Grant Wiggins with a great post on developmentally appropriate standards. Dan Willingham dives deeper here on what it means to use what we know about developmental psychology to inform instruction. A few notes:
He responds to complaints about 1st grade curriculum being too abstract, while 6 year olds are still in concrete operations (Piaget):
For example, how do children learn that some people they hear about (Peter Pan) are made up and never lived, whereas others (the Pharaohs) were real? Not by an inevitable process of neurological maturation that makes their brain “ready” for this information, whereupon they master it quickly. They learn it bit by bit, in fits and starts, sometimes seeming to get it, other times not.
Willingham’s point isn’t that all children are always ready for abstract thinking, but that we need to teach that thinking to them–they won’t spontaneously become ready for it on their own, and in particular that won’t happen for every child at the same time.
Willingham’s math application:
And you can’t always wait until children are “ready.” Think about mathematics. Children are born understanding numerosity, but they understand it on a logarithmic scale–the difference between five and ten is larger than the difference between 70 and 75. To understand elementary mathematics they must learn to think of numbers of a linear scale. In this case, teachers have to undo Nature. And if you wait until the child is “developmentally ready” to understand numbers this way, you’ll never teach them mathematics. It will never happen.
Really interesting parallel in mathematics. The logarithmic scale of human numerical intuition is fascinating–the link in Willingham’s quote leads to a paper entitled “Is It True That Some People Just Can’t Do Math?”. A gem for any math educator–may need its own post.