Both *Curriculum and Evaluation Standards for School Mathematics *and
*Benchmarks for Science Literacy* are documents that describe what
American students are expected to know and be able to do at various grade
levels during their K-12 education. *Benchmarks* includes mathematics
as an important area of learning both in its own right and for its usefulness
applied to science and technology. Although there are some significant
differences in format, content, and philosophy, a comparison of the two
documents provides important information for educators, especially those
involved in K-12 mathematics and science. At present, the mathematics content
of *Benchmarks* is not widely known in the mathematics education community.
As *Standards* and other reforms are implemented in mathematics, its
is important to look carefully at *Benchmarks*, especially in the
light of renewed attention to applications of mathematics and integration
with science and other subjects.

**Overall Content Comparisons**

In general, *Benchmarks* tends to provide outlines of the overall
literacy expected of students once they finish school, whereas *Standards*
states the learning outcomes expected during the study of mathematics in
school.* Benchmarks* statements are most often about what students
should *know*, whereas statements in *Standards* are about what
students should be able to *do*. However, it is clear in *Benchmarks*
that the way students *become* literate and know is through doing
and investigating. For this reason, some of the *Benchmarks* statements
in mathematics may focus on procedures or knowledge about how something
works, but imply a deeper understanding and sense of how and why it works.

*Benchmarks* contains explicit and comprehensive treatment of the
nature of mathematics, problem solving, and doing science. *Standards*
focuses on specific components of problem solving such as developing strategies
and verifying results without explicitly describing the nature of mathematics.

The ideas and processes of reasoning and critical thinking receive a
great deal of attention in *Benchmarks*. The ideas of creating arguments
and explanations is stressed. Even more important, however, is the notion
of being critical of unsound arguments or claims, especially those based
on faulty data or faulty reasoning or by persons who are not expert in
the field being discussed. In addition, the importance of openness to alternative
explanations, careful experimentation, and sound evidence are stressed
as features of good science and mathematics.

A great deal of attention is given to statistics in *Benchmarks*,
especially their interpretation and cautions about misinterpretation. Although
separate treatment of probability computations is not as extensive as in
*Standards*, *Benchmarks* has more on the conceptual role of
probability in expectation and prediction. Also, some of the statistics
benchmarks have implications and interrelationships with probability concepts.

There are some instances of differences in grade-level placement. Algebraic
ideas tend to be mentioned by *Benchmarks* in earlier grades than
by *Standards*, yet in the later grades, *Benchmarks* treats
algebra mainly as computational -stopping short of symbolic manipulation
and solution of equations. Graphs, however, are an important topic throughout
*Benchmarks*. Computation receives heavy emphasis in *Benchmarks*,
being carried into the high school grades. *Benchmarks* often integrates
the meaning and understanding of computations, connecting them with applications
in familiar contexts. Also, Benchmarks provides more concrete examples
of how a student's number sense and facility with computations should be
demonstrated.