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We are witnessing a surge of interest in the gifted child. This is evidenced by the increasing number of special educational programs, curriculum materials, professional articles, lectures, and research projects devoted to the subject.

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How many four-year-olds do you know who like to stomp, wiggle, and shout as they count to one hundred; go on a shape hunt to find examples of spheres, cubes, and rectangular prisms; help finish a story about a fantastic pasta maker by completing complex patterns; create and compare two towers of connecting cubes to figure out whose is taller and by how much; and use a map to locate objects in a room? Our answer is just about every four- and five-year-old we have observed over the past four years while developing the Big Math for Little Kids prekindergarten and kindergarten mathematics program. We began this process in the late 1990s because we were dissatisfied with the current state of early childhood mathematics. We observed teachers exposing young children to little or no interesting mathematics or instructing them to learn skills and concepts that they already knew (Greenes 1999). This observation contrasted with the wide range of mathematical ideas and skills that the children explored and employed during free play (Ginsburg 1999). We examined the historical record and learned that over the past two centuries, early childhood mathematics has gone through brief periods of richness followed by longer periods during which the mathematical interests and abilities of young children were seriously underestimated (Balfanz 1999). Aided by funding from the National Science Foundation, we decided to try to create an early childhood mathematics program that would build on the diverse mathematical interests and rich, implicit understandings of mathematics that young children hold.

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