New Jersey Mathematics Coalition

Volume V Number 3 October 1996

Inside This Issue

A publication of the New Jersey Mathematics Coalition © October 1996

Hold the Date

Coalition Annual Meeting

Thursday, November 21, 1996
7:00 p.m. - 9:00 p.m.

At Rutgers University,
New Brunswick

(see announcement)

Call Debby Toti at (908) 445-2894 for details.

In This Issue:

by Warren D. Crown

Well, it's the beginning of another school year and here is your official announcement that the Mathematics Education Community is alive and well and still very busy in the state of New Jersey: the fall issue of the NJMC Newsletter. This is actually a very important year for us in the state. It is the first year that we are starting with a state-adopted set of K-12 Core Curriculum Standards for Mathematics that defines very clearly what our expectations are for students. As part of the measurement of those expectations, the new fourth-grade assessment program is also well underway and we've been promised that we'll have a trial run of the test in the spring of 1997.

In order to help prepare teachers for the new assessment, and for standards-based teaching in general, the Coalition has been involved in a number of projects that are highlighted in this issue of the Newsletter. The most prominent of these is the publication of the long-awaited New Jersey Mathematics Curriculum Framework. Read the article right beside this column to see how the official version of the framework, expected to be out in January, will be distributed. If you read the article carefully, you will learn how to request your own personal copy of the document.

In addition to the framework distribution, another major effort of the Coalition that began this past summer was the Standards Dissemination Project. A group of twenty talented K-4 teachers spent the summer preparing themselves to do professional development in mathematics for their colleagues around the state. A discussion of that program, a list of participants, and the titles of the resulting workshops are included in the article on pages 4 and 5. If you are a teacher

in grades 5 through 8, don't miss the boxed announcement of Phase II of the Standards Dissemination Project, coming up this summer! You, too, could play a valuable role in improving mathematics education in the state.

Other important announcements in this issue include a recent grant to the Coalition to look at the effects of mathematics education reform in New Jersey, the initiation of work on a new Science Framework, the appointment of a new project director for the NJ SSI, and an evening-hours, annual meeting of the Coalition. Of course, as we do every fall, we are also taking the opportunity of this Newsletter to invite you to sponsor a Math, Science, and Technology Month event this April.

Distributing the Framework

The New Jersey Mathematics Curriculum Framework will be distributed at the end of 1996. Since the publication last year of the Preliminary Version, efforts have been ongoing to improve the document based on readers' comments, and to update the document so that it is consistent with the mathematics standards adopted by the State Board of Education. The writers of the revised framework are Janet Caldwell, Warren Crown, and Joseph G. Rosenstein, who is also coordinating the effort, with the assistance of Karin Rupp.

This effort is the culmination of a three-year effort by the Coalition, in collaboration with the New Jersey Department of Education, with funding provided through an Eisenhower grant from the United States Department of Education.

It is anticipated that two copies will be mailed to each public school in the state (one to the principal and one to the mathematics coordinator), and one copy will be made available for each private and parochial school. Please make sure that you inform the appropriate people in your school early in January that you would like to see the document when it arrives. It is also anticipated that the Department of Education will provide a limited number of copies of the framework to individual mathematics educators. If you would like to receive a copy, please indicate that on the Response Form.

The document will also be available (as is the Preliminary Version) from the Coalition's Web page. Get it at ! Once we complete the document, we plan to continue the framework development process on the Web page.


For $25 You Can Help Us Implement Our Programs

Now that the core curriculum content standards have been adopted, we must work to increase public awareness of our efforts to improve mathematics education, and more importantly, we must continue to help teachers, schools and districts implement the standards.

The Coalition needs your help to reach out to parents, business, and public policy makers, and to help implement the standards.

Become an Affiliate of the New Jersey Mathematics Coalition today! For a $25 donation you will be enabling your Coalition to accomplish these valuable tasks. Along with the knowledge that you are helping to improve mathematics education in New Jersey you will receive an attractive white mug with the distinctive blue Coalition license plate logo. These mugs will not be reordered, and they are only available on a first come first served basis.

Please join us in these important efforts. Just check off the AFFILIATION box on the response form and send us a check today.

