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In kindergartens and early-elementary classrooms, manipulative materials (such as Cuisenaire Rods and Pattern Blocks) play an important role in childrens learning, enabling children to explore mathematical and scientific concepts (such as number, shape, and size) through direct manipulation of physical objects. But as children grow older, and learn more advanced concepts, the educational focus shifts away from direct manipulation to more abstract formal methods. This paper discusses a new generation of computationally enhanced manipulative materials, called digital manipulatives, designed to radically change this traditional progression. These new manipulatives (such as programmable building bricks and communicating beads) aim to enable children to continue to learn with a kindergarten approach even as they grow olderand also to enable young children to learn concepts (in particular, systems concepts such as feedback and emergence) that were previously considered too advanced for them.
* In 1837 in Germany, Friedrich Froebel created the world's first kindergarten. Froebel's school was an important departure from previous educational institutions not only in the age of its students, but in its educational approach. Froebel had been deeply influenced by Swiss educator Johann Heinrich Pestalozzi, who argued that children need to learn through their senses and through physical activity. In Pestalozzi's words: "things before words, concrete before abstract" (Pestalozzi, 1803). In sharp contrast with previous schools, Froebel put physical objects and physical activity at the core of his kindergarten. He developed a set of 20 socalled "gifts"-objects such as balls, blocks, and sticks for children to use in the kindergarten. Froebel carefully designed these gifts to help children recognize and appreciate common patterns and forms found in nature. Froebel's gifts and ideas were eventually distributed throughout the world, deeply influencing the development of generations of young children. Some historians argue that Froebel's gifts deeply influenced the course of 20th century art; indeed, Frank Lloyd Wright credited his boyhood experiences with Froebel's gifts as the foundation of his architecture (Brosterman, 1997).
Today's kindergartens are still full of physical objects and physical activity. Walk into a kindergarten, and you are likely to see a diverse collection of manipulative materials such as Cuisenaire Rods and Pattern Blocks. As children build and experiment with these manipulative materials, they develop deeper understandings of mathematical concepts such as number, size, and...