Table Of Contents

  • The Goal
  • Quotes
  • The New Jersey Approach
  • The Vision
  • The Content
  • What You Can Do To Help Your Child Learn Mathematics
  • Activities To Do Together
  • Grades K-2
  • Grades 3 and 4
  • Grades 5 and 6
  • Grades 7-12
  • For All Ages
  • Read More About It
  • New Jersey Resources
  • Tangram Cutout
  • © Copyright 1994 New Jersey Mathematics Coalition

    This booklet has been produced by the New Jersey Mathematics Coalition. We welcome any comments or suggestions you may have that would improve the next version. Funds supporting this effort were provided by the Mid-Atlantic Eisenhower Consortium for Mathematics and Science Education based at Research for Better Schools, New Jersey's Statewide Systemic Initiative, and Scott Foresman and Company.

    Permission and encouragement is granted to copy and distribute this booklet in its entirety. Additional copies may be ordered from the Coalition for $10 per set of 30 copies.

    The New Jersey Mathematics Coalition, P.O. Box 10867,

    New Brunswick, NJ 08906 908-445-2894

    Go to Coalition Home


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

    "In emphasizing the importance of mathematics in education, we tend to forget how much fun it can be to work out a problem successfully. In other words, math is something parents and children can enjoy doing together. The New Jersey Mathematics Coalition suggests ways for parents to help their children learn math. I urge all parents to read this book and discover with their children that there can be magic in math."
    Christine Todd Whitman, Governor of New Jersey

    "The primary mission of the Department of Education is to create the opportunity for all children to demonstrate high levels of achievement in safe learning environments. To this end, the department will challenge schools to be innovative and dynamic. Engaging the public in discussion and debate and providing all stakeholders with appropriate information regarding the goals and visions we undertake is paramount to our mutual success as educators. I commend the Coalition for contributing to this forum."

    Leo Klagholz, New Jersey Commissioner of Education


    In 1989, the National Council of Teachers of Mathematics (NCTM), with the endorsement of other professional organizations, published an important document that serves as the blueprint for a national reform effort, the Curriculum and Evaluation Standards for School Mathematics. It established guidelines for the creation of excellent elementary and secondary mathematics programs which will prepare children for the mathematical challenges they will likely face in their lives.

    Since then, educators in New Jersey have been exploring ways to implement the NCTM recommendations. To support their efforts, the New Jersey Mathematics Coalition was formed in 1991. It is a partnership with representation from all sectors of the community: business and industry, K-12 and higher education, government, parents, and the general public.

    The Coalition has worked with the New Jersey Department of Education and many of the most knowledgeable educators throughout the state to develop a draft of the New Jersey Mathematics Standards. Although not official policy of the Department of Education, the document endorses the NCTM recommendations and goes further to create a vision of mathematics education tailored to New Jersey needs. The development effort is a component of the New Jersey Statewide Systemic Initiative to improve mathematics, science, and technology education.

    In this booklet, we share our vision with you and invite you to help make the vision a reality for your children and all of the children of New Jersey.


    This vision for mathematics education revolves around what takes place in classrooms. The draft of the New Jersey Mathematics Standards expresses this vision in eight recommendations that discuss the broader goals of mathematics education. As more and more New Jersey teachers incorporate these recommendations into their teaching, you should be able to see:

    Students who are excited by and interested in their activities. One of our principal goals is for children to learn to enjoy mathematics. Students who are excited by what they are doing are more likely to 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 real problem-solving spirit, 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 how mathematics is used and how it works. 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 skillb>

    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. Recent research shows that children often 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, children develop confidence in themselves as mathematics learners and enable teachers to better monitor their progress.

    Calculators and computers being used as important tools of learning. Technology can be used as an aid to 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 at home and at school, whenever they can use them 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. They are more ambitious than current expectations for most students, but are absolutely essential if together 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 replacing traditional short-answer tests. New strategies will include tests with open-ended problems, teacher interviews, long-term projects, and self- and peer-evaluations. All of these require more time, thought, and planning than traditional problems, but more closely reflect how people in the real world actually use mathematics.


    The draft of the New Jersey Mathematics Standards emphasizes that mathematics is not just arithmetic; it describes ten areas of mathematical content that should be explored and studied each year of a student's kindergarten through twelfth grade education. Although some of these topics are often thought of as only for the upper grades of high school, or only for the college-bound, we emphasize that young children can and should learn many of the basic concepts and explore these areas to deepen their understanding and appreciation of mathematics.

    Number Sense is an intuitive feel for numbers and a common sense approach to using them. It comes from comfort with what numbers represent, how different types of numbers (fractions, decimals, and so on) are related to each other, and how they can best be used to describe a particular situation. Number sense is a quality that all successful users of mathematics possess.