New Jersey Mathematics Coalition

Opinions in signed articles are those of the authors and do not necessarily reflect positions of the New Jersey Mathematics Coalition. Readers are invited to submit responses to these (or other) articles. We encourage you to submit articles for future issues of the newsletter on topics that would be of interest to our readers.

Joseph G. Rosenstein
Warren D. Crown

Newsletter Production:
Peter Sobel
Chris Magarelli

To comment on any topic related to the Newsletter, send e-mail, write or call:


NJMC Newsletter
P.O. Box 10867
New Brunswick, NJ 08906

(908) 445-2894
FAX: (908) 445-3477

The New Jersey Mathematics Coalition

Joseph G. Rosenstein
Associate Director:
Warren D. Crown
Assistant Director:
Peter Sobel

Chair of the Board of Governors:
Manya Ungar

Math, Science, and Technology Month 1997

Sponsor an Event!

by Peter A. Sobel

Reaching out to all parents, gaining their understanding about the importance of mathematics, science, and technology education in their children's lives, and showing them that learning these subjects can be fun, exciting, and engaging, is of paramount importance.

We all know that parents can be excellent motivators with their children and their schools. This is why we developed and coordinate Math, Science, and Technology Month each April. We want to get parents involved with their children's education and make them aware of educational reform that will affect their future.

Math, Science and Technology Month (MSTM) is a series of events that is coordinated by an extraordinarily diverse group of educators, museums, organizations, and business and industry representatives.

In 1996, over 89,000 parents, children, and educators participated in over 450 hands-on standards-based events. We anticipate an even larger MSTM '97!

Now is the time to commit yourself to sponsor an event during April 1997. Your event can involve a single classroom of students and their parents, or it can encompass a whole district or town. Join your colleagues throughout the state in participating in this statewide celebration of mathematics, science, and technology. If you coordinate one event, MSTM will be successful!

This how you can be a part of MSTM ' 97:

  1. Sponsor an event. Indicate on the response form that you would like further information about MSTM.
  2. Contact your colleagues in other schools and districts and encourage them to obtain information about MSTM, and then to sponsor events.
  3. Let us know of any businesses or corporations that might be able to support our MSTM activities.
For all of the above, please contact Peter Sobel at 908-445-2894, or at

MSTM Event Goals

A good MSTM event should...

  1. actively involve parents with their children in engaging, hands-on learning experiences in mathematics, science, and technology.
  2. reinforce the importance of knowledge and skill in these areas to your students' future lives and careers.
  3. highlight the changes in the teaching and learning of these disciplines that are being proposed by national professional organizations and that are being implemented in your local district.
  4. convey to parents the vision and recomendations of the mathematics and science standards adopted by the State Board of Education.
  5. dynamically demonstrate the advantages that come from the thoughtful integration of math, science, and technology in the school fun and informative for everyone involved.

Standards Dissemination Project a Huge Success

by Warren D. Crown

From July 1 through July 16, 1996, twenty of the most talented K-4 mathematics teachers and supervisors in the state met and worked hard with a very dedicated staff to try to create ways to share their knowledge and expertise with others who teach at the same level. The inaugural summer of the Standards Dissemination Project was funded by Johnson & Johnson and resulted in the development of eight powerful workshops that will help K-4 teachers implement the new New Jersey Mathematics Standards in their classrooms.

The twenty teachers were selected for participation from over ninety applications submitted in the spring. The participants represent diversity geographically and in terms of grade-level and responsibility. They are:

Participant School School District
Leslee Atiram Princeton Day School
Lynn Barberi Indian Fields School South Brunswick
Laura Behm Mansion Avenue School Audubon
Rosalind K. Blinder Lincoln School Newark
Ellen Bloomberg Jewish Education Center
Irene Bognar Florence M. Gaudineer M.S. Springfield
Patricia R. Burton Pine Grove Manor School Franklin Township
Mary Costner Washington Avenue School Chatham
Freddi DiGeronimo Elizabeth Avenue School Franklin Township
Anna Marie Dunn George J. Mitchell School Little Egg Harbor
Paula Giblin Forest Avenue School Verona
Janet Gill Greenbrook School South Brunswick
Diane Glace Rutgers Preparatory School
Katrina L. Lacovara Haines School Medford Township
Richard N. Lacovara Jr. Allen School Medford Township
Linda E. Nicholls Central School Great Meadows Regional
Jim Occhino Dwight-Englewood School
Elsie Rebovich M.L. King Elementary School Edison
Kathleen Shankman Lincoln School Englewood
Vi Thompson South Valley School Moorestown

