbolic abstraction ofnumbers to the reality of a quantity of things sitting in front ofyou is a big step in early learning. In fact, it was a big step inour development as a species to be able to do this. If you and your kids ever want to think about just how big a step, the Terry Jones documentary The Story of 1 is a fun look at the history of how numbers became numbers. We're so used to being able to think of four chairs or four apples or four fingers as just “4” that it's easy to underestimate how hard it is for the brand new learner.
Next comes the even harder in counting up past your fingers. Going beyond ten means beginning to see a pattern in the way we structure our numbers and understanding placevalue. This is where counters can be useful to start, but can quicklybecome tedious. Different possibilities begin to really open up. Kids