Childhood, it is often said, is a recent invention. Children used to be treated as small adults to be put to work as soon as possible. Education meant discipline and punishment. Then came the 20th century and the idea that children are fundamentally different from adults and should be treated accordingly. The ideal child, a creature of terrific potential, became an inspiring symbol of futurity, and the care and education of actual children exercised the minds of great thinkers, including many from the fields of art and design.

“Century of the Child: Growing by Design, 1900-2000,” a big, wonderful show at the Museum of Modern Art, examines the intersection of Modernist design and modern thinking about children. A rich and thought-provoking study of a great subject, it is loaded with intriguing things to look at — some 500 items, including furniture, toys, games, posters, books and much more.