Contents -- 1. Focus on the Preschooler -- 2. Training Studies Reconsidered -- 3. More Capacity Than Meets the Eye: Direct Evidence -- 4. Number Concepts in the Preschooler? -- 5. What Numerosities Can the Young Child Represent? -- 6. How Do Young Children Obtain Their Representations of Numerosity? -- 7. The Counting Model -- 8. The Development of the How-To-Count Principles -- 9. The Abstraction and Order-Irrelevance Counting Principles -- 10. Reasoning about Number -- 11. Formal Arithmetic and the Young Child's Understanding of Number -- 12. What Develops and How -- Conclusions -- References -- Index.