number of items in the set), and comparing the number of bears in the two sets. These kinds of mathematics learning opportunities help children learn to mathematize or engage in processes that involve focusing on the mathematical aspects of an everyday situation, learn to represent and elaborate a model of the situation, and use that model to solve problems.
Conclusion 3: Children need adult support and instruction to build and extend their early knowledge and learn to focus on and elaborate the mathematical aspects of everyday situations—to mathematize.
The committee was keenly aware of the influence that developmental and contextual variations have on children’s learning opportunities and the quality of their educational environments both inside and outside the classroom. Understanding individual differences in children’s development—for example, in executive function or in opportunities to learn about mathematics in their everyday environments—is fundamental to supporting the development of competence in mathematics. Although all children need extensive exposure to mathematics, there is a wide range of individual variation across all domains of learning. This affects the kinds of learning experiences and instruction that individual children need. The need to support early childhood mathematics education in ways that are appropriate for diverse learners and contexts is a theme throughout the committee’s discussion of early childhood mathematics.
Conclusion 4: Due to individual variation, which is related to a combination of previous experiences, opportunities to learn, and innate ability, some children need more extensive support in mathematics than others.
It is important to understand the sources of observed differences in children’s competence and not confuse one source of individual variation for another. For example, low performance might be attributed to a deficit in a child’s ability to learn mathematics, when it actually results from other factors, such as that child’s lack of opportunities to learn mathematics or difficulties stemming from linguistic and cultural barriers between teacher and child.
Opportunities to explore the mathematics of everyday life differ depending on children’s background, including their socioeconomic status (SES) and cultural group. Mathematics knowledge and skills vary within and between cultural groups due to a variety of factors, including language and relative emphasis placed on mathematics. Cultural, linguistic, and socioeconomic factors interact in complex ways that are difficult to tease apart.