I've written before about how teachers, mistaking labels for concepts,
assume that a child who doesn't know what a "number sentence" is doesn't understand the concept of number sentences, or that an autistic child who doesn't know what "because" means doesn't understand cause and effect.The renowned, Piaget-trained education expert Constance Kamiii has used this sort of reasoning to argue that third and fourth graders don't understand place value. And Reform Math educators, Common Core authors, and Common Core test developers have used this sort of reasoning to argue that kids only understand what they're doing mathematically if they can explain it verbally.
The rippling effects of this conflation of labels and concepts include depriving huge numbers of students all over this country of an appropriately challenging math education, and making math tedious for the majority of students for whom verbal explanations are pointless busywork.
In her most recent WSJ column, Alison Gopnik reports further findings showing children's grasp of concepts developing independently, and in advance, of their knowledge of labels--in this instance the concept of sameness:
The conventional wisdom has been that young children also can't learn this kind of abstract logical principle. Scientists like Jean Piaget believed that young children's thinking was concrete and superficial. And in earlier studies, preschoolers couldn't solve this sort of "same/different" problem.All the more so if they have language delays.
But in those studies, researchers asked children to say what they thought about pictures of objects. Children often look much smarter when you watch what they do instead of relying on what they say. [Boldface mine.]
I'm reminded of how, back when J was in kindergarten and still speaking in Pidgin English, his precocious math skills were evident to his evaluators only thanks to linguistic serendipity. Following his interest in all things lunar, we'd taught him the terms for the different phases of the moon. When he was later assessed for his next classroom placement, the school distract evaluator, testing his math skills, asked him to label the fraction represented by a circle that was three-quarters shaded. Not knowing the label "three-quarters," J said "gibbous."
Of course, we all know about the Gibbous Moon, but most of us don't know its label. Luckily, J's evaluator was curious enough about "gibbous", and about J, to look up what it meant. And then to place him not in a Life Skills class, but in a class for kids with... language delays.
Where would J be now without the Gibbous Moon?