New Jersey Core Curriculum Conte

The vision of the mathematics standards is focused on achieving one crucial goal:

To enable ALL of New Jersey’s children to acquire the mathematical skills, understandings, and attitudes that they will need to be successful in their careers and daily lives.

We want ALL students to achieve the standards. There may be exceptions, but those exceptions should be exceptional.

Perhaps the most compelling reason for this vision is that all of our children, as well as our state and our nation, will be better served by higher expectations, by curricula that go far beyond basic skills and include a variety of mathematical models, and by programs which devote a greater percentage of instructional time to problem‑solving and active learning.

Many students respond to the traditional curriculum with boredom and discouragement. They feel that mathematics will never be useful in their lives, and they develop the perception that success in mathematics depends on some innate ability that they simply do not have.[1] We must overcome the feelings among students that they don’t like mathematics, they don’t need mathematics, and they can’t do mathematics. Curricula that evoke these responses in students, curricula that assume student failure, are bound to fail; we need to develop curricula that assume student success.

Our curricula are often preoccupied with what national reports call “shopkeeper arithmetic,”[2] competency in the basic operations that were needed to run a small store several generations ago. The 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. To compete in today’s global, information‑based economy, students must be able to solve real problems, reason effectively, and make logical connections.

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. Our state and our country need people with the skills to develop and manage these new technologies. Jobs increasingly require mathematical knowledge and skills in areas such as data analysis, problem‑solving, pattern recognition, statistics, and probability. 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.

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. These mathematics standards were not designed as minimum standards, but rather as world‑class standards which will enable all of our students to compete in the global marketplace of the 21st century.

· establishing learning environments that facilitate student learning of mathematics;

· defining the critical goals of mathematics education today--what students should know and be able to do (i.e., content and processes).

The 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. Making the vision a reality is an achievable goal.

The vision, if it is to be realized, must include learning environments with the following characteristics, as described in the mathematics standards adopted in 1996[3]:

Students excited by and interested in their activities. A principal aim 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 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 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 working together to learn mathematics. Children learn mathematics well in cooperative settings, where they can share ideas and approaches with their classmates.

Students writing and talking 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.

Students using calculators and computers 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.

Students whose 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.

Students being assessed by a variety of assessment strategies, not just 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.

In order for all their students to succeed in mathematics, districts will need to commit themselves to the principles of equity and excellence, which comprised Standard 16 in the 1996 version of the mathematics standards, and which remain an important priority for all New Jersey schools. The equity and excellence component of the vision has four features:

Fostering respect for the power of mathematics. All students should learn that mathematics is integral to the development of all cultures and civilizations, and in particular to the advances in our own society. They should be aware that the adults in their world (parents, relatives, mentors, community members, role models) use mathematics on a daily basis. And they should know that success in mathematics may be a critical gateway to success in their careers, citizenship, and lives.

Setting high expectations. All students should have high expectations of themselves. These high expectations should be fostered by their teachers, administrators, and parents all of whom should themselves believe that all students can and will succeed in mathematics. This belief in his or her abilities often makes it possible for a child to succeed.

Providing opportunities for success. High expectations can only be achieved if students are provided with the appropriate opportunities. At all grade levels, students should receive instruction by teachers who have had the training and professional development appropriate for their grade level. Students should receive prompt and appropriate services essential to ensure that they can learn the mathematical skills and concepts included in the core curriculum, and to ensure that their weaknesses do not result in trapping them in a cycle of failure. Students should receive equitable treatment without regard to gender or ethnicity, and should not be conditioned to fail by predetermined low expectations.

Encouraging all students to go beyond the standards. Teachers should help students develop a positive attitude about mathematics by engaging them in exploring and solving interesting mathematical problems, by using mathematics in meaningful ways, by focusing on concepts and understanding as well as on rules and procedures, and by consistently expecting them to go beyond repetition and memorization to problem solving and understanding. Every effort should be made to ensure that all students are continuously encouraged, nurtured, and challenged to maximize their potential at all grade levels and to become prepared for college-level mathematics. Students who have achieved the standards should be encouraged to go beyond the standards. If schools challenge all students at lower grade levels, they will attain the goal of having advanced mathematics classrooms whose students reflect the diversity of the school’s total population.

New Jersey’s mathematics standards[4] rest on the notion that an appropriate mathematics curriculum results from a series of critical decisions about three inseparably linked components: content, instruction, and assessment. The standards will only promote substantial and systemic improvement in mathematics education if the what of the content being learned, the how of the problem-solving orientation, and the where of the active, equitable, involving learning environment are synergistically woven together in every classroom. The mathematical environment of every child must be rich and complex and all students must be afforded the opportunity to develop an understanding and a command of mathematics in an environment that provides for both affective and intellectual growth.

Although ours is a geographically small state, it has a widely diverse population. Children enter our schools from a tremendous variety of backgrounds and cultures. One of the roles of New Jersey’s mathematics standards, therefore, is to specify a set of achievable high‑level expectations for the mathematical understanding and performance of all students. The expectations included in the standards are substantially more ambitious than traditional expectations for most students, but we believe that they are attainable by all students in the state. Those New Jersey students who can achieve more than this set of expectations must be afforded the opportunity and encouraged to do so.

In May 1996, the New Jersey State Board of Education adopted Core Curriculum Content Standards, including a set of 16 standards in mathematics. The development and review of the 1996 version of the New Jersey’s mathematics standards spanned a four-year period and involved two working panels and hundreds of educators and other citizens.

The adoption of the standards was followed in December by the publication of the New Jersey Mathematics Curriculum Framework that was developed to provide assistance and guidance to districts and teachers in how to implement these standards, in translating the vision into reality. The development of the framework was a joint effort of the New Jersey Mathematics Coalition and the New Jersey State Department of Education, with funding from the United States Department of Education.

