The vision of the Mathematics Standards of the New Jersey State Department of Education's Core Curriculum Content Standards revolves around what takes place in classrooms like those described in the previous pages. It is focused on achieving one crucial goal:

GOAL:

To enable ALL of New Jersey's children to move into the twenty-first century with the mathematical skills, understandings, and attitudes that they will need to be successful in their careers and daily lives.

As more and more New Jersey teachers incorporate the recommendations of the Mathematics Standards into their teaching, we should be able to see the following results (as described in Mathematics to Prepare Our Children for the 21st Century: A Guide for New Jersey Parents, published by the New Jersey Mathematics Coalition in September 1994).

Students who are excited by and interested in their activities. A principal goal is for children to learn to enjoy mathematics. Students who are excited by what they are doing are more likely to truly understand the material, to stay involved over a longer period of time, and to take more advanced courses voluntarily. When math is taught with a problem-solving spirit, and when children are allowed to make their own hands-on mathematical discoveries, math can be engaging for all students.

Students who are learning important mathematical concepts rather than simply memorizing and practicing procedures. Student learning should be focused on understanding when and how mathematics is used and how to apply mathematical concepts. With the availability of technology, students need no longer spend the same amount of study time practicing lengthy computational processes. More effort should be devoted to the development of number sense, spatial sense, and estimation skills.

Students who are posing and solving meaningful problems. When students are challenged to use mathematics in meaningful ways, they develop their reasoning and problem-solving skills and come to realize the potential usefulness of mathematics in their lives.

Students who are working together to learn mathematics. Children learn mathematics well in cooperative settings, where they can share ideas and approaches with their classmates.

Students who write and talk about math topics every day. Putting thoughts into words helps to clarify and solidify thinking. By sharing their mathematical understandings in written and oral form with their classmates, teachers, and parents, students develop confidence in themselves as mathematical learners; this practice also enables teachers to better monitor student progress.

Calculators and computers being used as important tools of learning. Technology can be used to aid teaching and learning, as new concepts are presented through explorations with calculators or computers. But technology can also be used to assist students in solving problems, as it is used by adults in our society. Students should have access to these tools,both in school and after school, whenever they can use technology to do more powerful mathematics than they would otherwise be able to do.

Teachers who have high expectations for ALL of their students. This vision includes a set of achievable, high-level expectations for the mathematical understanding and performance of all students. Although more ambitious than current expectations for most students, these standards are absolutely essential if we are to reach our goal. Those students who can achieve more than this set of expectations must be afforded the opportunity and encouraged to do so.

A variety of assessment strategies rather than sole reliance on traditional short-answer tests. Strategies including open-ended problems, teacher interviews, portfolios of best work, and projects, in combination with traditional methods, will provide a more complete picture of students' performance and progress.

Learning environments like this should and can become the reality in virtually all New Jersey classrooms before the turn of the century. Making this vision a reality is both necessary and achievable.

The Necessity of the Vision

Perhaps the most compelling reason for this vision of mathematics education is that our children will be better served by higher expectations, by curricula which go far beyond basic skills and include a variety of mathematical models, and by programs which devote a greater percentage of instructional time to problemsolving and active learning. Many students respond to the current curriculum with boredom and discouragement, develop the perception that success in mathematics depends on some innate ability which they simply do not have, and feel that, in any case, mathematics will never be useful in their lives. Learning environments like the one described in the vision will help students to enjoy and appreciate the value of mathematics, to develop the tools they need for varied educational and career options, and to function effectively as citizens and consumers.

Preparing our students for careers in the twentyfirst century also requires that we make this vision a reality. Our curricula are often preoccupied with what national reports call "shopkeeper mathematics," competency in the basic operations that were needed to run a small store several generations ago; yet very few of our students will have careers as shopkeepers. To compete in today's global, informationbased economy, students must also be able to solve real problems, reason effectively, and make logical connections. Jobs requiring mathematical knowledge and skills in areas such as data analysis, problemsolving, pattern recognition, statistics, and probability are growing at nearly twice the rate of growth of overall employment. To prepare students for such careers, the mathematics curriculum must change.

We must take seriously the goal of preparing all students for twentyfirst century careers. In order to do this, we must overcome the all too common perception among students that they simply lack mathematical ability. Everybody Counts, a 1989 report prepared by the Mathematical Sciences Education Board of the National Academy of Sciences, notes the following:

Only in the United States do people believe that learning mathematics depends on specialability. In other countries, students, parents, and teachers all expect that most students can master mathematics if only they work hard enough. The record of accomplishment in these countries - and in some intervention programs in the United States - shows that most students can learn much more mathematics than is commonly assumed in this country (MSEB, 1989, 10).

Curricula that assume student failure are bound to fail; we need to develop curricula that assume student success.

Not only will our students need to find employment in the twentyfirst century, but our state and country will need to find employees. American schools have done well in the past at producing a relatively small mathematical elite that adequately served the needs of an industrial/mechanical economy. But that level of "production" is no longer good enough. The global economy in which graduates of our schools will seek employment is more competitive than ever and is rapidly changing in response to advances in technology. Products and factories are being designed by mathematical models and computer simulations, computers are controlling production processes and plants, and robots are replacing workers on assembly lines. Our state and our country need people with the skills to develop and manage these new technologies. In the past, industry moved in search of cheap labor; today, industry frequently moves in search of skilled labor. Our unemployment problem is not only one of too few jobs, but also one of too few skilled workers for existing jobs. We must not only strive to provide our graduates with the skills for 21st century jobs, but also to ensure that the number of graduates with those skills is sufficient for the needs of our state and our nation.

Toward Achieving the Vision

To achieve the vision, the first step is to translate it into specific goals. That is the purpose of the Mathematics Standards. The term standards as used here encompasses both goals and expectations, but it also is meant to convey the older meaning of standards, a banner, or a rallying point. These mathematics standards are intended to be a definition of excellent practice, and a description of what can be achieved if all New Jersey communities rally behind the standards, so that this excellent practice becomes common practice.

This vision of excellent mathematical education is based on the twin premises that all students can learn mathematics and that all students need to learn mathematics. Therefore, for all of the reasons mentioned previously, it is essential that we offer students the very highest quality of mathematics education possible. The Mathematics Standards were not designed as minimum standards, but rather as worldclass standards which will enable all of our students to compete in the global marketplace of the 21st century.

Sixteen mathematics core curriculum content standards, describing what students should know and be able to do, have been adopted by the New Jersey State Board of Education. Two additional standards explicitly address how the learning environment in classrooms can foster success in mathematics for all students and can link assessment to learning and instruction.

These eighteen standards define the critical goals of mathematical education today. In addition to more familiar content, there are many topics which have not been part of the traditional curriculum. Included also are new emphases on the whys and hows of mathematics learning: posing and solving real world problems, effectively communicating mathematical ideas, making connections within mathematics and between mathematics and other areas, active student involvement, the uses of technology, and the relationship between assessment and instruction.

In the future these standards may undergo revision. The standards must be dynamic, and we must beprepared to revise them with changes in mathematics and its use.