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.
|Fig. 1. A calculator activity to help
develop understanding of place value
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.