The Mathematics Standards consist of eighteen statements which describe what is essential to excellent mathematics education and presents a view of mathematics teaching and learning that integrates the processes of mathematical activity, the content of the mathematics, and the learning environment in the classroom. The following sixteen standards were adopted by the New Jersey State Board of Education.

1. All students will develop the ability to pose and solve mathematical problems in mathematics, other disciplines, and everyday experiences.

2. All students will communicate mathematically through written, oral, symbolic, and visual forms of expression.

3. All students will connect mathematics to other learning by understanding the interrelationships of mathematical ideas and the roles that mathematics and mathematical modeling play in other disciplines and in life.

4. All students will develop reasoning ability and will become self-reliant, independent mathematical thinkers.

5. All students will regularly and routinely use calculators, computers, manipulatives, and other mathematical tools to enhance mathematical thinking, understanding, and power.

6. All students will develop number sense and an ability to represent numbers in a variety of forms and use numbers in diverse situations.

7. All students will develop spatial sense and an ability to use geometric properties and relationships to solve problems in mathematics and in everyday life.

8. All students will understand, select, and apply various methods of performing numerical operations.

9. All students will develop an understanding of and will use measurement to describe and analyze phenomena.

10. All students will use a variety of estimation strategies and recognize situations in which estimation is appropriate.

11. All students will develop an understanding of patterns, relationships, and functions and will use them to represent and explain realworld phenomena.

12. All students will develop an understanding of statistics and probability and will use them to describe sets of data, model situations, and support appropriate inferences and arguments.

13. All students will develop an understanding of algebraic concepts and processes and will use them to represent and analyze relationships among variable quantities and to solve problems.

14. All students will apply the concepts and methods of discrete mathematics to model and explore a variety of practical situations.

15. All students will develop an understanding of the conceptual building blocks of calculus and will use them to model and analyze natural phenomena.

16. All students will demonstrate high levels of mathematical thought through experiences which extend beyond traditional computation, algebra, and geometry.

In addition, the New Jersey State Department of Education's Core Curriculum Content Standards includes, in its Introduction to the Mathematics Standards, the following two "learning environment standards."

17. All students' mathematical learning will embody the concepts that engagement in mathematics is essential, and that decision-making, risk-taking, cooperative work, perseverance, self-assessment, and self-confidence are frequently keys to success.

18. All students will be evaluated by using a diversity of assessment tools and strategies, to provide multiple indicators of the quality of every student's mathematical learning and of overall program effectiveness.

Descriptive Statements and Cumulative Progress Indicators

Accompanying each of the Mathematics Standards is a "descriptive statement" and "cumulative progress indicators," which together provide a brief elaboration of the standard. The descriptive statement expands the simple statement of the standard into a paragraph which outlines the meaning and significance of the standard. The cumulative progress indicators describe what students who are working to achieve the standard should understand and be able to do at each of grades 4, 8, and 12. These materials begin on page 15.

Vignettes

Following the descriptive statements and cumulative progress indicators are a series of short vignettes which suggest how the standards can be effectively integrated in classroom settings. The vignettes are intended to make the standards user-friendly; they serve as examples, as illustrations, of how individual educators can incorporate the standards into their classroom instruction.