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Two kindergarten teachers sit down for lunch during a professional development workshop. One says, "I think it's ridiculous. The children are still babies. They're trying to teach them too much." Her friend nods. Soon they are joined by a colleague from another school, who bubbles, "Isn't this great? The children are going to know so much more!"
Most of US can sympathize with both perspectives. What should we be teaching in the early grades? Three research findings provide some guidance in mathematics instruction.
1. Learning substantial math is critical for primary grade children.
The early years are especially important for math development. Children's knowledge of math in these years predicts their math achievement for later years - and throughout their school career. Furthermore, what they know in math predicts their later reading achievement as well (Duncan et al. in press). Given that early math learning predicts later math and reading achievement, math appears to be a core component of learning and thinking.
2. All children have the potential to learn challenging and interesting math.
Primary grade children have an often surprising ability to do abstract math - that is, math that is done by reasoning mentally, without the need for concrete objects. Listen to the worries of this first-grader.
"I find it easier not to do it [simple addition] with my fingers because sometimes 1 get into a big muddle with them [and] 1 find it much harder to add up because I am not concentrating on the sum. I am concentrating on getting my fingers right ... It can take longer to work out the sum [with fingers] than it does to work out the sum in my head." [In her head, Emily imagined dot arrays. Why didn't she just use those?] "If we don't use our fingers, the teacher is going to think, 'Why aren't they using their fingers . . . they are just sitting there thinking' . . . We are meant to be using our fingers because it is easier . . . which it is not." (Gray & Pitta 1997, 35)
Should the teacher encourage Emily to use concrete objects to solve math problems? Or should she encourage children like Emily...