Rueda et al. (Neuropsychologia 42/8; 2004) found that children cannot keep two things in mind at the same time until after age 7. (They used an Eriksen attention task.) Have you accounted for the brain links that need to grow before children can think about length and width at the same time in dealing with area? For middle/upper class children, area/volume will begin to make sense at age 8 or later; for children growing up in the toxic stress of poverty (see Early Childhood studies from Harvard), that brain growth is delayed. Children from low income families may not have the ability to keep two things in mind at the same time until age 9 or later.
Hi,
GOOD to hear from you! I believe it really depends on what "things" you are talking about...do you agree? Since we have 4's measuring (but concretely, etc.) I know that they can get multiple "things" in mind (and see all they an build--hard to believe it's "one thing at a time" only!). Still, if this is like "M-Space"--Case's theory--the "thing" may be a "large" cognitive unit. We don't really do "length times width" with young children--right? It's arrays of tiles covering a space.
Poverty is horrible and must be addressed. But early interventions may certainly mean we do not have to wait until age 9!
Doug
I agree that early interventions at the concrete level are a must. My comment, though, relates to seeing the pieces (the tiles) versus seeing the whole area. Children at age 4 see the one or the other, but not both at the same time (per Steffe & Cobb's research). If you cover the area, the children see the tiles. If you remove the tiles, they see the area-figure as a unit. They may be able to tell you how many tiles they used to cover the area, but do they connect the area of each tile to the area of the area-figure?
My question above question is like this one: When a two-year-old is counting the steps as she climbs, is she counting the steps (the concrete object) or raising her foot (her actions)? How do we know what the child is counting?
Through a research conducted in order to investigate the early numeracy of young children with Down syndrome in Greece, it was found that children aged between 7;02 (y;m) and 14;07 (M = 10.07, SD = 2.06), do not have the ability to keep two things in mind at the same time. Participants were 40 children with Down syndrome enrolled in special school programs. Their mental age ranged between 4;00 (y;m) and 7;01 (M = 4.86, SD = 0.96).
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