Instructional programs from
prekindergarten through grade 12 should enable all students to--
- recognize and use connections among mathematical ideas;
- understand how mathematical ideas interconnect and build on one another to
produce a coherent whole;
- recognize and apply mathematics in contexts outside of
mathematics.
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Mathematics is an integrated field of study, even
though it is often partitioned into separate topics. Students from
prekindergarten through grade 12 should see and experience the rich interplay
among mathematical topics, between mathematics and other subjects, and between
mathematics and their own interests. Viewing mathematics as a whole also helps
students learn that mathematics is not a set of isolated skills and arbitrary
rules.
An emphasis on mathematical connections helps
students recognize how ideas in different areas are related. Students should
come both to expect and to exploit connections, using insights gained in one
context to verify conjectures in another. For example, elementary school
students link their knowledge of the subtraction of whole numbers to the
subtraction of decimals or fractions. Middle school students might collect and
graph data for the circumference (C) and diameter (d) of various
circles. They could extend their previous knowledge in algebra and data analysis
to recognize that the values nearly form a straight line, so C/d is
between 3.1 and 3.2 (a rough estimation of 
).
The opportunity to experience mathematics in context
is important. Students should connect mathematical concepts to their daily
lives, as well as to situations from science, the social sciences, medicine, and
commerce. For example, high school students worked with a drug store chain to
determine where it should locate a new pharmacy in their neighborhood on the
basis of analyses of demographic and economic data. Students should recognize
the value of mathematics in examining personal and societal issues.