Each participant helped to produce and is now prepared to deliver two of the workshops that were developed during the summer. While each has a specific content focus derived from one or more of the content standards, there were other design specifications for the workshops. Each workshop created had to actively involve the teacher participants, had to elaborate upon and explain the standards that were its focus, had to incorporate at least one piece of children's literature, had to incorporate concrete manipulative materials, had to specifically address the four process standards, and had to involve technology. If you think that's a tall order, well, it is, but the participants were up to the task! If you get the chance this year, attend one of the resulting workshops and see what a good job they did. The titles and focuses of the eight workshops are:

The staff of the intensive two-week institute were:

School District
Candace Beattys South Orange-Maplewood
Kaye Crown South Brunswick
Warren Crown Rutgers University
Bob Krech West Windsor-Plainsboro
Ruth Ziznewski Metuchen

Warren Crown served as Director of the Institute.

After the insitute was completed, fourteen workshops were offered over seven days in August at Academy South, Central and North. Over 100 teachers took part in these workshops and gained a better understanding of how to implement the New Jersey Mathematics Standards in their K-4 classrooms.

Would you like to hear about current directions in mathematics education in New Jersey?

The New Jersey Mathematics Coalition is offering to provide a speaker who will come to your PTA or PTO, School Board or community meeting and talk about

"Mathematics to Prepare Our Children for the 21st Century"

The title of this presentation is also the title of a guide for New Jersey parents, published by the Coalition, which discusses the vision and recommendations of the newly adopted New Jersey Mathematics Standards and current efforts to implement the Standards. The presentation lasts for 30 minutes and is free.

If your Board of Education, PTA or other civic group is interested, please check off the PRESENTATION box on the response form.

Standards Dissemination Project

Phase 2

We are currently in the process of submitting an application to Johnson & Johnson for a second year of funding. This second year (summer '97) would focus on grades 5 through 8. Teacher participants will be invited to submit applications early in the year. If you are interested, or know someone who would make a good participant, please look for the announcement in the next issue of this Newsletter and respond.

December Workshops Have Been Scheduled

The Coalition will offer the following workshops during the first two weeks of December at the Academies for Professional Development of the New Jersey Department of Education . The cost for a full day (2 workshops) is $75. This price includes lunch. Contact Debby Toti at (908) 445-2894 to sign up.

December 2, 1996

Academy Central - Edison
Patterns and Relationships (Kindergarten - 4th grade)
Measurement and Geometry (Kindergarten - 2nd grade)

December 3, 1996

Academy Central - Edison
New Directions in Content (Kindergarten - 4th grade)
Number Sense and Operations (Kindergarten - 2nd grade)

December 5, 1996

Academy South - Sewell
Measurement and Geometry (3rd grade - 4th grade)
Number Sense and Operations (3rd grade - 4th grade)

How Do I Schedule One Of These K-4 Math Standards Workshops In My School?

If you would like one or more of the K-4 Mathematics Standards Workshops in your school, please contact Peter Sobel, Assistant Director of the Coalition at (908) 445-2894, FAX (908) 445-3477 or e-mail (Note: The workshops are not free of charge!)


The Coalition has developed a database of workshop leaders who are available to give in-service workshops based on the New Jersey Mathematics Standards. Access to this database will be provided to districts which affiliate with the Coalition. Contact Peter Sobel at (908) 445-2894 or e-mail for more information.

Coalition Receives Grant to Assess Mathematics Education in New Jersey

The Coalition has received a $30,000 grant from The Fund for New Jersey to develop and publish an annual report entitled The Condition of Mathematics Education in New Jersey. We anticipate that these reports will document over time the impact of all of our efforts to improve mathematics education in the state, and in particular will document the implementation and impact of the recently adopted mathematics standards. We also anticipate that the information provided in the report will itself have an impact on both state and local policy. The target date for publication of the first report is April 1997.

