A Comparison of
Benchmarks for Science Literacy and
Curriculum and Evaluation Standards for School Mathematics


Gerald Kulm

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.