Overview: Prekindergarten through Grade 2

Developing a solid mathematical foundation from prekindergarten through second grade is essential for every child. In these grades, students are building beliefs about what mathematics is, about what it means to know and do mathematics, and about themselves as mathematics learners. These beliefs influence their thinking about, performance in, and attitudes toward, mathematics and decisions related to studying mathematics in later years.

Children develop many mathematical concepts, at least in their intuitive beginnings, even before they reach school age. Infants spontaneously recognize and discriminate among small numbers of objects, and many preschool children possess a substantial body of informal mathematical knowledge. Adults can foster children's mathematical development from the youngest ages by providing environments rich in language and where thinking is encouraged, uniqueness is valued, and exploration is supported.

Children are likely to enter formal school settings with different levels of mathematics understanding, reflecting their opportunity to have learned mathematics. Some children will need additional support so that they do not start school at a disadvantage. Early assessments should be used not to sort children but to gain information for teaching and for potential early interventions.

All students deserve high-quality programs that include significant mathematics presented in a manner that respects both the mathematics and the nature of young children. These programs must build on and extend students' intuitive and informal mathematical knowledge. They must be grounded in a knowledge of child development and provide environments that encourage students to be active learners and accept new challenges. They need to develop a strong conceptual framework while encouraging and developing students' skills and their natural inclination to solve problems.

At the core of mathematics programs in prekindergarten through grade 2 are the Number and Operations and Geometry Standards. For example, it is absolutely essential that students develop a solid understanding of the base-ten numeration system in prekindergarten through grade 2. They must recognize that the word ten may represent a single entity (1 ten) or ten separate units (10 ones) and that these representations are interchangeable. Using concrete materials and calculators in appropriate ways can help students learn these concepts.

Understandings of patterns, measurement, and data contribute to the understanding of number and geometry and are learned in conjunction with them. Similarly, the Process Standards of Problem Solving, Reasoning and Proof, Communication, Connections, and Representation both support and augment the Content Standards. Even at this age, guided work with calculators can enable students to explore number and patterns, focus on problem-solving processes, and investigate realistic applications. See, for example, the problem in figure 1.

In the elementary grades, it often happens that specific blocks of time are not allotted to instruction in particular subjects. It is essential for students in the elementary grades to study mathematics for an hour a day under the guidance of teachers who enjoy mathematics and are prepared to teach it well. This basic requirement takes thoughtful arrangements of scheduling and staffing--whether by shared teaching responsibilities, the use of mathematics specialists, or other creative administrative means.