The Fund for New Jersey provided important financial support to the New Jersey Mathematics Coalition in its initial three years, and, in providing us these funds, recognizes the important contribution that the Coalition is making. The award letter notes: "The New Jersey Mathematics Coalition was founded to promote best practices and statewide standards in the teaching and curriculum of math in New Jersey's schools. The Coalition is in large part responsible for the strong math content contained in the Governor's promulgated statewide standards."

Annual Meeting November 21 -- Focus on Redefining the Coalition

With the adoption of the mathematics standards and the completion of the curriculum framework, during the coming year the Coalition will review its mission, goals, and programs. Your opportunity to participate in this process of "redefining the Coalition" is the Annual Meeting of the Coalition which will take place on Thursday November 21 from 7:00 to 9:00 p.m. at the CoRE Building on Busch Campus, Rutgers University. (Food may be purchased from a variety of vendors in the Busch Campus Center near the CoRE Building.) Please call Debby Toti at 908/445-2894 to let us know that you're coming, or send us the Response Form.

New Jersey Department of Education and Merck Institute to Design Science Curriculum Framework

Commissioner of Education Leo Klagholz announced in June that the State Department of Education entered into a partnership with the Merck Institute for Science Education (MISE) to design a science curriculum framework. Frameworks for the seven content standards will be phased in over the next several years. The science frameworks would be the second set of frameworks, after mathematics, to be developed.

A broad based task force, with representatives including teachers, administrators, parents, members of higher education, business and industry and the educators who contributed to creating the science standards, was assembled this summer. Their task is to develop a draft of the science framework by June 1997. This framework development project is supported by NJ SSI, The Mid Atlantic Eisenhower Consortium at Research for Better Schools, MISE and the Department of Education. The leadership team consists of Dr. Carlo Parravano (MISE), John Shafransky (Edison Township Schools) and Dr. Deborah Cook (NJ SSI). It is estimated that it will take a year to eighteen months to complete the framework. As of September 1996 materials for drafts of three of the seven content chapters were being prepared. These chapters will include five process standards and the cross content readiness standards interwoven with the content.

The Department is looking for feedback on the first sections of this large project. There will be feedback opportunities at the New Jersey Science Teachers Convention on October 8 and 9. Additional opportunities to provide feedback on parts of the draft framework will be available in December. For more information on these sessions, call Dr. Bruce Marganoff at the Department of Education (609) 984-1805. Mathematics educators are encouraged to participate. It is anticipated that a draft of the entire framework will be ready in June '97. After additional review, the final version will be disseminated during the '97 - '98 school year.

NJ SSI Appoints New Project Director

by Claudia Dowling, NJ SSI

Dr. Deborah H. Cook, former science specialist and a coordinator of New Jersey's core curriculum content standards for the New Jersey State Department of Education, has been appointed Project Director for New Jersey's Statewide Systemic Initiative to improve mathematics, and science education. The announcement came in September from Dr. Gerald Goldin, the Principal Investigator for NJ SSI and Director of the Rutgers University Center for Mathematics, Science and Computer Education, with whom Dr. Cook will be working.

NJ SSI is a statewide collaborative project involving 9 institutions of higher education, 1069 K-8 teachers in 408 elementary schools and over 600 K-12 teachers from 236 schools in 32 districts. This multifaceted project focuses on systemic reform of mathematics and science education, including curriculum, assessment and new technology.

Dr. Cook joins the team at Rutgers University with statewide science and educational leadership experience. In addition to working with NJ SSI and managing a broad spectrum of curriculum activities including core course proficiencies, core curriculum content standards and the development of the science framework, she has also been involved in the development of NJ's statewide assessment in science at grades 4, 8, and 11. Dr. Cook also administered statewide staff development programs, served on technology committees and worked on the NJ School Report Card. Prior to her service with the Department of Education, she was a director of curriculum and instruction and she taught and supervised mathematics and science in New Jersey public schools. Dr. Cook received her B.S. from the Philadelphia College of Pharmacy and Science, and an Ed.M. and Ed.D. in Science Education from Temple University.

