Appendix B
Overview of Content Standards from the National Science Education Standards and the Principles and Standards for School Mathematics
Science Content Standards for Grades K12
(From the National Science Education Standards, National Research Council, 1996a, excerpted from pages 103119)
RATIONALE
The eight categories of content standards are

Unifying concepts and processes in science

Science as inquiry

Physical science

Life science

Earth and space science

Science and technology

Science in personal and social perspectives

History and nature of science
Unifying Concepts and Processes Standard
Unifying concepts and processes include

Systems, order, and organization

Evidence, models, and explanation

Change, constancy, and measurement

Evolution and equilibrium

Form and function
Science as Inquiry Standards
Engaging students in inquiry helps students develop

Understanding of scientific concepts

An appreciation of “how we know” what we know in science

Understanding of the nature of science

Skills necessary to become independent inquirers about the natural world

The dispositions to use the skills,

abilities, and attitudes associated with science
Physical Science, Life Science, and Earth and Space Science Standards
The standards for physical science, life science, and earth and space science describe the subject matter of science using three widely accepted divisions of the domain of science. Science subject matter focuses on the science facts, concepts, principles, theories, and models that are important for all students to know, understand, and use.
Science and Technology Standards
The science and technology standards establish connections between the natural and designed worlds and provide students with opportunities to develop decisionmaking abilities. They are not standards for technology education; rather, these standards emphasize abilities associated with the process of design and fundamental understandings about the enterprise of science and its various linkages with technology.
Science in Personal and Social Perspectives Standards
An important purpose of science education is to give students a means to understand and act on personal and social issues. The science in personal and social perspectives standards help students develop decisionmaking skills. Understandings associated with these concepts give students a foundation on which to base decisions they will face as citizens.
History and Nature of Science Standards
In learning science, students need to understand that science reflects its history and is an ongoing, changing enterprise. The standards for the history and nature of science recommend the use of history in school science programs to clarify different aspects of scientific inquiry, the human aspects of science, and the role that science has played in the development of various cultures.
FORM OF THE CONTENT STANDARDS
Below is an example of a content standard.
Physical Science (Example)
As a result of the activities in grades K4, all students should develop an understanding of

Properties of objects and materials

Position and motion of objects

Light, heat, electricity, and magnetism
Content is fundamental if it

Represents a central event or phenomenon in the natural world.

Represents a central scientific idea and organizing principle.

Has rich explanatory power.

Guides fruitful investigations.

Applies to situations and contexts common to everyday experiences.

Can be linked to meaningful learning experiences.

Is developmentally appropriate for students at the grade level specified.
CRITERIA FOR THE CONTENT STANDARDS
Three criteria influence the selection of science content.

The first is an obligation to the domain of science. The subject matter in the physical, life, and earth and space science standards is central to science education and must be accurate.

The second criterion is an obligation to develop content standards that appropriately represent the development and learning abilities of students.

The third criterion is an obligation to present standards in a usable form for those who must implement the standards.
USE OF THE CONTENT STANDARDS
Persons responsible for science curricula, teaching, assessment and policy who use the Standards should note the following

None of the eight categories of content standards should be eliminated. For instance, students should have opportunities to learn science in personal and social perspectives and to learn about the history and nature of science, as well as to learn subject matter, in the school science program.

No standards should be eliminated from a category. For instance, “biological evolution” cannot be eliminated from the life science standards.

Science content can be added. The connections, depth, detail, and selection of topics can be enriched and varied as appropriate for individual students and school science program.

The content standards must be used in the context of the standards on teaching and assessments. Using the standards with traditional teaching and assessment strategies defeats the intentions of the National Science Education Standards.
Mathematics Content Standards for Grades K12
(From National Council of Teachers of Mathematics, 2000, excerpted from pages 2871)
PREKINDERGARTEN THROUGH GRADE 12^{1}
Number and Operations Standard
Instructional programs from prekindergarten through grade 12 should enable all students to—

Understand numbers, ways of representing numbers, relationships among numbers, and number systems;

Understand meanings of operations and how they relate to one another;

Compute fluently and make reasonable estimates.
Algebra Standard
Instructional programs from prekindergarten through grade 12 should enable all students to—

Understand patterns, relations, and functions;

Represent and analyze mathematical situations and structures using algebraic symbols;

Use mathematical models to represent and understand quantitative relationships;

Analyze change in various contexts.
Geometry Standard
Instructional programs from prekindergarten through grade 12 should enable all students to—

Analyze characteristics and properties of two and threedimensional geometric shapes and develop mathematical arguments about geometric relationships;

Specify locations and describe spatial relationships using coordinate geometry and other representational systems;

Apply transformations and use symmetry to analyze mathematical situations;

Use visualization, spatial reasoning, and geometric modeling to solve problems.
Measurement Standard
Instructional programs from prekindergarten through grade 12 should enable all students to—

Understand measurable attributes of objects and the units, systems, and processes of measurement;

Apply appropriate techniques, tools, and formulas to determine measurements.
Data Analysis and Probability Standard
Instructional programs from prekindergarten through grade 12 should enable all students to—

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them;

Select and use appropriate statistical methods to analyze data;

Develop and evaluate inferences and predictions that are based on data;

Understand and apply basic concepts of probability.
Problem Solving Standard
Instructional programs from prekindergarten through grade 12 should enable all students to—

Build new mathematical knowledge through problem solving;

Solve problems that arise in mathematics and in other contexts;

Apply and adapt a variety of appropriate strategies to solve problems;

Monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof Standard
Instructional programs from prekindergarten through grade 12 should enable all students to—

Recognize reasoning and proof as fundamental aspects of mathematics;

Make and investigate mathematical conjectures;

Develop and evaluate mathematical arguments and proofs;

Select and use various types of reasoning and methods of proof.
Communication Standard
Instructional programs from prekindergarten through grade 12 should enable all students to—

Organize and consolidate their mathematical thinking through communication;

Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;

Analyze and evaluate the mathematical thinking and strategies of others;

Use the language of mathematics to express mathematical ideas precisely.
Connections Standard
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.
Representation Standard
Instructional programs from prekindergarten through grade 12 should enable all students to—

Create and use representations to organize, record, and communicate mathematical ideas;

Select, apply, and translate among mathematical representations to solve problems;

Use representations to model and interpret physical, social, and mathematical phenomena.