    Spatial Sense includes traditional geometry topics but also a whole collection of other, less formal ways of looking at two- and three-dimensional space. Geometry is all around us in art, nature, and the things we make. Understandings about properties of shapes, what happens when they are transformed are important parts of the curriculum that help children deal with the world around them.

    Numerical Operations are an essential part of the math curriculum. Students must understand how to add, subtract, multiply, and divide whole numbers, fractions, and other kinds of numbers. But, with the availability of calculators which can perform these operations quickly and accurately , the instructional emphasis now must be on understanding the meanings and uses of the operations and on estimation and mental skills rather than on developing pencil-and-paper skills.

    Measurement is important because it helps describe the world around us using numbers. We use numbers to describe simple things like length, weight, and temperature, but also complex things such as pressure, speed, and brightness. An understanding of how we attach numbers to those phenomena, familiarity with common measurement units like inches, liters, and miles per hour, and a practical knowledge of measurement tools are critical for children's understanding of the world around them.

    Estimation is a process that is used all the time by mathematically capable adults, and it is one that can be easily mastered by children. It involves an educated guess about a quantity or a measure or an intelligent prediction of the outcome of a computation. The growing use of calculators makes it more important than ever that students know when a computed answer is reasonable; the best way to make that decision is through estimation. Equally important is an awareness of those many situations in which an approximate answer is as good as, or even preferable to, an exact answer.

    Patterns, Relationships, and Functions comprise the backbone of mathematics. From the earliest age, students should be encouraged to investigate the patterns that they find in numbers, shapes, and expressions, and, by doing so, to make true mathematical discoveries. These explorations present unending opportunities for problem solving, making and verifying generalizations, and building mathematical understanding and confidence.

    Probability and Statistics are the mathematics we use to understand chance and to collect, organize, and analyze numerical data. From weather reports to sophisticated studies of genetics, from election results to toothpaste preference surveys, probability and statistical language and concepts are increasingly present in the media and in everyday conversations. Our children need this mathematics to help them judge the correctness of an argument supported by data or the believability of a persuasive advertisement.

    Algebra is the language of mathematics. Largely because of technology, the emphasis in algebra instruction has been evolving from a focus on rules and symbol manipulation to a view which sees algebra as a tool which all students can use to model real situations and answer questions about them. New graphing calculators allow the graphing of an equation at the touch of a button so that students can focus on what the graph means as it represents some real-life phenomenon. Formal procedures are still important, but the focus should be increasingly on the development of algebraic thought -- on how quantities are related to each other and the search for methods to express those relationships.

    Discrete Mathematics is a new branch of mathematics that deals with some of the most practical problems we face in life. It deals with ways to find the best route from one place to another, the best way to schedule a list of tasks to be done, the manner in which computers store data and CDs record music, and strategies for winning games. Increasingly, it is the mathematics used by decision makers in our society, from workers in government to those in health care, transportation, and telecommunications. The logical and practical emphases of discrete math problems and solutions help students see the relevance of mathematics in the real world.

    Underpinnings of Calculus are usually thought of as high school topics for only the very brightest academic students. Some basic fundamentals of calculus, though, are important for everyone to understand. How quantities such as world population change, how fast they change, and what will happen if they keep changing at the same rate are questions that can be discussed by elementary school children. Another fascinating topic for all mathematics students is the concept of infinity -- the infinitely large or the infinitesimally small. Early explorations in these areas can broaden students' interest in and understanding of a very important area of applied mathematics.


    There are many things you can do to help your child learn mathematics. Even if your own early mathematics experiences were not always positive, you can convey to your child an upbeat attitude toward math by finding ways to have fun with your child while doing mathematical things. You can play games and work with other activities that are designed to help your child better understand a particular aspect of mathematics. Suggestions for some of these are given on the next four pages. But, in addition, you should try to set the proper tone in your family for mathematics learning and exploration. Here are some hints:


    Grades K-2

    Grades 3 and 4

    Grades 5 and 6

    Grades 7-12

    For All Ages


    There are many fine sources of additional information about the reform in mathematics education and ways in which you can help your child learn math. Here are some of the best. Your child's school will know about others and will have catalogs of mathematical materials such as toys, tools, and games..


    There are many people, groups, and institutions in New Jersey who are working to promote this new vision of mathematics education. You would be welcome to additional information from any one of them, or to volunteer to help in the effort. A short directory:

    In the square below are the seven pieces of a tangram. Print them out. Can you use the seven pieces to make the designs in this document?