The national search for a project director coincided with NJ SSI's successful completion of its midpoint review with the National Science Foundation (NSF) this year. According to Dr. Goldin, "NJ SSI is at a pivotal point. We have harnessed a wealth of talent and knowledge statewide, and we are documenting successful professional development and school reform practices in the state. We now must refine these powerful working models for demonstration of how mathematics and science teaching, learning and student achievement can reach new levels of excellence so that all New Jersey's students can benefit from the SSI experience. Dr. Cook rounds out our outstanding team and will help us to implement the next phase of SSI." Goldin also thanked NJ SSI Co-Principal Investigator, Rebecca Lubetkin, who heads the Consortium for Educational Equity, who also served as Deputy Director of NJ SSI for one year prior to Dr. Cook joining the project.

The National Science Foundation recently commended NJ SSI for the state's adoption of challenging core curriculum content standards, specifically the mathematics and science standards which NJ SSI partners helped to develop and are currently utilizing as the basis for professional development programs for K-8 teachers. In this specialized training, teachers explore new mathematical and scientific ideas, conduct science experiments to bring back to the classroom, perform data analysis and use calculators, computers and telecommunications networking as tools to transform thinking and learning.

The NSF also recognized the efforts of the NJ SSI school reform initiative involving 32 districts which were selected for their demonstrated commitment to reform, and represent a cross-section of the state including urban, suburban and rural areas. These districts are participating in an in-depth, school-based, district wide initiative to restructure mathematics, science, and technology in grades K-12. Districts leverage resources and form partnerships with statewide groups, business, community resources, colleges and universities and others to develop and implement a long term strategic plan with specific benchmarks, including equity, assessment, and participation in intensive professional development tied to the new mathematics and science standards.

"Math is Everywhere" Contest

Reading Rainbow, the award-winning PBS television show is sponsoring a "Math is Everywhere" contest for children between the ages of 5 and 8. The children should submit essays of 100 words or less describing how they use math in everyday life. Examples of everyday math might include: measuring ingredients for a recipe, counting the coins needed to buy a sheet of stickers, or even counting the number of cars that go by when the family is driving down the highway. The contest deadline is November 15, and entries may be accompanied by illustrations.

A panel of judges will select the top ten entries based on creativity and originality. Every child who enters will receive a certificate of merit.

To enter, the child should send their essay along with their name, address, and phone number to:

Reading Rainbow "Math is Everywhere" Contest
411 Park Street
Upper Montclair, NJ 07043


Applications are being accepted for January 1997

The next series of training programs for the National Science Foundation funded FAMILY TOOLS & TECHNOLOGY Program will take place on January 6,7,8,15, and 16, 1997 at Rutgers University. Only 20 teachers (10 teams of 2) can be accepted to this program, so apply early.

FAMILY TOOLS & TECHNOLOGY is intended to make design technology (pre-engineering) accessible and exciting to a diverse population of students, especially females and minorities, and to promote parental involvement in the intellectual development and academic achievement of all children. It focuses on technological challenges in pre-engineering, architecture and physical science, not traditionally found in the elementary curriculum.

For applications and more information about Rutgers FAMILY TOOLS & TECHNOLOGY, FAMILY SCIENCE or FAMILY MATH, contact:

Jeanette Corris, Coordinator, Center for Family Involvement in Schools
c/o Consortium for Educational Equity,
Rutgers University
4090 Livingston Campus
New Brunswick, NJ 08903
(908)445-2071 Fax (908) 445-0027

Election Special: Using Preferential Ballots

(reprinted from October 1992 issue of In Discrete Mathematics: Using Discrete Mathematics in the Classroom)

L. Charles Biehl and Joseph G. Rosenstein

The election is over. All 430 votes have all been tallied. But there is no winner, for the top three candidates all received the same number of votes. Enter preferential ballots.

In preferential balloting, each person votes for all candidates, indicating his/her order of preference of the candidates. Thus, with four candidates in the race, there are altogether 4! = 24 possible ways a person can vote, reflecting the 24 possible orderings, or preference schedules, of the four candidates, Frumpf, Gluck, Ray, and Smiff. The results of the election can then be described by listing how many people voted for each of 24 preference schedules. This is depicted in the table below; the first column, for example, indicates that for 14 people, their order of preference was F,G,R,S.

