The New York Times has an article about some new (though I don’t know how new) research showing that children are capable of understanding much more complicated math concepts much earlier than we usually assume — and about some preschool programs trying to take advantage of this fact.
The really cool thing is that cognitive scientists are researching how the brain develops and what it can do at certain ages (and when the optimal times for learning certain things start and end), and that mainstream educators are starting to pay attention to this research. I nonetheless feel compelled to point out that these insights aren’t new. Montessori observed a century ago that children have an instinct for numbers and can develop fairly sophisticated mathematical abilities at a very young age — if the math is presented in the right way. Montessori schools have been helping preschoolers learn to understand the concept of number and our decimal number system; to add, subtract, multiply, and divide; to recognize geometric shapes (in two and three dimensions); and to work with fractions for over a hundred years. Ways to learn math and reading are only the tip of the Montessori iceberg, but they seem to be the tips that most concern mainstream educators, the mainstream media, and most of American society.