to expand their knowledge and competence and enjoy their early informal experiences with mathematics, such as spontaneously counting toys, excitedly asking who has more, or pointing out shapes.
Conclusion 1: Young children have the capacity and interest to learn meaningful mathematics. Learning such mathematics enriches their current intellectual and social experiences and lays the foundation for later learning.
Knowledge and competencies acquired through everyday experiences provide a starting point for mathematics learning. Infants’ and toddlers’ natural curiosity initially sparks their interest in understanding the world from a mathematical perspective, and the adults and communities that educate and care for them also provide experiences that serve as the basis for further mathematics learning. Children’s everyday environments are rich with mathematics learning opportunities, for example, using relational words, such as more than/less than, and counting and sorting objects by shape or size. These foundational, everyday mathematics experiences can be built on to move children further along in their understanding of mathematical concepts.
Conclusion 2: Children learn mathematics, in part, through everyday experiences in the home and the larger environment beginning in the first year of life.
Children need rich mathematical interactions and guidance, both at home and school to be well prepared for the challenges they will meet in formal schooling. Parents, other caregivers, and teachers can play a fundamental role in the organization of learning experiences that support mathematics because they can expose children to mathematically rich environments and engage them in mathematics activities. For example, parents and caregivers can teach children to see and name small quantities, count, and point out shapes in the world, “Here are two crackers. You have one in each hand. These crackers are square.”
One important way that young children’s mathematics learning can be enhanced is through adult support and instruction that is connected to and extends their preexisting mathematics knowledge. For example, a situation in which a young child insists on having “more” teddy bears than his playmate provides an opportunity for the adult to engage the child with a mathematical question (e.g., who has more and how can you find out?). In this instance, the adult can use several key mathematical ideas to help the child understand who has more bears, such as using the number word list to count, 1-to-1 counting correspondence, cardinality (i.e., knowing the total