But how do you tell who won?

There are a number of ways of tallying the ballots. In the plurality method, the winner is the candidate who received the largest number of first-place votes; preferences in effect are ignored, as is the case with standard elections where each person votes for just one candidate. In the run-off method, all but the two candidates A and B who received the most first place votes are eliminated; the winner is the one of A and B who, accordingly to the preference schedules, would have received the most votes in a two-candidate race. In the sequential run-off method, the candidate with the least number of first place votes is eliminated, the preference schedules are retabulated and the process is repeated; when two candidates are left, the plurality method (or run-off method) is applied to determine the winner. In the Borda count method with four candidates, each candidate receives 3 points for each first-place vote, 2 points for each second-place vote, and 1 point for each third-place vote; the winner is the candidate who receives the greatest total count. In the Condorcet method, each candidate A is compared to each other candidate, and is assigned a number of points equal to the number of candidates that A would have defeated in an one-on-one election.

Your students can determine who would win the election by each of the methods above (answers are provided below) and then use preferential balloting for other situations, such as determining their favorite soft drink, rock star, or mathematician.

What is striking is that it is possible for these methods to lead to different winners. A situation where the methods give four different winners is featured in the videotapes accompanying For All Practical Purposes, as well as in the book itself, published by the Consortium for Mathematics and Its Applications (COMAP).

An entirely different approach to balloting is called approval voting. Here each person can vote for any number of candidates, all those who he or she would approve of. After all the ballots are collected, the person who has been "approved" by the largest number of voters is elected. Imagine the impact on a three-person race if each person could vote for either one or two candidates! This system is now being used for elections of officers in many professional societies, and although it has many advantages over the standard form of balloting, it has not yet been adopted in any major political election. (In the table below, who would win if we assumed that voters "approved" their top two choices?)

Answers: Neither the plurality method nor the run-off method determines a winner, since three candidates are tied for first place. Using the sequential run-off method, Ray is eliminated first, and his name is deleted from each of the preference schedules -- for example, the 16 votes for preference schedule R-F-G-S now become 16 votes for F-G-S ; Smiff is eliminated next, and finally, we see that Frumpf defeats Gluck. Using the Borda count method, we find that Frumpf receives 694 points, Smiff 645 points, Ray 641 points, and Gluck 590 points, so that this method also gives the nod to Frumpf. Finally, using the Condorcet method, we find that F defeats G by 227-203, R by 224-206, and S by 243-188, so that Frumpf defeats all three other candidates in one-on-one elections and receives the maximum of 3 points. Frumpf is also "approved" by 249 votes, more than the other three candidates. On the whole, a convincing win for Frumpf.

Calendar of Events - Fall 1996

September 28.
MATYC-NJ Conference.

For more information contact Elaine Klett at (908) 842-1900 ext. 480.

October 23-25.
AMTNJ's Annual Conference.
Hilton, East Brunswick.
For more information contact Nancy Schultz at (201) 790-6184.

October 27-29.
AMTNY's 46th Annual Conference.
Concord Resort Hotel, Kiamesha Lake, NY.
For more information write to: Barb Stewart, 6531 Swamp Road, Conesus, NY 14435.

November 9.
MAA New Jersey 40th Anniversary Conference.
Held at Lucent Technologies in Murray Hill.
Contact Terry Michnowicz at (201)200-3219 for more information.

November 14 - 17.
MATYC National Conference.
Long Beach California.
For more information call Agnes Azzolino at (908) 739-3951.

Workshops on the standards for K-4 teachers.
December 2 at Academy Central, December 3 at Academy Central, and December 5 at Academy South.
See page 5 for details.

March 18.
Good Ideas in Precalculus ... Conference
(11th Annual). Busch Campus, Rutgers University, 8:30 a.m. to 3:30 p.m.
Call Bonnie Katz at 908/445-4065 for further information. Note change in date!

April 25-26.
Graphing Calculator Conference.
Busch Campus, Rutgers University, half-day Friday and/or full-day Saturday.
Call Debbie Toti at 908/445-2894 for further information. Hold the date!