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.
New Brunswick, NJ 08906 908-445-2894
"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."
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.
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.
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.
|0 + 1 = = = =|
Have your child do that, counting by ones aloud with the calculator. After awhile ask your child to say the number that will come up next, and then next, and then next, and press the equals key to verify the predictions. To make the activity a little more challenging, use the sequence above, but replace the "1" with a "2." Then, another time, try a "5" or "10" or "7."
|You enter:||23 +|
|You name the range for the answer:||60 to 70|
|Your child has to enter some number and hit the equals sign to make a number between 60 and 70 appear in the display. (42 would work.)|
To add to the challenge, use larger numbers or use subtraction, multiplication, or division as the operation.
Also available from NCTM are these pamphlets:
And this bibliography of mathematics-related children's literature: The Wonderful World of Mathematics: A Critically Annotated List of Children's Books in Mathematics edited by Diane Thiessen and Margaret Matthias. $17.00.