Wednesday, January 02, 2013

Have Some Math, Kids, It's Good For You

Like most preschools in the US, we have a large box of what are usually called "counting bears." They come in three sizes that the kids most commonly refer to as "mommies," "daddies," and "babies." Whether the mommies or daddies are represented by the largest size is a matter for debate. They also traditionally come in four colors -- the primaries, plus green -- although I know there are other colors out there. Otherwise they're all the same.

No one ever walks into the classroom and enthuses about them like they do when we have our trains or dinosaurs out, so I wouldn't say they're popular playthings, although they always get plenty of use, the way bottle caps or wine corks or anything of which we have "a lot" find their way into the children's play often in the form of stand-ins or markers or tools. 

I've seen them used as families or princesses or superheroes; they're sometimes employed as currency or board game pawns or teddy-shaped pegs to be inserted into round holes; all together in their box, they're a sensory item for hands and ears, for dumping, pouring, gather and scooping; we use them as obstacles to jump over, step through, and tip toe around. They are the perfect object in a game of knock-them-down-and-pick-them-up-again.

They call them "counting bears" because they're marketed as "pre-math" tools for teachers and parents who don't know that there is no such thing. I guess they're suggesting that math is properly something you do with symbols on paper, but what preschool kids naturally do with these bears is the real math: counting, sorting, weighing, and making patterns from them. 

They sell all sorts of things to go with these bears, I guess by way of making them more "hard core pre-math." We have, for instance, a set of cards that present illustrations of bears in various types of sequences. The idea, as near as I can figure, is for teachers to have young children match the patterns bear-for-bear, considering size and color, then to continue the sequence they've discovered beyond the end of the card. Since, as a teacher, I'm suspicious of any description of teaching in which part of the concept is to "have" the children do this or that, I sometimes put the cards on a table along with the bears as an invitation. Sometimes a child or two will take it on in "the right way," but usually the cards remain untouched while the bears move off to more interesting activities.

I know that there are some real math gourmets out there, but most of us really don't care to sit down at a table at which math as the only course. It's not that we don't like math, but it's like broccoli or beans; it's something best served on the side, as an accompaniment, to be used to enhance and balance the rest of our meal, not be the meal. In the early years, we're pretty good, I think, about integrating math into our casseroles, salads, and soups, but as kids move up through our schools, more and more of what passes for math education is of the "Here, have some of this math, kids, it's good for you" variety. This is made only worse by the drive to evaluate education through the lazy man's means of standardized testing.

So this doesn't mean we don't do the counting, sorting, weighing, and patterning at Woodland Park, it's just that it emerges, as math always does for most of us in the real world beyond schools, as a means to an end, a tool, a way to use hard logic to solve a problem or take advantage of an opportunity. It's the symbols on paper that are abstractions, not these bears. What we do in preschool is math. That other stuff they're doing in middle school is more properly called post-math. What we do with these bears is called play: dramatic play, constructive play, manipulative play, sensory play, art play, cooperative play, science play, and yes, math play. 

Too many people think that play is the dessert, when, in fact, it's the recipe for a well-balanced meal . . . And yes, I've seen our counting bears served as food, usually to those ever-popular dinosaurs.

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1 comment:

Cass said...

You probably know the term "constructivism" but for the benefit of your readers it is a pedagogical term worth knowing.

What your children are being allowed to naturally do is to construct their own understanding of math concepts. This is without a doubt the strongest way for a child to understand maths.

As a uni student (high school math and IT teacher) I was lucky enough to have Dr John Green (USQ) as my math teaching tutor. He constantly challenged us to find ways to have students learn without being taught, he argued that it was better that a student came up with a formula on their own rather than memorizing it.

I think the theory is brilliant. In practice it is almost impossible in a high school setting (and he wrote a paper on this) because the key ingredient is time. I need three to four times as long (more even) to teach a child math using a constructive method. Now I would hypothesize that the student would remember it for much longer, but that is only my belief. Reality, as you mentioned, involves limited classroom time, lack of cross-curriculum teaching, and lots of testing.

You mentioned math using soups and casseroles. Well I argue that a person can learn all the math they ever need (up to uni level) without getting out of the car... And since they have plenty of time they can learn it constructively without any "have to do this". Start by giving your kids old street directories while you are in the car and seat them behind the passenger so that they can see the speedo and see the road mileage signs as they pass them.