New assessments have been introduced to reflect the new standards. The mathematics portions of New Jersey’s Statewide Assessments are all based on the mathematics standards adopted by the State Board of Education.

The mathematics standards adopted in 1996 were philosophically aligned with the Curriculum and Evaluation Standards for School Mathematics of the National Council of Teachers of Mathematics (NCTM, 1989), but went beyond that document in a number of ways, reflecting national discussions of that document between 1989 and 1996 and taking into consideration conditions specific to New Jersey. Since 1996, NCTM has published a new document, Principles and Standards for School Mathematics (NCTM, 2000), and 49 of the 50 states have now adopted mathematics standards.

The State Board of Education intended that a review of the standards take place after five years. The panel that drafted these revised standards, in preparing its recommendations, reviewed many of the state standards as well as Principles and Standards for School Mathematics (NCTM, 2000). The panel also took into consideration a review of New Jersey’s 1996 standards prepared by Achieve, Inc. with the support of the Department of Education and Prudential. The panel kept in mind two important principles:

1. Retain the content of the current standards and the structure of the current assessments, so that the standards will not be a major departure from what is currently expected of students.

2. Revise the presentation of the standards, so that teachers will find them easier to understand and implement, and so that standards and assessments are better aligned.

The content of the new mathematics standards is therefore largely the same as the previous version. However, the new standards are different in that:

· The new standards are organized into a smaller number of standards that correspond to the content clusters of the statewide assessments;

· The new standards are intended to serve as clear guides to the assessment development committees so that there should be no gaps between the standards and the test specifications; and

· The new standards include expectations at grades 2, 3, 5, 6, and 7, as well as at grades 4, 8, and 12.

There are five standards altogether, each of which has a number of lettered strands. These standards, and their associated strands, are enumerated below:

The first four of these “standards” also serve as what have been called “content clusters” in the current state assessments; the lettered strands replace what have been called “macros” in the directories of test specifications. The fifth standard will continue to provide the “power base” of the assessments. It is anticipated that the expectations presented here will be used as the basis for test specifications for the next version of the statewide assessments.

For the first four standards, student expectations are provided for each strand at each of eight grade levels: 2, 3, 4, 5, 6, 7, 8, and 12. The expectations for the fifth standard are intended to address every grade level. With the exception of indicators for grades 3, 5, and 7, which were developed at a later time, items presented at one grade level are not generally repeated at subsequent grade levels.[5] Teachers at each grade will need to refer to the standards at earlier grade levels to know what topics their students should have learned at earlier grades.

Bulleted items that appear below expectations indicate terminology, concepts, or content material addressed in that expectation. When an indicator is followed by bulleted content material, the list provided is intended to be exhaustive; content material not mentioned is therefore not included in the expectation at that grade level.[6] When examples are provided, they are always introduced with “e.g.” and are not intended to be exhaustive.

Implicit in the vision and standards is the notion that there should be a core curriculum for grades K-12. What does a “core curriculum” mean? It means that every student will be involved in experiences addressing all of the expectations of each of the content standards. It also means that all courses of study should have a common goal of completing this core curriculum, no matter how students are grouped or separated by needs and/or interests.

A core curriculum does not mean that all students will be enrolled in the same courses. Students have different aptitudes, interests, educational and professional plans, learning habits, and learning styles. Different groups of students should address the core curriculum at different levels of depth, and should complete the core curriculum according to different timetables. Nevertheless, all students should complete all elements of the core curriculum recommended in the mathematics standards.

All students should be challenged to reach their maximum potential. For many students, the core curriculum described here will indeed be challenging. But if we do not provide this challenge, we will be doing our students a great disservice — leaving them unprepared for the technological and information age of the 21st century.

For other students, this core curriculum itself will not be a challenge. We have to make sure that we provide these students with appropriate mathematical challenges. We have to make sure that the raised expectations for all students do not result in lowered expectations for our high achieving students. A core curriculum does not exclude a program that challenges students beyond the expectations set in the mathematics standards. Indeed, the vision of equity and excellence calls for schools to provide opportunities for their students to learn more mathematics than is contained in the core curriculum.

These refined mathematics standards, and the vision imbedded in them, offer a powerful challenge to all teachers, all schools, and all districts in New Jersey — to enable all of our students to step into this new century with the mathematical skills, understandings, and attitudes that they will need to be successful in their careers and daily lives. It will not be easy to meet this challenge, nor can it happen overnight. But it can happen if all of us together decide to make it happen. We must not let our awareness of the obstacles we face become yet another obstacle. We shall work together to make the vision of New Jersey’s mathematics standards a reality!

Mathematical Sciences Education Board. (1989). Everybody counts. Washington, DC: National Academy Press.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

New Jersey State Department of Education. (1996). Core curriculum content standards. Trenton, NJ : Author.

New Jersey Mathematics Coalition. (1994). Mathematics to prepare our children for the 21st century: A guide for New Jersey parents.

New Jersey Mathematics Coalition and New Jersey State Department of Education. (1996). New Jersey mathematics curriculum framework.

Footnotes:

[1] “Only in the United States do people believe that learning mathematics depends on special ability. 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.” Everybody Counts, Mathematical Sciences Education Board, National Academy of Sciences (1989)

[2] Everybody Counts, Mathematical Sciences Education Board, National Academy of Sciences (1989).

[3] Based on 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.

[4] 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.

[5] Since students learn at different rates, narrowing indicators to a single grade level was not always possible; thus indicators at grade levels 3, 5, and 7 are generally similar to, or modifications of, indicators developed for the next higher grade level.

[6] In the standards for content areas other than mathematics, bulleted lists are not intended to be exhaustive.