With profound implications for classroom practice, this text examines the significance of children’s understanding and learning of mathematical notations in their development as mathematics learners. Using a series of interviews and in-depth conversations with kindergarten and elementary school children, the author investigates young children’s understanding of different mathematical notations, including written numbers and the written number system, commas and periods in numbers, notations for fractions, data tables, number lines, and graphs. Logically organized according to the ages of the children, with each chapter focusing on one to three children and one aspect of notations, this seminal work discusses key concepts, such as: The relationship between conceptual understanding and notations. The interaction between children’s inventions and conventional notations. How children appropriate conventional notations and transform them to make sense of them, and how the classroom culture can encourage, foster, and take advantage of children’s invented notations.