Four-year-old children discover the world with all their senses and invent mathematics by touching, moving, tasting, hearing, seeing, and creating. They construct mathematical concepts such as sorting and matching, patterns and symmetries, numbers, geometry, space and time, weighing, measuring and comparing, graphing, and statistics while handling pocket treasures and everyday materials. They discover mathematics as a way to structure and explore the world themselves. In words and pictures, the book is a specialized didactic master class, a well-reasoned plea, supported by many examples, to give children the time, materials, and opportunity to develop their own mathematical ways of thinking before confronting them with abstract signs and symbols. The masterful photographs accompanying this book were taken during a visit.